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We calculate the relativistic Fermi liquid parameters (RFLPs) for the description of the nuclear saturation energy using a chiral effective Lagrangian. Analytical expressions of Fermi liquid parameters (FLPs) are presented both for the direct and exchange contributions by retaining the meson masses. We present a comparative study of perturbative calculation with mean field results. The FLPs, so determined, are then used to calculate the chemical potential, energy densities, and binding energy for dense nuclear matter interacting via the exchange of σ, ω, and π mesons. In addition, we also estimate bulk quantities like incompressibility and first sound velocity in terms of RFLPs for dense nuclear matter.

We perform a detailed analysis for the asymptotic behaviour for the multi-scalar field Chiral cosmological scenario. We present the asymptotic behaviour for the one-field, two-fields and three-fields Chiral models. From these results, and deriving conserved quantities, we present a Theorem for the $N$-fields model for the Chiral model with $N$--fields. We find that the maximum number of scalar fields which provide interesting physical results is two-fields, while for $N>2$ the new stationary points are only of mathematical interest since they do not describe new exact solutions different from those recovered for $N=2$., 10 pages, no figures

A classification of discrete compounds in binary chiral systems of single and different substances (homo- and heteromolecular compounds) is presented. It considers both chemical and crystallographic characteristics of such compounds. Using amino acids as chiral model systems, features of crystal structures of equimolar and non-equimolar heteromolecular compounds are reviewed. In this connection, the concept of homo- and heteromolecular dimers in compounds formed by amino acids is introduced and analyzed. As a result, a correlation between the molecular dimer type and the side chain structure (linear or branched) and the conformation (extended or folded) of the relevant compounds' molecules is derived. Two non-equimolar discrete heterocompounds discovered in the chiral systems L-valine–L-isoleucine and L-valine–L-leucine are discussed using the concepts proposed. The previously studied first system features a 2 : 1 (Val : Ile) compound. A newly investigated second system is found to form a 3 : 1 (Val : Leu) compound, and its crystal structure is described and evaluated.

It was demonstrated recently [Dunajski, Ferapontov and Kruglikov (2014)] that the Manakov-Santini system describes a local form of general Lorentzian Einstein-Weyl geometry. We introduce integrable matrix extension of the Manakov-Santini system and show that it describes (2+1)-dimensional integrable chiral model in Einstein-Weyl space. We develop a dressing scheme for the extended MS system and define an extended hierarchy. Matrix extension of Toda type system connected with another local form of Einstein-Weyl geometry is also considered., Comment: 11 pages

In the case of two-scalar field cosmology and, specifically for the Chiral model, we determine an exact solution for the field equations with a anisotropic background space. The exact solution can describe anisotropic inflation with a Kantowski-Sachs geometry and it can be seen as the anisotropic analogue of the hyperbolic inflation. Finally, we investigate the evolution for the homogeneous perturbations around the new asymptotic solution., 12 pages, 1 figure, to appear in Universe

We derive the $2$d Zakharov-Mikhailov action from $4$d Chern-Simons theory. This $2$d action is known to produce as equations of motion the flatness condition of a large class of Lax connections of Zakharov-Shabat type, which includes an ultralocal variant of the principal chiral model as a special case. At the $2$d level, we determine for the first time the covariant Poisson bracket $r$-matrix structure of the Zakharov-Shabat Lax connection, which is of rational type. The flatness condition is then derived as a covariant Hamilton equation. We obtain a remarkable formula for the covariant Hamiltonian in term of the Lax connection which is the covariant analogue of the well-known formula "$H=Tr L^2$"., 16 pages. Final authors' version with added references and explanations

We numerically study quenches from a fully ordered state to the ferromagnetic regime of the chiral ${\mathbb{Z}}_{3}$ clock model, where the physics can be understood in terms of sparse domain walls of six flavors. As in the previously studied models, the ballistic spread of entangled domain wall pairs generated by the quench leads to a linear growth of entropy with time, up to a time $\ensuremath{\ell}/2{v}_{g}$ in size-$\ensuremath{\ell}$ subsystems in the bulk, where ${v}_{g}$ is the maximal group velocity of domain walls. In small subsystems located in the bulk, the entropy continues to grow, approaching $ln3$, as domain walls traverse the subsystem and increment the population of the two oppositely ordered states, restoring the ${\mathbb{Z}}_{3}$ symmetry. The latter growth in entropy is seen also in small subsystems near an open boundary in a nonchiral clock model. In contrast to this, in the case of the chiral model, the entropy of small subsystems near an open boundary saturates. We rationalize the difference in behavior in terms of qualitatively different scattering properties of domain walls at the open boundary in the chiral model. We also present empirical results for entropy growth, correlation spread, and energies of longitudinal-field-induced bound states of domain wall pairs in the chiral model.

We consider the chiral model of twisted bilayer graphene introduced by Tarnopolsky-Kruchkov-Vishwanath (TKV). TKV have proved that for inverse twist angles $\alpha$ such that the effective Fermi velocity at the moir\'e $K$ point vanishes, the chiral model has a perfectly flat band at zero energy over the whole Brillouin zone. By a formal expansion, TKV found that the Fermi velocity vanishes at $\alpha \approx .586$. In this work, we give a proof that the Fermi velocity vanishes for at least one $\alpha$ between $.57$ and $.61$ by rigorously justifying TKV's formal expansion of the Fermi velocity over a sufficiently large interval of $\alpha$ values. The idea of the proof is to project the TKV Hamiltonian onto a finite dimensional subspace, and then expand the Fermi velocity in terms of explicitly computable linear combinations of modes in the subspace, while controlling the error. The proof relies on two propositions whose proofs are computer-assisted, i.e., numerical computation together with worst-case estimates on the accumulation of round-off error which show that round-off error cannot possibly change the conclusion of the computation. The propositions give a bound below on the spectral gap of the projected Hamiltonian, an Hermitian $80 \times 80$ matrix whose spectrum is symmetric about $0,$ and verify that two real 18th order polynomials, which approximate the numerator of the Fermi velocity, take values with definite sign when evaluated at specific values of $\alpha$. Together with TKV's work our result proves existence of at least one perfectly flat band of the chiral model., Comment: 61 pages (last 7 pages are supplementary material), 11 figures. Improved after review comments: (1) proved that the Fermi velocity perturbation series converges for $|\alpha| < 1/3$ (2) added proof that round-off error cannot affect the conclusions of our numerical computations (3) more extensive discussion of related work

Twisted bilayer graphene (TBG) has been experimentally observed to exhibit almost flat bands when the twisting occurs at certain magic angles. In this letter, we report new results on the continuum model of twisted bilayer graphene and its electronic band structure. Under we show that in the approximation of vanishing AA-coupling, the magic angles (at which there exist entirely flat bands) are given as the eigenvalues of a non-hermitian operator, and that all bands start squeezing exponentially fast as the angle $\theta$ tends to $0$. In particular, as the interaction potential changes, the dynamics of magic angles involves the non-physical complex eigenvalues. Using our new spectral characterization, we show that the equidistant scaling of inverse magic angles, is special for the choice of tunnelling potentials in the continuum model, and is not protected by symmetries. While we also show that the protection of zero-energy states holds in the continuum model as long as particle-hole symmetry is preserved, we observe that the existence of flat bands and the exponential squeezing are special properties of the chiral model.

The $\eta N$ interactions are investigated in the hot magnetized asymmetric nuclear matter using chiral SU(3) model and chiral perturbation theory (ChPT). In the chiral model, the in-medium properties of $\eta$-meson are calculated by the medium modified scalar densities under the influence of an external magnetic field. Further, in the combined approach of chiral model and ChPT, off-shell contributions of $\eta N$ interactions are evaluated from the ChPT effective $\eta N$ Lagrangian, and the in-medium effect of scalar densities are incorporated from the chiral SU(3) model. We observe a significant effect of magnetic field on the in-medium mass and optical potential of $\eta$ meson. We observe a deeper mass-shift in the combined approach of ChPT and chiral model compared to the effect of solo chiral SU(3) model. In both approaches, no additional mass-shift is observed due to the uncharged nature of $\eta$ mesons in the presence of magnetic field., Comment: 34 pages, 11 figures

A class of two-dimensional sigma models interpolating between $CP^1$ and the $SU(2)$ principal chiral model is discussed. We add the Wess-Zumino-Novikov-Witten term and examine the renormalization group flow of the two coupling constants which characterize the model under consideration. The model flows to the $SU(2)$ WZNW conformal field theory in the IR. There is an ordinary phase in which the model flows from the asymptotically free $CP^1$ model coupled to an extra massless degree of freedom in the UV. At higher loop order we discover that there is also a phase in which the model can flow from non-trivial fixed points in the UV. A non-perturbative confirmation of these extra fixed points would be desirable., Comment: v4. Updated acknowledgements

This chapter will introduce the notion of classical integrability of non-linear sigma models in two dimensions. In general, non-linear sigma models are not classically integrable in general dimensions and even in two dimensions. However, there are well-known integrable examples in two dimensions such as principal chiral model and symmetric coset sigma model. Here for these two examples, the classical integrability will be described by explicitly presenting a classical Lax pair and the associated infinite-dimensional algebra, Yangian.

An intriguing subject is to consider integrable deformations of 2D non-linear sigma models such as principal chiral models and symmetric coset sigma models. There had been no systematic way to perform integrable deformations for a long time. However, recently an elegant and systematic way, the so-called Yang–Baxter deformation, was invented by Klimcik. We firstly introduce Yang–Baxter deformations of the principal chiral model and present the associated classical Lax pair. Then the deformation procedure is generalized to the symmetric coset sigma model.

The phenomena of deconfinement of hadronic matter into quark matter at high density, relevant to hybrid star (HS) cores, is studied in the present work. The effective chiral model describes the pure hadronic phase while for the quark phase the MIT bag model is chosen with density dependent bag pressure. Phase transition is achieved using Maxwell construction. The effect of variation of the asymptotic value of the bag pressure ($B_{as}$) is analyzed w.r.t to the mass and radius of the HSs. The presence of hyperons in the hadronic sector also has significant effect on the choice of the value of $B_{as}$. Both the hadronic composition and the choice of $B_{as}$ significantly affect the stability of the star. The gross structural properties of the resultant HS are calculated in static condition and compared with the various constraints on them from different observational and empirical perspectives. The static properties like the maximum gravitational mass of the HS, obtained with $B_{as}$=80 MeV fm$^{-3}$, is consistent with the limits imposed from the observational analysis of PSR J0348+0432 and PSR J0740+6620. The estimates of $R_{1.4}$ and $R_{1.6}$ of HSs are found to be within the range prescribed from GW170817 analysis. Also the $M-R$ solutions of the HSs are in excellent agreement with the recently obtained NICER data for PSR J0030+0451. The results of maximum surface redshift, obtained with hybrid equation of state, satisfy the constraints from 1E 1207.4-5209 and RX J0720.4-3125. The work is also extended to obtain the tidal deformation properties of the HSs. The obtained value of $\Lambda_{1.4}$ is consistent with the bound obtained from GW170817 data analysis., Comment: 19 pages, 7 figures ; Accepted in Journal of Physics G: Nuclear and Particle Physics

We show that the flat bands in the chiral model of magic-angle twisted bilayer graphene remain exactly flat in the presence of a perpendicular magnetic field. This is shown by an exact mapping between the model and the lowest Landau level wavefunctions at an effective magnetic field, in which the external field is either augmented or reduced by one flux quantum per unit cell. When the external field reaches one flux quantum per unit cell, the model exhibits a topological phase transition. These findings allow us to analyze a Jain-series of Fractional Chern Insulators states in the exactly flat band, and to point out an unconventional dependence of the energy gap on the magnetic field., Comment: 10 pages, 2 figures

We study the integrable bi-Yang-Baxter deformation of the $SU(2)$ principal chiral model (PCM) and its finite action uniton solutions. Under an adiabatic compactification on an $S^1$, we obtain a quantum mechanics with an elliptic Lam\'e-like potential. We perform a perturbative calculation of the ground state energy in this quantum mechanics to large orders obtaining an asymptotic series. Using the Borel-Pad\'e technique, we determine the expected locations of branch cuts in the Borel plane of the perturbative series and show that they match the values of the uniton actions. Therefore, we can match the non-perturbative contributions to the energy with the uniton solutions which fractionate upon adiabatic compactification. An off-shoot of the WKB analysis, is to identify the quadratic differential of this deformed PCM with that of an $\mathcal{N}=2$ Seiberg-Witten theory. This can be done either as an $N_f=4$ $SU(2)$ theory or as an elliptic quiver $SU(2)\times SU(2)$ theory. The mass parameters of the gauge theory are given by the deformation parameters of the PCM., Comment: 50 pages, 18 figures

We study the $\eta N$ interactions in the hot and dense isospin asymmetric nuclear matter using two different approaches. In the first approach, the in-medium mass and optical potential of $\eta$-meson have been calculated in the chiral SU(3) model, considering the effect of explicit symmetry breaking term and range terms in the $\eta N$ interaction Lagrangian density. In the second scenario, the conjunction of chiral perturbation theory and chiral SU(3) model is employed. In this case, the next-to-leading order $\eta N$ interactions are evaluated from the chiral perturbation theory (ChPT), and the in-medium contribution of scalar densities are taken as input from chiral SU(3) model. We observe a larger negative mass-shift in the ChPT+chiral model approach compared to the chiral SU(3) model alone as a function of nuclear density. Moreover, the increase in the asymmetry and temperature cause a decrease in the magnitude of mass-shift. We have also studied the impact of $\eta N$ scattering length $a^{\eta N}$ on the $\eta$ meson mass $m^*_\eta$ and observed that the $m^*_\eta$ decrease more for increasing the value of scattering length., Comment: 30 Pages and 9 figures

A large class of integrable deformations of the Principal Chiral Model, known as the Yang-Baxter deformations, are governed by skew-symmetric R-matrices solving the (modified) classical Yang-Baxter equation. We carry out a systematic investigation of these deformations in the presence of the Wess-Zumino term for simple Lie groups, working in a framework that treats both inhomogeneous and homogeneous deformations on the same footing. After analysing the cohomological conditions under which such a deformation is admissible, we consider an action for the general Yang-Baxter deformation of the Principal Chiral Model plus Wess-Zumino term and prove its classical integrability. We also show how the model is found from a number of alternative formulations: affine Gaudin models, E-models, 4-dimensional Chern-Simons theory and, for homogeneous deformations, non-abelian T-duality., 45 pages; v2: 46 pages, comments added, matches published version

Motivated by the swampland program, we show that the Weil-Petersson geometry of the moduli space of a Calabi-Yau manifold of complex dimension $d\leq4$ is a gravitational instanton (i.e. a finite-action solution of the Euclidean equations of motion of gravity with matter). More precisely, the moduli geometry of Calabi-Yau $d$-folds ($d\leq4$) describes instantons of (E)AdS Einstein gravity coupled to a standard chiral model. From the point of view of the low-energy physics of string/M-theory compactified on the Calabi-Yau $X$, the various fields propagating on its moduli space are the couplings appearing in the effective Lagrangian $\mathscr{L}_\text{eff}$., Comment: 18 pages; more details on the geometry and finite action

We develop a study of the low energy kaon-$\mathrm{\ensuremath{\Xi}}$ interaction taking into account nonlinear chiral invariant Lagragians. We extend a model proposed to describe the $\ensuremath{\pi}N$ interaction to the $K\mathrm{\ensuremath{\Xi}}$ and $\overline{K}\mathrm{\ensuremath{\Xi}}$ interactions, considering $\mathrm{\ensuremath{\Lambda}}, \mathrm{\ensuremath{\Sigma}}$, and $\mathrm{\ensuremath{\Omega}}$ hyperons and the $\mathrm{\ensuremath{\Omega}}(2012)$ resonance in the intermediate states. We calculate their total cross sections, phase shifts, angular distributions, and polarizations in the center-of-mass frame of reference, accordingly to the proposed formalism.

The masses and decay widths of charmonium states are studied in the presence of strong magnetic fields. The mixing between the pseudoscalar and vector charmonium states at rest is observed to lead to appreciable negative (positive) shifts in the masses of the pseudoscalar (longitudinal component of the vector) charmonium states in vacuum/hadronic medium in the presence of high magnetic fields. The pseudoscalar and vector charmonium masses in the hadronic medium, calculated in an effective chiral model from the medium changes of a scalar dilaton field, have additional significant modifications due to the mixing effects. The masses of the $D$ and $\bar D$ mesons in the magnetized hadronic matter are calculated within the chiral effective model. The partial decay widths of the vector charmonium state to $D\bar D$ are computed using a field theoretical model for composite hadrons with quark/antiquark constituents, and are compared to the decay widths calculated using an effective hadronic Lagrangian. The effects of the mixing are observed to lead to significant contributions to the masses of the pseusoscalar and vector charmonium states, and an appreciable increase in the decay width $\psi(3770) \rightarrow D\bar D$ at large values of the magnetic fields. These studies of the charmonium states in strong magnetic fields should have observable consequences on the dilepton spectra, as well as on the production of the open charm mesons and the charmonium states in ultra relativistic heavy ion collision experiments., Comment: 31 pages, 5 figures,to be published in Phys. Rev. C

We present homogeneous Yang-Baxter deformations of the AdS$_5\times$S$^5$ supercoset sigma model as boundary conditions of a 4D Chern-Simons theory. We first generalize the procedure for the 2D principal chiral model developed by Delduc et al [arXiv:1909.13824] so as to reproduce the 2D symmetric coset sigma model, and specify boundary conditions governing homogeneous Yang-Baxter deformations. Then the conditions are applicable for the AdS$_5\times$S$^5$ supercoset sigma model case as well. In addition, homogeneous bi-Yang-Baxter deformation is also discussed., Comment: 26 pages, v2: title changed, further clarifications added

We study $\eta$-deformations of principal chiral model (PCM) from the viewpoint of a 4D Chern-Simons (CS) theory. The $\eta$-deformed PCM has originally been derived from the 4D CS theory by Delduc, Lacroix, Magro and Vicedo [arXiv:1909.13824]. The derivation is based on a twist function in the rational description. On the other hand, we start with a twist function in the trigonometric description and discuss possible boundary conditions. We show that a certain boundary condition reproduces the usual $\eta$-deformed PCM and another one leads to a new kind of Yang-Baxter deformation., Comment: 45 pages, 1 figure: minor modifications, further clarifications and references added. Matches the published version in NPB

In the approach recently proposed by K. Costello and M. Yamazaki, which is based on a four-dimensional variant of Chern-Simons theory, we derive a simple and unifying two-dimensional form for the action of many integrable $\sigma$-models which are known to admit descriptions as affine Gaudin models. This includes both the Yang-Baxter deformation and the $\lambda$-deformation of the principal chiral model. We also give an interpretation of Poisson-Lie $T$-duality in this setting and derive the action of the $\mathsf{E}$-model., Comment: 37 pages

The in-medium mass and decay width of the $\phi$ meson in the hot asymmetric strange hadronic matter are calculated using an effective Lagrangian approach for $\phi$ $K\bar K$ interaction. The in-medium contributions of $K \bar K$ loop to the $\phi$ meson self-energy are computed by the medium modified kaon and antikaon mass which is evaluated using the chiral SU(3) model. To deal with the ultraviolet divergence, we regularize the loop integral of self-energy with a dipole form factor, and present the results for cut-off mass, $\Lambda_c$=3 GeV. In chiral model calculations, for strange matter, we find that the mass of kaons and antikaons decreases with the increase in baryonic density whereas the finite temperature causes an increase in the mass. We observed that the in-medium $\phi$ meson mass decreases slowly with baryonic density whereas the decay width increases rapidly. The results in the present investigation support result in the literature which indicate a small downward shift in mass and a large broadening in the decay width. In the asymmetric strange hadronic matter, the study of the $\phi$ mesons can be relevant for the compressed strange baryonic matter and experimental observables such as dilepton spectra which can result from the experiments in the future FAIR facility at GSI., Comment: 27 pages and 7 figures

Resumen: Se presenta un modelo bioplasmático-quiral que caracteriza la cabeza humana y analiza su comportamiento cuando es radiada por las microondas de sistemas inalámbricos. La técnica del método de las diferencias finitas en el dominio del tiempo permite calcular numéricamente los campos electromagnéticos y simular la tasa de absorción especifica. Los resultados se obtuvieron para el corte 35 del modelo de imágenes de resonancia magnética. La conclusión más importante de nuestro trabajo es que, considerando que el tejido cerebral es un bioplasma quiral, se produce mayor absorción, respecto de los modelos clásicos, de la radiación de microonda que emiten los sistemas WiFi y Wi-Max. Abstract: A chiral-bioplasma model that characterizes the human head and analyzes its behavior when it is radiated by the microwave of wireless systems is presented. The technique of the method of finite differences in the domain of time allows numerical calculation of electromagnetic fields and simulates the specific absorption rate. The results were obtained for section 35 of the magnetic resonance imaging model. The most important conclusion of our work is that, considering that the brain tissue is a chiral bioplasma, there is greater absorption, compared to the classic models, of the microwave radiation emitted by the WiFi and Wi-Max systems.

In the present paper we study flag manifold sigma-models that admit a zero-curvature representation. It is shown that these models may be naturally considered as interacting (holomorphic and anti-holomorphic) $\beta\gamma$-systems. Besides, using the theory of nilpotent orbits of complex Lie groups, we establish a relation to the principal chiral model., Comment: 12 pages

We build on the results of [1] for generalised frame fields on generalised quotient spaces and study integrable deformations for ℂPn. In particular we show how, when the target space of the Principal Chiral Model is a complex projective space, a two-parameter deformation can be introduced in principle. The second parameter can however be removed via a diffeomorphism, which we construct explicitly, in accordance with the results stemming from a thorough integrability analysis we carry out. We also elucidate how the deformed target space can be seen as an instance of generalised Kähler, or equivalently bi-Hermitian, geometry. In this respect, we find the generic form of the pure spinors for ℂPn and the explicit expression for the generalised Kähler potential for n = 1, 2.

Duality properties of the $SU(2)$ Principal Chiral Model are investigated starting from a one-parameter family of its equivalent Hamiltonian descriptions generated by a non-Abelian deformation of the cotangent space $T^*SU(2) \simeq SU(2) \ltimes \mathbb{R}^3$. The corresponding dual models are obtained through $O(3,3)$ duality transformations and result to be defined on the group $SB(2,\mathbb{C})$, which is the Poisson-Lie dual of $SU(2)$ in the Iwasawa decomposition of the Drinfel'd double $SL(2,\mathbb{C})=SU(2) \bowtie SB(2,\mathbb{C})$.These dual models provide an explicit realization of Poisson-Lie T-duality. A doubled generalized parent action is then built on the tangent space $TSL(2,\mathbb{C})$. Furthermore, a generalization of the $SU(2)$ PCM with a WZ term is shortly discussed., Comment: 25 pages, Contribution to the Proceedings of Corfu Summer Institute 2019 "Schools and Workshops on Elementary Particle Physics and Gravity"

We use a chiral model for pion interactions, in the inverse amplitude formalism, to perform a simultaneous analysis of lattice QCD results for pion-pion scattering in all three isospin channels. The input is the finite-volume two-pion spectrum computed using lattice QCD from six ensembles on lattices elongated in one of the spatial dimensions. A two-flavor dynamical lattice QCD action is used with two quark masses corresponding to a pion mass of 315 MeV and 224 MeV. The spectrum in the elastic region is subjected to a global fit which takes into account full correlations across isospin, pion mass and decay constant. The parameters from the fit are used to perform a chiral extrapolation to the physical point. The cross-channel fit results in a more precise determination of the parameters of the model when compared with single channel fits. We obtain $m_\pi a_0^{I=0}=0.2132(9)$, and $m_\pi a_0^{I=2}=0.0433(2)$ as well as $m_\sigma=443(3)-i221(6)$ MeV and $m_\rho=724(4)-i67(1)$ MeV. Several aspects of scale setting and consistency with previous analyses of lattice QCD results are discussed as well., Comment: 11 pages, 3 figures

Following arXiv:1907.04737, we continue our investigation of the relation between the renormalizability (with finitely many couplings) and integrability in 2d σ- models. We focus on the “λ-model,” an integrable model associated to a group or symmetric space and containing as special limits a (gauged) WZW model and an “interpolating model” for non-abelian duality. The parameters are the WZ level k and the coupling λ, and the fields are g, valued in a group G, and a 2d vector A± in the corresponding algebra. We formulate the λ-model as a σ-model on an extended G × G × G configuration space (g, h,h¯), defining h and h¯ by A+ = h∂+h−1, A_ = h¯ ∂−h¯ −1. Our central observation is that the model on this extended configuration space is renormalizable without any deformation, with only λ running. This is in contrast to the standard σ-model found by integrating out A±, whose 2-loop renormalizability is only obtained after the addition of specific finite local counterterms, resulting in a quantum deformation of the target space geometry. We compute the 2-loop β-function of the λ-model for general group and symmetric spaces, and illustrate our results on the examples of SU(2)/U(1) and SU(2). Similar conclusions apply in the non-abelian dual limit implying that non-abelian duality commutes with the RG flow. We also find the 2-loop β-function of a “squashed” principal chiral model., Journal of High Energy Physics, 2019 (12), ISSN:1126-6708, ISSN:1029-8479

We initiate a systematic, non-perturbative study of the large-$N$ expansion in the two-dimensional $\text{SU}(N)\times \text{SU}(N)$ Principal Chiral Model (PCM). Starting with the known infinite-$N$ solution for the ground state at fixed chemical potential \cite{Fateev:1994dp,Fateev:1994ai}, we devise an iterative procedure to solve the Bethe ansatz equations order by order in $1/N$. The first few orders, which we explicitly compute, reveal a systematic enhancement pattern at strong coupling calling for the near-threshold resummation of the large-$N$ expansion. The resulting double-scaling limit bears striking similarities to the $c=1$ non-critical string theory and suggests that the double-scaled PCM is dual to a non-critical string with a $(2+1)$-dimensional target space where an additional dimension emerges dynamically from the $\text{SU}(N)$ Dynkin diagram., 6 pages, 1 figure, v2: typos fixed, minor corrections

Molecular helices based on self-organized aromatic oligoamide foldamers have been designed and prepared in their two enantiomeric forms in order to probe their second-order nonlinear chiroptical properties in solution. The quinoline oligoamides were rationally functionalized by electron-donating and electron-withdrawing groups to afford a gradual increase of the electronic polarization of the helical architectures. Their hyper-Rayleigh scattering (HRS) responses in solution were accordingly assessed, using either linearly polarized or circularly polarized incident light. Both methods allowed us to observe nonlinear optical activity that was quantified, for the first time for molecular systems, through circular differential scattering intensity ratios. The hyper-Rayleigh optical activity study reveals important charge-transfer differences within the aromatic oligomers, depending on the helix handedness and on the extent of electronic polarization induced by the appended substituents. The origin of the enantiomeric difference is discussed considering both achiral and chiral contributions. Overall, using aromatic oligoamide foldamers as a chiral model, we demonstrate the capabilities of HRS as a complementary chiroptical method, ideally suited for the analysis of various chiral molecular and supramolecular systems in solution. The reliability and chiral discrimination sensitivity of the method can be further improved through dynamic measurements using standard polarization modulation and heterodyning techniques.