We reinvestigate the classic example of the chiral anomaly in (1+1) dimensional spacetime. By reviewing the derivation of charge conservation using the semiclassical Boltzmann equation, we show that chiral anomalies could emerge in (1+1) dimensions without Berry curvature corrections to the kinetic theory. The pivotal step depends only on the asymptotic behavior of the distribution function of the quasiparticle--and thus its dispersion relation--in the limit of $\mathbf p\to\pm\infty$ rather than the detailed functional form of the dispersion. We address two subjects motivated by this observation. First, we reformulate (1+1)-dimensional chiral anomaly using kinetic theory with the current algebra approach and the gradient expansion of the Dirac Lagrangian, adding a complementary perspective to existing approaches. Second, we demonstrate the universality of the chiral anomaly across various quasiparticle dispersions. For two-band models linear in the temporal derivative, with Fujikawa's method we show it is sufficient to have a chirality-odd strictly monotonic dispersion in order to exhibit the chiral anomaly.
A model where a Dirac fermion is coupled to background dilaton field is considered to study s-wave scattering of fermion by a background dilaton black hole. It is found that the anomaly plays a dual role on information loss scenario. Some time it protects the fermion from the dangerous information loss problem and some times it itself through it up towards that danger.
Universality in anomaly flow by an Aharonov-Bohm (AB) phase $θ_H$ is shown in the flat $M^4 \times (S^1/Z_2)$ spacetime and in the Randall-Sundrum (RS) warped space. We analyze $SU(2)$ gauge theory with doublet fermions. With orbifold boundary conditions the $U(1)$ part of gauge symmetry remains unbroken at $θ_H = 0$ and $π$. Chiral anomalies smoothly vary with $θ_H$ in the RS space. It is shown that anomaly coefficients associated with this anomaly flow are expressed in terms of the values of the wave functions of gauge fields at the UV and IR branes in the RS space. The anomaly coefficients …
We study the large $N$ 't Hooft expansion of the chiral partition function of 2d $U(N)$ Yang-Mills theory on a torus. There is a long-standing puzzle that no explicit holomorphic anomaly equation is known for the partition function, although it admits a topological string interpretation. Based on the chiral boson interpretation we clarify how holomorphic anomaly arises and propose a natural anti-holomorphic deformation of the partition function. Our deformed partition function obeys a fairly traditional holomorphic anomaly equation. Moreover, we find a closed analytic expression for the deform…
Axial and gravitational anomaly of field theories, when embedded in string theory, must be accompanied by canceling inflow. We give a self-contained overview for various world-volume theories, and clarify the role of smeared magnetic sources in I-brane/D-brane cases. The proper anomaly descent of the source, as demanded by regularity of RR field strengths H's, turns out to be an essential ingredient. We show how this allows correct inflow to be generated for all such theories, including self-dual cases, and also that the mechanism is now insensitive to the choice between the two related but in…
In the anomaly equation for the singlet axial current the chiral limit of the quark mass term does not vanish but comprises contribution from fermion zero modes whose integral exactly cancels the topological charge arising from the Adler-Bell-Jackiw anomaly. This signals chiral symmetry and opens a window for restoring the status of Goldstone boson for the singlet $η^\prime$ without having to invoke the large $N_c$ limit in the underlying QCD. We construct the anomaly term in the effective action that incorporates the chiral symmetry property and yet accounts for the excess mass of $η^\prime$ …
The universal behavior of Hawking radiation is originated in the conformal symmetries of matter fields near the black hole horizon. We explain the origin of this universality based on (1) the gravitational anomaly and its higher-spin generalizations and (2) conformal transformation properties of fluxes.
In the context of the superconformal N=4 SYM theory the Konishi anomaly can be viewed as the descendant $K_{10}$ of the Konishi multiplet in the 10 of SU(4), carrying the anomalous dimension of the multiplet. Another descendant $O_{10}$ with the same quantum numbers, but this time without anomalous dimension, is obtained from the protected half-BPS operator $O_{20'}$ (the stress-tensor multiplet). Both $K_{10}$ and $O_{10}$ are renormalized mixtures of the same two bare operators, one trilinear (coming from the superpotential), the other bilinear (the so-called "quantum Konishi anomaly"). Only…
The one-loop structure of the trace anomaly is investigated using different regularizations and renormalization schemes: dimensional, proper time and Pauli-Villars. The universality of this anomaly is analyzed from a very general perspective. The Euler and Weyl terms of the anomalous trace of the stress tensor are absolutely universal. The pure derivative $ \square R$-term is shown to be universal only if the regularization breaks conformal symmetry softly. If the breaking of conformal symmetry by the regularization method is hard the coefficient of this term might become arbitrary which point…
We show that the diffeomorphism anomaly together with the trace anomaly reveal a chiral Virasoro algebra near the event horizon of a black hole. This algebra is the same irrespective of whether the anomaly is covariant or consistent, thereby manifesting its universal character and the fact that only the outgoing modes are relevant near the horizon. Our analysis therefore clarifies the role of the trace anomaly in the diffeomorphism anomaly approach \cite{wilczek, isowilczek, shailesh, shailesh2, sunandan, sunandan10, rabin10} to the Hawking radiation.
We consider theories with gauged chiral fermions in which there are abelian anomalies, and no nonabelian anomalies (but there may be nonabelian gauge fields present). We construct an associated theory that is gauge-invariant, renormalizable, and with the same particle content, by adding a finite number of terms to the action. Alternatively one can view the new theory as arising from the original theory by using another regularization, one that is gauge-invariant. The situation is reminiscent of the mechanism of adding Fadeev-Popov ghosts to an unsatisfactory gauge theory, to arrive at the usua…
We reinvestigate the dilaton coupling in the string theory, which comes from a wrapped membrane. The ghost number anomaly associated with the string worldsheet diffeomorphism is shown to induce the dilaton coupling.
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 supersym…
We study discrete R-symmetries, which appear in 4D low energy effective field theory derived from hetetoric orbifold models. We derive the R-symmetries directly from geometrical symmetries of orbifolds. In particular, we obtain the corresponding R-charges by requiring that the couplings be invariant under these symmetries. This allows for a more general treatment than the explicit computations of correlation functions made previously by the authors, including models with discrete Wilson lines, and orbifold symmetries beyond plane-by-plane rotational invariance. Surprisingly, for the cases cove…
A derivation of the anomaly-induced transport phenomena---the chiral magnetic/vortical effect---is revisited based on the imaginary-time formalism of quantum field theory. Considering the simplest anomalous system composed of a single Weyl fermion, we provide two derivations: perturbative (one-loop) evaluation of the anomalous transport coefficient, and the anomaly matching for the local thermodynamic functional.
In addition to the existing strong indications for lepton flavour university violation (LFUV) in low energy precision experiments, CMS recently released an analysis of non-resonant di-lepton pairs which could constitute the first sign of LFUV in high-energy LHC searches. In this article we show that the Cabibbo angle anomaly, an (apparent) violation of first row and column CKM unitarity with $\approx3\,σ$ significance, and the CMS result can be correlated and commonly explained in a model independent way by the operator $[Q_{\ell q}^{(3)}]_{1111} = (\bar{\ell}_1γ^μσ^I\ell_1)(\bar{q}_1γ_μσ^Iq_1…
Applying functional renormalization group methods, we describe two inequivalent ways of defining the renormalization group of matter-coupled four dimensional gravity, in the approximation where only the conformal factor is dynamical and taking the trace anomaly explicitly into account. We make contact with earlier work and briefly discuss the presence or absence of fixed points, depending on the truncation of the action and other approximations.
We reveal elegant relations between the shape dependence of the Casimir effects and Weyl anomaly in boundary conformal field theories (BCFT). We show that for any BCFT which has a description in terms of an effective action, the near boundary divergent behavior of the renormalized stress tensor is completely determined by the central charges of the theory. These relations are verified by free BCFTs. We test them with holographic models of BCFT and find exact agreement. We propose that these relations between Casimir coefficients and central charges hold for any BCFT. With the holographic model…
Motivated by the search for possible CP violating terms in the trace of the energy-momentum tensor in theories coupled to gravity we revisit the problem of trace anomalies in chiral theories. We recalculate the latter and ascertain that in the trace of the energy-momentum tensor of theories with chiral fermions at one-loop the Pontryagin density appears with an imaginary coefficient. We argue that this may break unitarity, in which case the trace anomaly has to be used as a selective criterion for theories, analogous to the chiral anomalies in gauge theories. We analyze some remarkable consequ…
We study low-energy dynamics of $[SU(N)]^K$ chiral quiver gauge theories in connection with $\mathcal{N}=1$ super Yang-Mills (SYM) theory, and quantum chromodynamics with bi-fundamental fermions (QCD(BF)). These theories can be obtained by $\mathbb{Z}_K$ orbifold projections of $\mathcal{N}=1$ $SU(NK)$ SYM theory, but the perturbative planar equivalence does not extend nonperturbatively for $K\ge 3$. In order to study low-energy behaviors, we analyze these systems using 't~Hooft anomaly matching and reliable semiclassics on $\mathbb{R}^3\times S^1$. Thanks to 't~Hooft anomaly that involves $1$…
We show that generic U(1) superfluids with a U(1)^3 anomaly feature universal anomalous transport at low temperature. This universal behavior had been encountered before for a class holographic models by performing explicit computations: anomalous conductivities were found to either vanish or to be 1/3 of the value they present for ordinary fluids. In this note we argue in favor of the fact that at zero temperature chiral conductivities are fully determined by anomaly coefficients. We also compute them and show explicitly where their particular value arises from. The proof is based on Ward Ide…
Nonperturbative Chiral Anomaly Cancellation and Irrelevant Operators
Università degli Studi Roma Tre, Mathematics and Physics Department（罗马第三大学数学与物理系）；Università degli Studi di Roma “La Sapienza”, Physics Department（罗马第一大学物理系）；SISSA, Mathematics Area（的里雅斯特国际高等研究学校数学区）
This paper deals with magnetic equations of the type dH=J where the current J is a delta-function on a brane worldvolume and H a p-form field strength. In many situations in M-theory this equation needs to be solved for H in terms of a potential. A standard universality class of solutions, involving Dirac-branes, gives rise to strong intermediate singularities in H which in many physically relevant cases lead to inconsistencies. In this paper we present an alternative universality class of solutions for magnetic equations in terms of Chern-kernels, and provide relevant applications, among whic…
In six dimensions, cancellation of gauge, gravitational, and mixed anomalies strongly constrains the set of quantum field theories which can be coupled consistently to gravity. We show that for some classes of six-dimensional supersymmetric gauge theories coupled to gravity, the anomaly cancellation conditions are equivalent to tadpole cancellation and other constraints on the matter content of heterotic/type I compactifications on K3. In these cases, all consistent 6D supergravity theories have a realization in string theory. We find one example which may arise from a novel string compactific…
We investigate the nature of the finite-temperature chiral transition in QCD with two light flavors, in the case of an effective suppression of the the U(1)_A symmetry breaking induced by the axial anomaly, which implies the symmetry breaking U(2)_L X U(2)_R -> U(2)_V, instead of SU(2)_L X SU(2)_R -> SU(2)_V. For this purpose, we perform a high-order field-theoretical perturbative study of the renormalization-group (RG) flow of the corresponding three-dimensional multiparameter Landau-Ginzburg-Wilson Phi4 theory with the same symmetry-breaking pattern. We confirm the existence of a stable fixe…
We study an 't Hooft anomaly of massless QCD at finite temperature. With the imaginary baryon chemical potential at the Roberge-Weiss point, there is a $\mathbb{Z}_2$ symmetry which can be used to define confinement. We show the existence of a mixed anomaly between the $\mathbb{Z}_2$ symmetry and the chiral symmetry, which gives a strong relation between confinement and chiral symmetry breaking. The anomaly is a parity anomaly in the QCD Lagrangian reduced to three dimensions. It is reproduced in the chiral Lagrangian by a topological term related to Skyrmion charge, matching the anomaly befor…
We discuss two dimensional Yang -- Mills theories with massless fermions in arbitrary representations of a gauge group $G$. It is shown that the physics (spectrum and interactions) of the massive states in such models is independent of the detailed structure of the model, and only depends on the gauge group $G$ and an integer $k$ measuring the total anomaly. The massless physics, which does depend on the details of the model, decouples (almost) completely from that of the massive one. As an example, we discuss the equivalence of QCD$_2$ coupled to fermions in the adjoint, and fundamental repre…
Six-dimensional supergravity theories with N=(1,0) supersymmetry must satisfy anomaly equations. These equations come from demanding the cancellation of gravitational, gauge and mixed anomalies. The anomaly equations have implications for the geometrical data of Calabi-Yau threefolds, since F-theory compactified on an elliptically fibered Calabi-Yau threefold with a section generates a consistent six-dimensional N=(1,0) supergravity theory. In this paper, we show that the anomaly equations can be summarized by three intersection theory identities. In the process we also identify the geometric …
Using the chiral algebra bootstrap, we revisit the simplest Argyres-Douglas (AD) generalization of Argyres-Seiberg S-duality. We argue that the exotic AD superconformal field theory (SCFT), $T_{3,{3\over2}}$, emerging in this duality splits into a free piece and an interacting piece, T_X, even though this factorization seems invisible in the Seiberg-Witten (SW) curve derived from the corresponding M5-brane construction. Without a Lagrangian, an associated topological field theory, a BPS spectrum, or even an SW curve, we nonetheless obtain exact information about T_X by bootstrapping its chiral…
The low-temperature thermodynamics of near-extremal rotating black holes has recently been revisited to incorporate one-loop contributions that are dominant in this regime. We discuss these quantum corrections to the gravitational path integral for asymptotically Anti de-Sitter black holes in four and five dimensions. In four dimensions we explicitly consider Kerr-AdS$_4$, Kerr-Newman-AdS$_4$ and the rotating black hole in ${\cal N}=4$ gauged supergravity with two scalars and two electric charges turned on. In five dimensions we explicitly address the asymptotically flat Myers-Perry black hole…
We revisit discrete gauge anomalies in chiral fermion theories in $3+1$ dimensions. We focus on the case that the full symmetry group of fermions is $\mathrm{Spin}(4)\times\mathbb{Z}_n$ or $(\mathrm{Spin}(4)\times\mathbb{Z}_{2m})/\mathbb{Z}_{2}$ with $\mathbb{Z}_2$ being the diagonal $\mathbb{Z}_2$ subgroup. The anomalies are determined by the consistency condition --- based on the Dai-Freed theorem --- of formulating a chiral fermion theory on a generic spacetime manifold with a structure associated with either one of the above symmetry groups and are represented by elements of some finite ab…
We review a recent development in the theoretical understanding of the nu=5/2 quantum Hall plateau and propose a new conformal field theory, slightly different from the Moore-Read one, to describe another universality class relevant for this plateau. The ground state is still given by the Pfaffian and is completely polarized, however, the elementary quasiholes are charge 1/2 anyons with abelian statistics theta=pi/2, which obey complete spin-charge separation. The physical hole is represented by two such quasiholes plus a free neutral Majorana fermion. We also compute the periods and amplitude…
We consider the theory of Rarita-Schwinger field interacting with a field with spin 1/2, in the case of finite temperature, chemical potential and vorticity, and calculate the chiral vortical effect for spin 3/2. We have clearly demonstrated the role of interaction with the spin 1/2 field, the contribution of the terms with which to CVE is 6. Since the contribution from the Rarita-Schwinger field is -1, the overall coefficient in CVE is 6-1=5, which corresponds to the recent prediction of a gauge chiral anomaly for spin 3/2. The obtained values for the coefficients $μ^2$ and $T^2$ are proporti…
