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We study $ \text{T}\overline{\text{T}} $ deformations of chiral bosons using the formalism due to Sen. For arbitrary numbers of left- and right-chiral bosons, we find that the $ \text{T}\overline{\text{T}} $-deformed Lagrangian can be computed in closed form, giving rise to a novel non-local action in Sen's formalism. We establish that at the limit of infinite $ \text{T}\overline{\text{T}} $ coupling, the equations of motion of deformed theory exhibits chiral decoupling. We then turn to a discussion of $ \text{T}\overline{\text{T}} $-deformed chiral fermions, and point out that the stress tensor of the $ \text{T}\overline{\text{T}} $-deformed free fermion coincides with the undeformed seed theory. We explain this behaviour of the stress tensor by noting that the deformation term in the action is purely topological in nature and closely resembles the fermionic Wess-Zumino term in the Green-Schwarz formalism. In turn, this observation also explains a puzzle in the literature, viz. why the $ \text{T}\overline{\text{T}} $ deformation of multiple free fermions truncate at linear order. We conclude by discussing the possibility of an interplay between $ \text{T}\overline{\text{T}} $ deformations and bosonisation., v2: 26 pages. Substantial changes in Sections 4 and 5. Abstract updated, typos corrected, references and acknowledgement added

This thesis studies boundary states in spin conformal field theories in two dimensions, and their connection to the monopole-fermion problem in four dimensions, as well as to symmetry-protected topological phases in two and three dimensions. We begin by motivating the study of conformal boundary states for 2d fermions preserving chiral symmetries. Our main motivation is the question of defining magnetic line operators in 4d chiral gauge theories. Such line operators were originally introduced by 't Hooft in the 1970s, and have seen a recent upsurge in interest after their refinement by Kapustin and Seiberg, but have only ever been defined for gauge theories without chiral fermions. The difficulty in extending these operators to chiral theories is known as the "fermion-monopole problem". Using a 4d - 2d partial wave reduction, we show that the problem of defining magnetic lines in chiral gauge theories reduces to defining boundary states for an effective 2d theory of Dirac fermions with certain chiral symmetries. For this to be possible, various 2d anomalies must vanish, which places constraints on the matter content of the 4d gauge theory. Next, to obtain the boundary states, we turn to boundary conformal field theory. After a brief review of this framework, we explain its limitations in addressing the fermion-monopole problem. In particular, while the theory is fully established for bosonic RCFTs, it has seen little to no progress for irrational CFTs, and also remains to be fully explored for fermionic RCFTs. These factors motivate the study of a particular family of boundary states preserving maximal abelian symmetries. We classify all such symmetries, and construct all boundary states preserving them. The most interesting part of the construction involves taking care of the normalisation of states to ensure a consistent spectrum. This involves a new subtlety that only arises for fermionic CFTs, related to the classification of SPT phases in two dimensions, involving factors of √2. We show that consistency of the spectrum indeed holds, but in a nontrivial way, with the details involving lattice theory and F2-linear algebra. Next, as further exploration of our family of boundary states, we work out the structure of boundary RG flows that connect different states. The theory of boundary RG is very similar to that of bulk RG: there are boundary operators, which can be classed as relevant or irrelevant, and relevant boundary operators drive flows to boundary states of lower Affleck-Ludwig central charge. We derive the spectrum of boundary operators, and construct all RG flows generated by boundary operators of definite charge. We show that a consistent picture emerges by virtue of a striking dimension formula which determines the IR central charge from the UV central charge and the dimension of the perturbing operator. Next, we return to the fermion-monopole problem, and determine which of these boundary states can serve to define magnetic line operators. To do this, we carefully derive the full amount of chiral symmetry that is preserved by each boundary state. The result is always a maximal-rank subgroup of SO(2N), where N is the number of Dirac fermions, and we give a simple prescription to determine it from the data describing the boundary state. Due to the maximal-rank property, we conclude that generic magnetic lines cannot be described by boundary states of this kind, and to find these states would require radically different techniques. Next we turn to the connection between boundary states and SPT phases. Using Fidkowski and Kitaev's example of symmetric mass generation as an example, we illustrate the mapping between 2d boundary states and 2d gapped phases, in particular the subtle way symmetries correspond under this mapping. We also consider how properties of 2d boundary states can encode those of 3d SPT phases. To do this, we derive criteria for when the boundary states in our family preserve certain discrete symmetries. We make contact with the mod-8 classification of 3d SPT phases protected by a unitary Z2 symmetry by proving a simple theorem about lattices. In the final part of this thesis, we turn from boundary states for Dirac fermions to those of more general fermionic CFTs, specifically, the recently-introduced family of fermionic minimal models, which are derived by fermionising the more familiar bosonic minimal models. We construct the boundary states for these models, and explain how our results and their interpretation in terms of 2d SPTs carry over from the Dirac fermion case. Furthermore, in order to explain certain coincidences among our results, we construct all unitary global Z2 symmetries of these models using the modular bootstrap, and compute their anomalies. The method rests upon a combinatorial conjecture which we expect to have an interpretation in terms of Fermat curves. Our results agree with other works that appeared around the same time where they overlap., Cambridge Trust, The Simons Foundation

We study the impact of quantum gravity on a system of chiral fermions that are charged under an Abelian gauge group. Under the impact of quantum gravity, a finite value of the gauge coupling could be generated and in turn drive four-fermion interactions to criticality. We find indications that the gravity-gauge-fermion interplay protects the lightness of fermions for a large enough number of fermions. On the other hand, for a smaller number of fermions, chiral symmetry may be broken, which would be in tension with the observation of light fermions., 12 pages, 6 figures. Match the published version

In principle, there is no obstacle to gapping fermions preserving any global symmetry that does not suffer a 't Hooft anomaly. In practice, preserving a symmetry that is realised on fermions in a chiral manner necessitates some dynamics beyond simple quadratic mass terms. We show how this can be achieved using familiar results about supersymmetric gauge theories and, in particular, the phenomenon of confinement without chiral symmetry breaking. We present simple models that gap fermions while preserving a symmetry group under which they transform in chiral representations. For example, we show how to gap a collection of 4d fermions that carry the quantum numbers of one generation of the Standard Model, but without breaking electroweak symmetry. We further show how to gap fermions in groups of 16 while preserving certain discrete symmetries that exhibit a mod 16 anomaly., 21 pages. v2: references added

The chirality of chiral multifold fermions in reciprocal space is related to the chirality of crystal lattice structures in real space. In this study, we propose a strategy to detect and identify multifold fermions of opposite chirality in nonmagnetic systems using second-order optical transports. Chiral crystals related with inversion operations cannot be made to overlap with each other via any experimental operation. Further, chiral multifold fermions within such crystals host opposite chiralities corresponding to a given $k$ point. A change in chirality is indicated by a corresponding change in the sign of the second-order charge current dominated by chiral fermions. This property can be exploited to study the relationship between chiralities in reciprocal and real spaces by utilizing bulk transport.

Quantum anomaly is a fundamental feature of chiral fermions. In chiral materials the microscopic anomaly leads to nontrivial macroscopic transport processes such as the Chiral Magnetic Effect (CME), which has been in the spotlight lately across disciplines of physics. The quark-gluon plasma (QGP) created in relativistic nuclear collisions provides the unique example of a chiral material consisting of intrinsically relativistic chiral fermions. Potential discovery of CME in QGP is of utmost significance, with extensive experimental searches carried out over the past decade. A decisive new collider experiment, dedicated to detecting CME in the collisions of isobars, was performed in 2018 with analysis now underway. In this paper, we develop the state-of-the-art theoretical tool for describing CME phenomenon in these collisions and propose an appropriate isobar subtraction strategy for best background removal. Based on that, we make quantitative predictions for signatures of CME in the collisions of isobars. A new and robust observable that is independent of axial charge uncertainty -- the ratio between isobar-subtracted $\gamma-$ and $\delta-$ correlators, is found to be $- ( 0.41 \pm 0.27 )$ for event-plane measurement and $ - ( 0.90 \pm 0.45 )$ for reaction-plane measurement., Comment: 7 pages, 4 figures; final published version

We derive the entanglement entropy of chiral fermions on the circle at arbitrary temperature. The spin-sector contribution depends only on the total length of the entangling region, regardless of the configuration of the intervals. Thus three-partite information provides a global indicator for the spin boundary conditions. Together with the modular Hamiltonian, our results provide a systematic way of obtaining relative entropy on the torus., Comment: 8 pages, 2 figures; corrected error in section C, some improvements to the exposition

We consider a lattice implementation of the eta-invariant, using the complex phase of the determinant of the simplified domain-wall fermion, which couples to an interpolating five-dimensional gauge field. We clarify the relation to the effective action for chiral Ginsparg-Wilson fermions. The integrability, which holds true for anomaly-free theories in the classical continuum limit, is not assured on the lattice with a finite spacing. A lattice expression for the five-dimensional Chern-Simons term is obtained., Comment: 38 pages, LaTeX, revised version

Motivated by the emergent fermions in the chiral topological semimetal RhSi, which has bulk higher-spin chiral fermions with a topological charge of $\ifmmode\pm\else\textpm\fi{}2$, respectively, we studied the shift vector induced nonlinear optical conductivity ${\ensuremath{\sigma}}_{zxy}^{(2)}(0;\ensuremath{\omega},\ensuremath{-}\ensuremath{\omega})$ of bulk RhSi by first-principles calculation. Our calculation demonstrates that the maximal ${\ensuremath{\sigma}}_{zxy}^{(2)}(0;\ensuremath{\omega},\ensuremath{-}\ensuremath{\omega})$ is about $\ensuremath{\sim}180\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\text{A}/{\text{V}}^{2}$ under an optical field with a photon energy of $\ensuremath{\sim}20$ meV. With a photon energy large than 450 meV, ${\ensuremath{\sigma}}_{zxy}^{(2)}(0;\ensuremath{\omega},\ensuremath{-}\ensuremath{\omega})$ is relatively small. Especially, the calculated ${\ensuremath{\sigma}}_{zxy}^{(2)}(0;\ensuremath{\omega},\ensuremath{-}\ensuremath{\omega})$ is almost vanishing within a photon energy range of 450--500 meV. Below 300 meV, our calculation also reveals that the dielectric function and reflectivity decreases with an increase of photon energy, while the absorption coefficient increases with an increase of photon energy. Therefore, RhSi has a potential application for optoelectronic detection in the terahertz range.

The rotation of polarization occurs for light interacting with chiral materials. It requires the light states with opposite chiralities interact differently with the materials. We demonstrate analogous rotation of polarization also exists for chiral fermions interacting with quantum electrodynamics plasma with vorticity using chiral kinetic theory. We find that the rotation of polarization is perpendicular both to vorticity and fermion momentum. The effect also exists for chiral fermions in quantum chromodynamics plasma with vorticity. It could lead to generation of a vector current when the probe fermions contain momentum anisotropy., Comment: 11 pages, section on generalization to QCD plasma added, journal version

We study renormalization group flows in strongly interacting field theories with fermions that correspond to transitions between a theory without Lorentz invariance at high energies down to a theory with approximate Lorentz symmetry in the infrared. Holographic description of the strong coupling is used. The emphasis is made on emergence of chiral fermions in the low-energy theory., Comment: 28 pages, 2 figures

We determine the reduced density matrix of chiral fermions on the torus, for an arbitrary set of disjoint intervals and generic torus modulus. We find the resolvent, which yields the modular Hamiltonian in each spin sector. Together with a local term, it involves an infinite series of bi-local couplings, even for a single interval. These accumulate near the endpoints, where they become increasingly redshifted. Remarkably, in the presence of a zero mode, this set of points 'condenses' within the interval at low temperatures, yielding continuous non-locality., Comment: Several minor changes done in order to improve readability. Accepted for publication in PRL

The Standard Models contain chiral fermions coupled to gauge theories. It has been a long-standing problem to give such gauged chiral fermion theories a quantum non-perturbative definition. By classification of quantum anomalies and symmetric invertible topological orders via a mathematical cobordism theorem for differentiable and triangulable manifolds, and the existence of symmetric gapped boundary for the trivial symmetric invertible topological orders, we propose that Spin(10) chiral fermion theories with Weyl fermions in 16-dimensional spinor representations can be defined on a 3+1D lattice, and subsequently dynamically gauged to be a Spin(10) chiral gauge theory. As a result, the Standard Models from the 16n-chiral fermion SO(10) Grand Unification can be defined non-perturbatively via a 3+1D local lattice model of bosons or qubits. Furthermore, we propose that Standard Models from the 15n-chiral fermion SU(5) Grand Unification can also be realized by a 3+1D local lattice model of fermions., 24 pages. Two columns. v3: Refinement with detailed discussions. Appendices include viewpoints from perturbative local anomalies and non-perturbative global anomalies (e.g. arXiv:1810.00844, SU(2) = Spin(3) $\subset$ Spin(10)), and co/bordism theories (e.g. $\Omega_{D}^{{(\mathrm{Spin}(D) \times \mathrm{Spin}(10))}/{\mathbb{Z}_2^f}}$)

International audience; We study the question of whether a helicity-transporting current is generated in a rotating photon gas at finite temperature. One problem is that there is no gauge-invariant local notion of helicity or helicity current. We circumvent this by studying not only the optical helicity current but also the gauge-invariant “zilch” current. In order to avoid problems of causality, we quantize the system on a cylinder of finite radius and then discuss the limit of infinite radius. We find that net helicity and zilch currents are only generated in the case of the finite radius and are due to duality-violating boundary conditions. A universal result exists for the current density on the axes of rotation in the high-temperature limit. To lowest order in the angular velocity, it takes a form similar to the well-known temperature dependence of the chiral vortical effect for chiral fermions. We briefly discuss possible relations to gravitational anomalies.

We describe a simple model that automatically generates the sum over gauge group representations and chiralities of a single generation of fermions in the Standard Model, augmented by a sterile neutrino. The model is a modification of the world-line approach to chiral fermions. Keywords: Standard Model, Unification, Super Wilson loop

In a theory of a Dirac fermion field coupled to a metric-axial-tensor (MAT) background, using a Schwinger-DeWitt heat kernel technique, we compute non-perturbatively the two (odd parity) trace anomalies. A suitable collapsing limit of this model corresponds to a theory of chiral fermions coupled to (ordinary) gravity. Taking this limit on the two computed trace anomalies we verify that they tend to the same expression, which coincides with the already found odd parity trace anomaly, with the identical coefficient. This confirms our previous results on this issue., Comment: 43 pages, some additions in section 6.3 and 6.5 plus minor corrections

In our recent study of two-flavor lattice QCD using chiral fermions, we find strong suppression of axial U(1) anomaly above the critical temperature of chiral phase transition. Our simulation data also indicate suppression of topological susceptibility. In this talk, we present both of our theoretical and numerical evidence for disappearance of axial U(1) anomaly, emphasizing the importance of controlling lattice chiral symmetry violation, which is enhanced at high temperature., 11 pages, 5 figures, talk given at the 35th International Symposium on Lattice Field Theory, 18-24 June 2017, Granada, Spain, references added

Disordered 2D chiral fermions provide an effective description of several materials including graphene and topological insulators. While previous analysis considered delta correlated disorder and no ultraviolet cut-offs, we consider here the effect of short range correlated disorder and the presence of a momentum cut-off, providing a more realistic description of condensed matter models. We show that the density of states is anomalous with a critical exponent function of the disorder and that conductivity is universal only when the ultraviolet cut-off is removed, as consequence of the supersymmetric cancellation of the anomalies.

Chiral anomaly induces a new kind of macroscopic quantum behavior in relativistic magnetohydrodynamics, including the chiral magnetic effect. In this talk we present two new quantum effects present in fluids that contain charged chiral fermions: 1) the turbulent inverse cascade driven by the chiral anomaly; 2) quantized chiral magnetic current induced by the reconnections of magnetic flux. We also discuss the implications for the evolution of the quark-gluon plasma produced in heavy ion collisions., United States. Department of Energy (Grant DE-FG-88ER40388), United States. Department of Energy (Grant DE-AC02-98CH10886), United States. Department of Energy (Grant DE-SC0011090)

We calculate the trace anomaly of a Weyl fermion coupled to gravity by using Fujikawa's method supplemented by the choice of a consistent regulator. The latter is constructed out of Pauli-Villars regulating fields. The motivation for presenting such a calculation stems from recent studies that suggest that the trace anomaly of chiral fermions in four dimensions might contain an imaginary part proportional to the Pontryagin density. We find that the trace anomaly of a Weyl fermion is given by half the trace anomaly of a Dirac fermion, so that no imaginary part proportional to the Pontryagin density is seen to arise., 25 pages, added references and acknowledgments

We study microscopic processes responsible for chirality flips in the thermal bath of Quantum Chromodynamics at finite temperature and zero baryon chemical potential. We focus on the temperature range where the crossover from chirally broken phase to quark-gluon plasma takes place, namely $T \simeq (150, 200)$ MeV. The processes we consider are quark-quark scatterings mediated by collective excitations with the quantum number of pions and $\sigma$-meson, hence we refer to these processes simply as \sugg{to} one-pion (one-$\sigma$) exchange\sugg{s}. We use a Nambu-Jona-Lasinio model to compute equilibrium properties of the thermal bath, as well as the relevant scattering kernel to be used in the collision integral to estimate the chiral relaxation time $\tau$. We find $\tau\simeq 0.1 \div 1$ fm/c around the chiral crossover., Comment: 16 pages, 8 figures. One figure (lower panel of Fig. 6) added in comparison with V1. New version to appear on Phys. Rev. D

I will talk on my recent works related to the flavor grand unification, weak CP violation, and the phases in the CKM and PMNS matrices., Talk presented at ICHEP 2016, Chicago, Aug. 3-10, 2016

The nature of chiral phase transition for two flavor QCD is an interesting but unresolved problem. One of the most intriguing issues is whether or not the anomalous U(1) symmetry in the flavor sector is effectively restored along with the chiral symmetry. This may determine the universality class of the chiral phase transition. Since the physics near the chiral phase transition is essentially non-perturbative, we employ first principles lattice techniques to address this issue. We use overlap fermions, which have exact chiral symmetry on the lattice, to probe the anomalous U(1) symmetry violation of 2+1 flavor dynamical QCD configurations with domain wall fermions. The latter also optimally preserves chiral and flavor symmetries on the lattice, since it is known that the remnant chiral symmetry of the light quarks influences the scaling of the chiral condensate in the crossover transition region. We observe that the anomalous U(1) is not effectively restored in the chiral crossover region. We perform a systematic study of the finite size and cut-off effects since the signals of U(1) violation are sensitive to it. We also provide a glimpse of the microscopic topological structures of the QCD medium that are responsible for the strongly interacting nature of the quark gluon plasma phase. We study the effect of these microscopic constituents through our first calculations for the topological susceptibility of QCD at finite temperature, which could be a crucial input for the equation of state for anomalous hydrodynamics., 4 Pages, 3 Figures, Proceedings of Quark Matter 2015, Kobe, Japan, version accepted for publication in Nucl. Phys. A

Tunneling between different topological sectors with dynamical chiral fermions is difficult because of a poor mass scaling of the pseudo-fermion estimate of the determinant. For small fermion masses it is virtually impossible using standard methods. However, by projecting out the small Wilson eigenvectors from the overlap operator, and treating the correction determinant exactly, we can significantly increase the rate of topological sector tunneling and reduce substantially the auto-correlation time. We present and compare a number of different approaches, and advocate a method which allows topological tunneling even at low mass with little addition to the computational cost., Comment: 17 pages; v2 as accepted in computer Physics Communications

We study the consistency of dynamical fermionic matter with the asymptotic safety scenario of quantum gravity using the functional renormalisation group. Since this scenario suggests strongly coupled quantum gravity in the UV, one expects gravity-induced fermion self-interactions at energies of the Planck-scale. These could lead to chiral symmetry breaking at very high energies and thus to large fermion masses in the IR. The present analysis which is based on the previous works \cite{Christiansen:2015rva, Meibohm:2015twa}, concludes that gravity-induced chiral symmetry breaking at the Planck scale is avoided for a general class of NJL-type models, regardless of the number of fermion flavours. This suggests that the phase diagram for these models is topologically stable under the influence of gravitational interactions., 14 pages, 9 figures

We show that a hot rotating fluid of relativistic chiral fermions possesses a new gapless collective mode associated with coherent propagation of energy density and chiral density waves along the axis of rotation. This mode, which we call the Chiral Heat Wave, emerges due to a mixed gauge-gravitational anomaly. At finite density the Chiral Heat Wave couples to the Chiral Vortical Wave while in the presence of an external magnetic field it mixes with the Chiral Magnetic Wave. The coupling of the Chiral Magnetic and Chiral Vortical Waves is also demonstrated. We find that the coupled waves - which are coherent fluctuations of the vector, axial and energy currents - have generally different velocities compared to the velocities of the individual waves., 33 pages, 6 figures; v2: minor changes, published version

We study the non-dissipative transport effects appearing at second order in the hydrodynamic expansion for a non-interacting gas of chiral fermions by using the partition function formalism. We discuss some features of the corresponding constitutive relations, derive the explicit expressions for the conductivities and compare with existing results in the literature., Comment: 9 pages. Talk given by E.Megias at the 4th International Conference on New Frontiers in Physics (ICNFP 2015), 23-30 August 2015, Kolymbari, Crete, Greece

Lattice QCD calculations with chiral fermions of the $\pi$N sigma term $\sigma_{\pi N}$ and strangeness sigma term $\sigma_{sN}$ including chiral interpolation with continuum and volume corrections are provided in this work, with the excited-state contaminations subtracted properly. We calculate the scalar matrix element for the light/strange quark directly and find $\sigma_{\pi N}=45.9(7.4)(2.8)$ MeV, with the disconnected insertion part contributing 20(12)(4)\%, and $\sigma_{sN}=40.2(11.7)(3.5)$ MeV, which is somewhat smaller than $\sigma_{\pi N}$. The ratio of the strange/light scalar matrix elements is $y$ = 0.09(3)(1)., Comment: 7 pages, 5 figures, expanded version accepted for publication in PRD