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We present a generalization of the Frolov-Slavnov invariant regularization scheme for chiral fermion theories in curved spacetimes. local gauge symmetries of the theory, including local Lorentz invariance. The perturbative scheme works for…

There exist both continuum and lattice regularizations of gauge theories with fermions which preserve chiral U(1) invariance ("fermion number"). Such regularizations necessarily break gauge invariance but, in a covariant gauge, one recovers…

Using path integral method (Fujikawa's method) we calculate anomalies in noncommutative gauge theories with fermions in the bi-fundamental and adjoint representations. We find that axial and chiral gauge anomalies coming from non-planar…

We study domain walls and vortices in chiral symmetry breaking in a QCD-like theory with N flavors in the chiral limit. If the axial anomaly is absent, there exist stable Abelian axial vortices winding around the spontaneously broken U(1)_A…

The global chiral symmetry of a $SU(2)$ gauge theory is studied in the framework of renormalization group (RG). The theory is defined by the RG flow equations in the infrared cutoff $\L$ and the boundary conditions for the relevant…

Two-point functions related to the pion weak decay constant $f_\pi$ are calculated from the generating functional of chiral perturbation theory in the mean field approximation and the heavy-baryon limit. The aim is to demonstrate that…

The chiral symmetry breaking in the 4-dimensional QED with the chirally invariant four-fermion interaction is discussed by using a novel path integral expression in terms of the field-strength tensor. In the local potential approximation,…

In this paper, we discuss the chiral anomaly in a Lorentz-breaking extension of QED which, besides the common terms that are present in the Standard Model Extension, includes some dimension-five nonminimal couplings. We find, using the…

The discovery of a chiral anomaly in Weyl semimetals, the non-conservation of chiral charge and energy across two opposite chirality Weyl nodes, has sparked immense interest in understanding its impact on various physical phenomena. Here,…

In beginning quantum mechanics courses, symmetries of a physical system are usually introduced as operators which commute with the Hamiltonian. In this article we will consider chiral symmetries which anticommute with the Hamiltonian.…

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…

Quantum anomalies are the breakdowns of classical conservation laws that occur in quantum-field theory description of a physical system. They appear in relativistic field theories of chiral fermions and are expected to lead to anomalous…

Anomalous correlators of vector and axial currents which enter the Kubo formulae for the chiral magnetic and the chiral separation conductivities are explicitly calculated for free overlap fermions on the lattice. The results are confronted…

A flow invariant is a quantity depending only on the UV and IR conformal fixed points and not on the flow connecting them. Typically, its value is related to the central charges a and c. In classically-conformal field theories, scale…

A recently proposed formulation of chiral lattice gauge theories is reviewed, in which the locality and gauge invariance of the theory can be preserved if the fermion representation of the gauge group is anomaly-free.

It is well known that a local, unitary Poincare-invariant 2D QFT with a global scaling symmetry and a discrete non-negative spectrum of scaling dimensions necessarily has both a left and a right local conformal symmetry. In this paper we…

A systematic study of chiral effects is presented using an Effective Field Theory framework. By integrating out a massive Dirac fermion at finite temperature in presence of vector and axial background fields, the currents and their…

If there exists Lorentz and CPT violation in nature, then it is crucial to discover and understand the underlying mechanism. In this contribution, we discuss one such mechanism which relies on four-dimensional chiral gauge theories defined…

We construct the three-dimensional effective field theory which reproduces low-momentum static correlation functions in four-dimensional quantum field theories with U(1) axial anomalies and a dynamical vector gauge field, in thermal…

We study the transport properties of a relativistic fluid affected by chiral and gauge-gravitational anomalies. The computation is performed in the framework of the fluid/gravity correspondence for a 5 dim holographic model with…