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We study classical closed bosonic strings probing the near-horizon region of a non-extremal black hole and show that this corresponds to understanding string theory in the Carroll regime. This is done by first performing a Carroll expansion and then a near-horizon expansion of a closed relativistic string, subsequently showing that they agree. Concretely, we expand the phase space action in powers of $c^2$, where $c$ is the speed of light, assuming that the target space admits a string Carroll expansion (where two directions are singled out) and show that there exist two different Carroll strings: a magnetic and an electric string. The magnetic string has a Lorentzian worldsheet, whereas the worldsheet of the electric string is Carrollian. The geometry near the horizon of a four-dimensional (4D) Schwarzschild black hole takes the form of a string Carroll expansion (a 2D Rindler space fibred over a 2-sphere). We show that the solution space of relativistic strings near the horizon bifurcates and the two sectors precisely match with the magnetic/electric Carroll strings with an appropriate target space. Magnetic Carroll strings near a black hole shrink to a point on the two-sphere and either follow null geodesics or turn into folded strings on the 2D Rindler spacetime. Electric Carroll strings wrap the two-sphere and follow a massive geodesic in the Rindler space. Finally, we show that 4D non-extremal Kerr and Reissner-Nordstr\"om black holes also admit string Carroll expansions near their outer horizons, indicating that our formulation extends to generic non-extremal black holes., Comment: 42 pages including 4 appendices, 5 figures

A drastic variation in thermal conductivity (\k{appa}) for synthesized samples (TiCoSb1+x, x=0.0, 0.01, 0.02, 0.03, 0.04, and 0.06) is observed and ~47% reduction in \k{appa} is reported for TiCoSb1.02 sample. In depth structural analysis is performed, employing mixed-phase Rietveld refinement technique. Embedded phases and vacancy are analyzed from X-ray diffraction (XRD) and Scanning electron microscopy data. Local structures of the synthesized samples are explored for the first time by X-ray absorption spectroscopy measurements for TiCoSb system and corroborated with Rietveld refinement data. Lattice dynamics are revealed using Raman Spectroscopy (RS) measurements in unprecedented attempts for TiCoSb system. XRD and RS data accomplishes that variation in \k{appa} as a function of Sb concentration is observed owing to an alteration in phonon group velocity related to lattice softening. Polar nature of TiCoSb HH sample is revealed. LO-TO splitting (related to polar optical phonon scattering) in phonon vibration is observed due to polar nature of TiCoSb synthesized samples. Tailoring in LO-TO splitting due to screening effect, correlated with Co vacancies is reported for TiCoSb1+x synthesized samples. Lattice softening and LO-TO splitting lead to decreases in \k{appa}~47% for TiCoSb1.02 synthesized sample., Comment: Main article (17 pages, 10 figures), Supplemental article (5 pages, 7 figures), Comments are welcome

Starting from the computation of Symmetry Resolved Entanglement Entropy (SREE) for boosted intervals in a two dimensional Conformal Field Theory, we compute the same in various non-Lorentzian limits, viz, Galilean and Carrollian Conformal Field Theory in same number of dimensions. We approach the problem both from a limiting perspective and by using intrinsic symmetries of respective non-Lorentzian conformal algebras. In particular, we calculate the leading order terms, logarithmic terms, and the $\mathcal{O}(1)$ terms and explicitly show exact compliance with $\textit{equipartition of entanglement}$, even in the non-Lorentzian system. Keeping in mind the holographic origin of SREE for the Carrollian limit, we further compute SREE for BMS$_{3}$-Kac-Moody, which couples a $U(1)\times U(1)$ theory with bulk gravity., Comment: 38 pages, typos corrected, references updated, changes made in the section 4 and 6 regarding SREE for GCFT and BMS, conclusion remains unchanged, updated version to appear in JHEP

We investigate tensionless (or null) bosonic string theory with a Kalb-Ramond background turned on. In analogy with the tensile case, we find that the Kalb-Ramond field has a non-trivial effect on the spectrum only when the theory is compactified on an (\left(S^1\right)^{\otimes d}) background with (d\geq 2). We discuss the effect of this background field on the tensionless spectrum constructed on three known consistent null string vacua. We elucidate further on the intriguing fate of duality symmetries in these classes of string theories when the background field is turned on., Comment: 59 pages, 2 figures

At extreme energies, both low and high, the spacetime symmetries of relativistic quantum field theories (QFTs) are expected to change with Galilean symmetries emerging in the very low energy domain and, as we will argue, Carrollian symmetries appearing at very high energies. The formulation of Wilsonian renormalisation group seems inadequate for handling these changes of the underlying Poincare symmetry of QFTs and it seems unlikely that these drastic changes can be seen within the realms of relativistic QFT. We show that contrary to this expectation, changes in the spacetime algebra occurs at the very edges of parameter space. In particular, we focus on the very high energy sector and show how bilinears of $U(1)$ currents added to a two dimensional (massless) scalar field theory deform the relativistic spacetime conformal algebra to conformal Carroll as the effective coupling of the deformation is dialed to infinity. We demonstrate this using both a symmetric and an antisymmetric current-current deformation for theories with multiple scalar fields. These two operators generate distinct kinds of quantum flows in the coupling space, the symmetric driven by Bogoliubov transformations and the antisymmetric by spectral flows, both leading to Carrollian CFTs at the end of the flow., Comment: 46 pages, one figure, comments are welcome!

We demonstrate that strings near the horizon of a Schwarzschild black hole, when viewed by a stationary observer at infinity, probe a string Carroll geometry, where the effective lightspeed is given by the distance from the horizon. We expand the Polyakov action in powers of this lightspeed to find a theory of Carrollian strings. We show that the string shrinks to a point to leading order near the horizon, which follows a null geodesic in a two-dimensional Rindler space. At the next-to-leading order the string oscillates in the embedding fields associated with the near-horizon two-sphere., Comment: A Christmas Carroll: From All of Us to All of You (7 pages, letter format, 1 figure) v2: Added a reference

We study circle compactifications of tensionless bosonic string theory, both at the classical and the quantum level. The physical state condition for different representations of BMS$_3$, the worldsheet residual gauge symmetry for tensionless strings, admits three inequivalent quantum vacua. We obtain the compactified mass spectrum in each of these vacua using canonical quantization and explicate their properties., Comment: 55 pages

TiCoSb1+x (x=0.0, 0.01, 0.02, 0.03, 0.04, 0.06) samples have been synthesized, employing solid state reaction method followed by arc menting. Theoretical calculations, using Density Functional Theory (DFT) have been performed to estimate band structure and density of states (DOS). Further, energitic calculations, using first principle have been carried out to reveal the formation energy for vacancy, interstitial, anti-site defects. Detail structural calculation, employing Rietveld refinement reveals the presence of embedded phases, vacancy and interstitial atom, which is also supported by the theoretical calculations. Lattice strain, crystalline size and dislocation density have been estimated by Williamson-Hall and modified Williamson-Hall methods. Thermal variation of resistivity [\r{ho}(T)] and thermopower [S(T)] have been explained using Mott equation and density of states (DOS) modification near the Fermi surface due to Co vancancy and embedded phases. Figure of merit (ZT) has been calculated and 4 to 5 times higher ZT for TiCoSb than earlier reported value is obtained at room temperature., Comment: 12 pages, 12 figures (comments are welcome)

Scar eigenstates in a many-body system refers to a small subset of non-thermal finite energy density eigenstates embedded into an otherwise thermal spectrum. This novel non-thermal behaviour has been seen in recent experiments simulating a one-dimensional PXP model with a kinetically-constrained local Hilbert space realized by a chain of Rydberg atoms. We probe these small sets of special eigenstates starting from particular initial states by computing the spread complexity associated to time evolution of the PXP hamiltonian. Since the scar subspace in this model is embedded only loosely, the scar states form a weakly broken representation of the Lie Algebra. We demonstrate why a careful usage of the Forward Scattering Approximation (or similar strategies thereof) is required to extract an appropriate set of Lanczos coefficients in this case as the consequence of this approximate symmetry. This leads to a well defined notion of a closed Krylov subspace and consequently, that of spread complexity. We show how the spread complexity shows approximate revivals starting from both $|\mathbb{Z}_2\rangle$ and $|\mathbb{Z}_3\rangle$ states and how these revivals can be made more accurate by adding optimal perturbations to the bare Hamiltonian. We also investigate the case of the vacuum as the initial state, where revivals can be stabilized using an iterative process of adding few-body terms., Comment: 19 pages, 11 figures

The Carroll algebra is constructed as the $c\to0$ limit of the Poincare algebra and is associated to symmetries on generic null surfaces. In this paper, we begin investigations of Carrollian fermions or fermions defined on generic null surfaces. Due to the availability of two different (degenerate) metrics on Carroll spacetimes, there is the possibility of two different versions of Carroll Clifford algebras. We consider both possibilities and construct explicit representations of Carrollian gamma matrices and show how to build higher spacetime dimensional representations out of lower ones. Actions for Carroll fermions are constructed with these gamma matrices and the properties of these actions are investigated. We show that in condensed matter systems where the dispersion relation becomes trivial i.e. the energy is not dependent on momentum and bands flatten out, Carroll symmetry generically appears. We give explicit examples of this including that of twisted bi-layer graphene, where superconductivity appears at so called magic angles and connect this to Carroll fermions., Comment: Five figures, 40+ pages

Carroll symmetry is a very powerful characteristic of generic null surfaces, as it replaces the usual Poincar\'e algebra with a vanishing speed of light version thereof. These symmetries have found universal applications in the physics of null manifolds as they arise in diverse situations ranging from black hole horizons to condensed matter systems with vanishing Fermi velocities. In this work, we concentrate on fermions living on two dimensional ($2d$) null manifolds and explore the Carroll invariant structure of the associated field theories in a systematic manner. The free massless versions of these fermions are shown to exhibit $2d$ Conformal Carroll or equivalently the $3d$ Bondi-Metzner-Sachs (BMS) algebra as their symmetry. Due to the degenerate nature of the manifold, we show the presence of two distinct classes of Clifford Algebras. We also find that in two dimensions there are two distinct fermion actions. We study discrete and continuous symmetries of both theories, and quantize them using highest weight representation of the vacuum. We also discuss how the symmetries of $2d$ free fermion CFTs can be continually deformed by infinite boosts or degenerate linear transformations on coordinates, leading to the corresponding BMS invariant theory at singular points., Comment: 37 pages, no figures

Recently, bootstrap methods from conformal field theory have been adapted for studying the energy spectrum of various quantum mechanical systems. In this paper, we consider the application of these methods in obtaining the spectrum from the Schr\"odinger equation with periodic potentials, paying particular attention to the Kronig-Penney model of a particle in a one-dimensional lattice. With an appropriate choice of operator basis involving position and momenta, we find that the bootstrap approach efficiently computes the band gaps of the energy spectrum but has trouble effectively constraining the minimum energy. We show how applying more complex constraints involving higher powers of momenta can potentially remedy such a problem. We also propose an approach for analytically constructing the dispersion relation associated with the Bloch momentum of the system., Comment: 21 pages, 5 figures, typos corrected, version to appear in Physical Review D

A maximally symmetric non-linear extension of Maxwell's theory in four dimensions called ModMax has been recently introduced in the literature. This theory preserves both electromagnetic duality and conformal invariance of the linear theory. In this short paper, we introduce a Galilean cousin of the ModMax theory, written in a covariant formalism, that is explicitly shown to be invariant under Galilean Conformal Symmetries. We discuss the construction of such a theory involving Galilean electromagnetic invariants, and show how the classical structure of the theory is invariant under the action of Galilean Conformal Algebra (GCA)., Comment: Revised version to appear in PRD

We probe the contraction from $2d$ relativistic CFTs to theories with Bondi-Metzner-Sachs (BMS) symmetries, or equivalently Conformal Carroll symmetries, using diagnostics of quantum chaos. Starting from an Ultrarelativistic limit on a relativistic scalar field theory and following through at the quantum level using an oscillator representation of states, one can show the CFT$_2$ vacuum evolves smoothly into a BMS$_3$ vacuum in the form of a squeezed state. Computing circuit complexity of this transmutation using the covariance matrix approach shows clear divergences when the BMS point is hit or equivalently when the target state becomes a boundary state. We also find similar behaviour of the circuit complexity calculated from methods of information geometry. Furthermore, we discuss the hamiltonian evolution of the system and investigate Out-of-time-ordered correlators (OTOCs) and operator growth complexity, both of which turn out to scale polynomially with time at the BMS point., Comment: V3: To appear in PRD. Change of title has been implemented by the editors. It was simply titled "CFT to BMS: Complexity and OTOC" before

Bondi-Metzner-Sachs (BMS) symmetries, or equivalently Conformal Carroll symmetries, are intrinsically associated to null manifolds and in two dimensions can be obtained as an In{\"o}n{\"u}-Wigner contraction of the two-dimensional ($2d$) relativistic conformal algebra. Instead of performing contractions, we demonstrate in this paper how this transmutation of symmetries can be achieved by infinite boosts or degenerate linear transformations on coordinates. Taking explicit cues from the worldsheet theory of null strings, we show boosting the system is equivalent to adding a current-current deformation term to the Hamiltonian. As the strength of this deformation term reaches a critical value, the classical symmetry algebra "flows" from two copies of Virasoro to the BMS algebra. We further explore the situation where the CFT coordinates are asymmetrically transformed, and degenerate limits lead to chiral theories., Comment: v2: Minor modifications, version to appear in JHEP

The quaternary Heusler compound NiFeTiSn can be considered to be derived from the exotic pseudogap-compound Fe2TiSn by the replacement of one Fe atom by Ni. In contrast to Fe2TiSn, which shows a disorder-induced ferromagnetic phase, the ground state of NiFeTiSn is antiferromagnetic with the signature of spin canting. Interestingly, NiFeTiSn shows a Griffiths-like phase characterized by isolated ferromagnetic clusters before attaining the antiferromagnetic state. The Griffiths-like phase is possibly associated with the antisite disorder between Fe and Ti sites as evident from our powder X-ray diffraction study. The compound also shows rather an unusual temperature dependence of resistivity, which can be accounted for by the prevailing structural disorder in the system. NiFeTiSn turned out to be a rare example where a Griffiths-like phase is observed in a semiconducting 3d transition metal-based intermetallic compound with an antiferromagnetic ground state., Comment: 12 pages, 9 figures

Conformal Carroll symmetry generically arises on null manifolds and is important for holography of asymptotically flat spacetimes, generic black hole horizons and tensionless strings. In this paper, we focus on two dimensional (2d) null manifolds and hence on the 2d Conformal Carroll or equivalently the 3d Bondi-Metzner-Sachs (BMS) algebra. Using Carroll covariance, we write the most general free massless Carroll scalar field theory and discover three inequivalent actions. Of these, two viz. the time-like and space-like actions, have made their appearance in literature before. We uncover a third that we call the mixed-derivative theory. As expected, all three theories enjoy off-shell BMS invariance. Interestingly, we find that the on-shell symmetry of mixed derivative theory is a single Virasoro algebra instead of the full BMS. We discuss potential applications to tensionless strings and flat holography., Comment: v1: 49 pages, 1 figure; v2: 51 pages, 1 figure, added more discussion on Carroll geometry in section 2, added related discussions on Carroll geometry and Carroll symmetries at few other places, typos corrected, matches version to be published

The tensionless limit of string theory has recently been formulated in terms of worldsheet Rindler physics. In this paper, by considering closed strings moving in background Rindler spacetimes, we provide a concrete exemplification of this phenomenon. We first show that strings probing the near-horizon region of a generic non-extremal blackhole become tensionless thereby linking a spacetime Carroll limit to a worldsheet Carroll limit. Then, considering strings in $d$-dimensional Rindler spacetime we find a Rindler structure induced on the worldsheet. Novelties, including folds, appear on the closed string worldsheet pertaining to the formation of the worldsheet horizon. The closed string becomes segmented at these folding points and different segments go into the formation of closed strings in the different Rindler wedges. The Bondi-Metzner-Sachs (BMS) or the Conformal Carroll algebra emerges from the closed string Virasoro algebra as the horizon is hit. Quantum states on these accelerated worldsheets are discussed and we show the formation of boundary states from gluing conditions of the different segments of the accelerated closed string., Comment: 48 pages, various figures, slightly revised version to appear in JHEP

(Bi1-xSbx)2Te3 (x=0.60, 0.65, 0.68, 0.70, 0.75 and 0.80) mixed crystals have been synthesized by solid state reaction. In depth structural, thermal, transport and electronic properties are reported. Defect and disorder play a crucial role in structural and transport behaviour. Disorder induced iso-structural phase transition is observed at x=0.70, which is supported by the structural and transport properties data. Debye temperature has been estimated from the powder diffraction data. Differential scanning calorimetry (DSC) data confirms the glass transition in the material. Low temperature resistivity data shows Variable range hopping mechanism whereas high temperature data follows activated behaviour. Activation energy is calculated from the semiconducting region of resistivity data. Both Hall measurement and temperature dependent thermopower data (S(T)) confirms that samples are p-type in nature. Density of state effective mass has been estimated from Pisarenko relation and corroborated with resistivity data. Thermal conductivity (k) is estimated using experimentally obtained data. Figure of Merit (ZT) of the synthesized samples are calculated using resistivity, S(T) and k. Structural and transport properties are correlated, confirms the transition from disorder to order state. Defect and disorder are corroborated with structural and Thermoelectric properties of the synthesized samples.

Cryptocurrencies have received a lot of research attention in recent years following the release of the first cryptocurrency Bitcoin. With the rise in cryptocurrency transactions, the need for smart contracts has also increased. Smart contracts, in a nutshell, are digitally executed contracts wherein some parties execute a common goal. The main problem with most of the current smart contracts is that there is no privacy for a party's input to the contract from either the blockchain or the other parties. Our research builds on the Hawk project that provides transaction privacy along with support for smart contracts. However, Hawk relies on a special trusted party known as a manager, which must be trusted not to leak each party's input to the smart contract. In this paper, we present a practical private smart contract protocol that replaces the manager with an MPC protocol such that the function to be executed by the MPC protocol is relatively lightweight, involving little overhead added to the smart contract function, and uses practical sigma protocols and homomorphic commitments to prove to the blockchain that the sum of the incoming balances to the smart contract matches the sum of the outgoing balances., Comment: 9 pages, 6 figures, published in IEEE BRAINS'21 Conference Proceedings

In [1] we highlighted the fact that the log polynomial expansion employed in Nature Astron. 3, no.3, 272-277 (2019) [2] is a poor approximation to flat $\Lambda$CDM, so using it to infer deviations from flat $\Lambda$CDM is not well-motivated. The "orthogonalized logarithmic polynomials" recently presented in arXiv:2101.08278 [3] are an attempt to respond to the earlier criticism [1]. Here we demonstrate that this new technique [3] - interesting though it may be - fails to address the fundamental problem raised in [1]. Unfortunately, the claim made in [2] may still be lost in the expansion., Comment: This timely comment has been absorbed into the earlier preprint arXiv:2009.04109, which is now published at PLB. It no longer serves an independent purpose

Quasars show considerable promise as standard candles in a high-redshift window beyond Type Ia supernovae. Recently, Risaliti, Lusso \& collaborators \cite{Risaliti:2018reu, Lusso:2019akb, Lusso:2020pdb} have succeeded in producing a high redshift Hubble diagram ($ z \lesssim 7$) that supports "a trend whereby the Hubble diagram of quasars is well reproduced by the standard flat $\Lambda$CDM model up to $z \sim 1.5-2$, but strong deviations emerge at higher redshifts". This conclusion hinges upon a log polynomial expansion for the luminosity distance. In this note, we demonstrate that this expansion (or "improvements" thereof) typically can only be trusted up to $z \sim 1.5-2$. As a result, a breakdown in the validity of the expansion may be misinterpreted as a (phantom) deviation from flat $\Lambda$CDM. We further illustrate the problem through mock data examples., Comment: 4 pages; v2 plots added, matches published version

We construct the tensionless limit of bosonic string theory in terms of a family of worldsheets with increasing acceleration and show that the null string emerges in the limit of infinite acceleration when the Rindler horizon is hit. We discover a novel phenomenon we call null string complementarity, which gives two distinct observer dependent pictures of the emergence of open string physics from closed strings in the tensionless limit. The closed string vacuum as observed by the inertial worldsheet turns into a D-instanton in the tensionless limit, while in the complementary picture from the accelerated worldsheet one sees the emergence of a D-25 brane. We finally discuss approaching the Rindler horizon through time evolution at constant acceleration and also show how an open string picture arises very naturally., Comment: 5+\epsilon pages, three figures, In journal version title was changed to "Rindler Physics on the String Worldsheet"

Measuring the similarity between patches in images is a fundamental building block in various tasks. Naturally, the patch-size has a major impact on the matching quality, and on the consequent application performance. We try to use large patches instead of relatively small patches so that each patch contains more information. We use different feature extraction mechanisms to extract the features of each individual image patches which forms a feature matrix and find out the nearest neighbor patches in the image. The nearest patches are calculated using two different nearest neighbor algorithms in this paper for a query patch for a given image and the results have been demonstrated in this paper., Comment: 12 pages, 13 figures, Submitted to International Journal of Artificial Intelligence and Soft Computing

In this thesis the aim is to work on optimizing the modern machine learning models for personalized forecasting of Alzheimer Disease (AD) Progression from clinical trial data. The data comes from the TADPOLE challenge, which is one of the largest publicly available datasets for AD research (ADNI dataset). The goal of the project is to develop machine learning models that can be used to perform personalized forecasts of the participants cognitive changes (e.g., ADAS-Cog13 scores) over the time period of 6,12, 18 and 24 months in the future and the change in Clinical Status (CS) i.e., whether a person will convert to AD within 2 years or not. This is important for informing current clinical trials and better design of future clinical trials for AD. We will work with personalized Gaussian processes as machine learning models to predict ADAS-Cog13 score and Cox model along with a classifier to predict the conversion in a patient within 2 years.This project is done with the collaboration with researchers from the MIT MediaLab., Comment: 51 pages, 25 figures, 3 tables

Zero-knowledge proofs have always provided a clear solution when it comes to conveying information from a prover to a verifier or vice versa without revealing essential information about the process. Advancements in zero-knowledge have helped develop proofs which are succinct and provide non-interactive arguments of knowledge along with maintaining the zero-knowledge criteria. zk-SNARKs (Zero knowledge Succinct Non-Interactive Argument of Knowledge) are one such method that outshines itself when it comes to advancement of zero-knowledge proofs. The underlying principle of the Zcash algorithm is such that it delivers a full-fledged ledger-based digital currency with strong privacy guarantees and the root of ensuring privacy lies fully on the construction of a proper zk-SNARK. In this paper we elaborate and construct a concrete zk-SNARK proof from scratch and explain its role in the Zcash algorithm., Comment: 8 pages, 5 figures

Local determinations of the Hubble constant $H_0$ favour a higher value than Planck based on CMB and $\Lambda$CDM. Through a model-independent expansion, we show that low redshift ($z \lesssim 0.7$) data comprising baryon acoustic oscillations (BAO), cosmic chronometers and Type Ia supernovae has a preference for Quintessence models that lower $H_0$ relative to $\Lambda$CDM. In addition, we confirm that an exponential coupling to dark matter cannot alter this conclusion in the same redshift range. Our results leave open the possibility that a coupling in the matter-dominated epoch, potentially even in the dark ages, may yet save $H_0$ from sinking in the string theory Swampland., Comment: 4 pages; v2 comments, references added; v3 appendix added on CPL, matches published version

We theoretically investigate the dynamics of a time truncated Airy pulse under longitudinally varying dispersion. The realistic waveguide geometry is proposed that offers linear or oscillating dispersion profile. By solving the dispersion equation, we theoretically investigate how a linear variation of the group-velocity dispersion (GVD) over space affects the parabolic trajectory of an accelerating finite energy airy pulse (FEAP). It is demonstrated that, suitable adjustment of GVD can lead to unusual quasi-linear trajectory of the accelerating airy pulse. The impact of the periodic GVD on airy dynamics is more interesting where FEAP exhibits oscillatory trajectory with periodic peak power modulation. We theoretically estimate optimized length of the waveguide delivering maximum power at the output by solving the transcendental relation between GVD modulation strength and period. The effect of oscillatory higher order dispersion is dramatic for optical airy pulse where it experiences singularity points during propagation. At singularity points airy pulse loses its identity and flips over in time. The rich dynamics of FEAP near singular point is carefully investigated by solving the propagation equation analytically. In this report we provide detail theoretical analysis to achieve selective temporal focusing of FEAP which may be useful for application. All theoretical predictions are verified numerically and the agreement is found to be excellent., Comment: 11 pages,11 figures

Within the premise of canonical quantisation, we re-examine the quantum structure of bosonic tensionless string theory. In the classical theory, the worldsheet metric degenerates and the Bondi-Metnzer-Sachs (BMS) algebra arises as the residual symmetries on fixing the tensionless equivalent of the conformal gauge. In the quantum regime, we find, on careful examination, that there are multiple ways to impose constraints to restrict the physical Hilbert space, which in turn lead to three distinct choices of tensionless vacua. We analyse these vacua in detail, commenting on various aspects like the central charges and the spectrum around each of them., Comment: 56 pages, 1 figure

Risaliti, Lusso \& collaborators have constructed a high-redshift Hubble diagram of supernovae (SNe); quasars (QSO) and gamma-ray bursts (GRB) that shows a "$\sim 4 \, \sigma$ tension with the $\Lambda$CDM model" based on a log polynomial cosmographic expansion (Risaliti et.al 2018, Lusso et.al 2019). In this work, we demonstrate that the log polynomial expansion generically fails to recover flat $\Lambda$CDM beyond $z \sim 2$, thus undermining the $\sim 4 \, \sigma$ tension claim. Moreover, through direct fits of both the flat $\Lambda$CDM and the log polynomial model to the SNe+QSO+GRB dataset, we confirm that the flat $\Lambda$CDM model is preferred. Ultimately, we trace the tension to the QSO data and show that a best-fit of the flat $\Lambda$CDM model to the QSO data leads to a flat $\Lambda$CDM Universe with no dark energy within $1 \, \sigma$. This marks an irreconcilable tension between the Risaliti-Lusso QSOs and flat $\Lambda$CDM., Comment: v3 22 pages, 10 figures, a major revision; v4 wording improved, typos corrected, conclusions unchanged; v5 and v6 match published version

The main idea of this ISO is to use StarGAN (A type of GAN model) to perform training and testing on an emotion dataset resulting in a emotion recognition which can be generated by the valence arousal score of the 7 basic expressions. We have created an entirely new dataset consisting of 4K videos. This dataset consists of all the basic 7 types of emotions: Happy, Sad, Angry, Surprised, Fear, Disgust, Neutral. We have performed face detection and alignment followed by annotating basic valence arousal values to the frames/images in the dataset depending on the emotions manually. Then the existing StarGAN model is trained on our created dataset after which some manual subjects were chosen to test the efficiency of the trained StarGAN model.

We investigate the dynamics of an Airy pulse that experiences free carrier generated optical linear potential in the vicinity of zero group velocity dispersion (GVD) wavelength inside a Si based waveguide. The optically induced potential can be realized by an inhomogeneous medium which possesses a time dependent refractive index. We propose a pump-probe scheme in Si-based waveguide where a strong continuous wave (CW) pump excites free carriers that leads to a linear potential through a time dependent refractive index change which is experienced by the finite energy Airy pulse (FEAP) (probe). The linear potential significantly manipulate the dynamics of a FEAP and leads to a monotonous spectral shift. We mathematically model the dynamics of the Airy pulse using linear dispersion equation containing an optical potential term and establish the general solution of the pulse for non-vanishing third order dispersion (TOD). We derive the expression of the trajectory of FEAP which deviates significantly from its usual ballistic nature and can be tailored with the strength of the linear potential. For positive TOD, the propagating Airy pulse experiences a singularity and flips in time domain. We theoretically derive that for a specific potential strength the flipping region is squeezed to a point and revives thereafter. We propose an exact analytical solution beyond flipping region for this specific case. Our theoretical analysis corroborates well with the numerical results. The present study may be useful in applications related to pulse reshaping and trajectory manipulation

The $AdS_3\times S^3$ string sigma model supported both by NS-NS and R-R fluxes has become a well known integrable model, however a putative dual field theory description remains incomplete. We study the anomalous dimensions of twist operators in this theory via semiclassical string methods. We describe the construction of a multi-cusp closed string in conformal gauge moving in $AdS_3$ with fluxes, which supposedly is dual to a general higher twist operator. After analyzing the string profiles and conserved charges for the string, we find the exact dispersion relation between the charges in the `long' string limit. This dispersion relation in leading order turns out to be similar to the case of pure RR flux, with the coupling being scaled by a factor that depends on the amount of NS-NS flux turned on. We also analyse the case of pure NS flux, where the dispersion relation simplifies considerably. Furthermore, we discuss the implications of these results at length., Comment: 23 pages, 3 figures

We reconsider the tensionless limit on bosonic closed string theory, where the 3d Bondi-Metzner-Sachs (BMS) algebra appears as symmetries on the worldsheet, as opposed to two copies of the Virasoro algebra in the case of the usual tensile theory. This is an ultra-relativistic limit on the worldsheet. We consider the induced representations of the BMS algebra in the oscillator basis and show that the limit takes the tensile closed string vacuum to the "induced" vacuum which is identified as a Neumann boundary state. Hence, rather remarkably, an open string emerges from closed strings in the tensionless limit. We also follow the perturbative states in the tensile theory in the limit and show that there is a Bose-Einstein like condensation of all perturbative states on this induced vacuum. This ties up nicely with the picture of the formation of a long string from a gas of strings in the Hagedorn temperature, where the effective string tension goes to zero., Comment: 5 pages, 3 figures

We consider deformation of a generic $d$ dimensional ($d\geq 2$) large-$N$ CFT on a sphere by a spin-0 operator which is bilinear in the components of the stress tensor. Such a deformation has been proposed to be holographically dual to an $AdS_{d+1}$ bulk with a hard radial cut-off. We compute the exact partition function and find the entanglement entropy from the field theory side in various dimensions and compare with the corresponding holographic results. We also compute renormalized entanglement entropy both in field theory and holography and find complete agreement between them., Comment: Comments and clarifications added, references updated, version to appear in Nucl. Phys. B

We study non-perturbative interpolating functions to probe the physics of anomalous dimensions associated with twist-two operators in ${\cal N}=4$ SYM of finite and infinite spin. Compared to previous studies, the novel result of this paper is to introduce single multivariate functions of both coupling $g$ and spin $j$ to approximate such anomalous dimensions. We provide a unified framework to study such operators in interim ranges of the parameters which so far has eluded previous results. Explicitly, we consider twist-two anomalous dimensions in two distinct scenarios using interpolating functions. For the large $N$ case, we stick to simple Pad\'{e} approximants and its generalizations . For the finite $N$ case, ${\cal N}=4$ SYM is expected to be S-dual invariant, hence the observables are expected be modular invariant. To probe the finite $N$ physics, we take into account the non-planar and instanton contributions by constructing modular invariant interpolating functions to approximate the cusp and twist-two anomalous dimensions. We also consider interpolating functions for the twist-four operators and study level crossing phenomenon between the twist-two and twist-four operators., Comment: 50 pages(7 pages appendix), 15 figures, 1 tables, published version in JHEP

A new type of tensionless superstring theory, called the Inhomogeneous tensionless superstring, has been recently introduced. This is characterised by a residual symmetry algebra on the worldsheet richer in structure than the previously known symmetry algebra related to Homogeneous tensionless superstring. In this paper, we investigate theories of tensile superstring that the Inhomogeneous tensionless superstring with manifestly real fermions could arise from. We provide two different candidates for these parent tensile theories. The nature of the limit dictates that these theories have some exotic features., Comment: Version published in Phy. Lett. B

We report here the electrical transport and magnetic properties of the newly synthesized quaternary Heusler compound CoFeTiSn and CoFeVGa. We observe a striking change in the electronic transport properties of CoFeTiSn as the system undergoes the paramagnetic to ferromagnetic transition. While the sample shows an activated semiconducting behaviour in the paramagnetic phase, it turns abruptly to a metallic phase with the onset of ferromagnetic transition. We have compared the system with other Hesuler compounds showing similar anomaly in transport, and it appears that CoFeTiSn has much similarities with the Fe$_2$VAl compound having pseudogap in the paramagnetic phase. In sharp contrast, CoFeVGa shows a predominantly semiconducting behaviour down to 90 K, below which it shows a window of metallic region. Both the compositions show negative Seebeck coefficient varying linearly with temperature. The value of the Seebeck coefficient of CoFeTiSn is comparable to that of many Heusler alloys identified as potential thermoelectric materials.