Related papers: Axial gravity: a non-perturbative approach to spli…

We review recent discussions regarding the parity-odd contribution to the trace anomaly of a chiral fermion. We pay special attention to the perturbative approach in terms of Feynman diagrams, comparing in detail the results obtained using…

We study the trace and chiral anomalies of Weyl fermions in a non-abelian gauge background in four dimensions. Using a Pauli-Villars regularization we identify the trace anomaly, proving that it can be cast in a gauge invariant form, even…

Exact chiral symmetry at finite lattice spacing would preclude the axial anomaly. In order to describe a continuum quantum field theory of Dirac fermions, lattice actions with purported exact chiral symmetry must break the flavor-singlet…

Weyl semimetals are materials where electrons behave effectively as a kind of massless relativistic particles known asWeyl fermions. These particles occur in two flavours, or chiralities, and are subject to quantum anomalies, the breaking…

The first part is an introductory description of a small cross-section of the literature on algebraic methods in non-perturbative quantum gravity with a specific focus on viewing algebra as a laboratory in which to deepen understanding of…

We give a new twist to an old-fashioned topic in quantum field theory describing violations of the chiral charge conservation of massless fermions through Adler-Bell-Jackiw anomalies in the background of instanton fields in the context of…

We calculate the trace (conformal) anomaly for chiral fermions in a general curved background using Hadamard subtraction. While in intermediate steps of the calculation imaginary terms proportional to the Pontryagin density appear, imposing…

We study chiral symmetries of fermionic non commutative dipole theories. By using Fujikawa's approach we obtain explicit expressions of the anomalies for Dirac and chiral fermions in 2 and 4 dimensions.

We study the definition of trace anomalies for models of Dirac and Weyl fermions coupled to a metric and a gauge potential. While in the non-perturbative case the trace anomaly is the response of the effective action to a Weyl…

We compute the axial anomaly of a Lifshitz fermion theory with anisotropic scaling z=3 which is minimally coupled to geometry in 3+1 space-time dimensions. We find that the result is identical to the relativistic case using path integral…

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…

Particle production in strong electromagnetic fields is a recurring theme in solid state physics, heavy ion collisions, early universe cosmology and formal quantum field theory. In this paper we discuss the Dirac equation in a background of…

We study the axial anomaly of Dirac spinors on gravitational instanton backgrounds in the context of nonlinear electrodynamics. In order to do so, we consider Einstein gravity minimally coupled to a recently proposed conformal…

The $SU(N)$ Yang-Mills matrix model admits self-dual and anti-self-dual instantons. When coupled to $N_f$ flavors of massless quarks, the Euclidean Dirac equation in an instanton background has $n_+$ positive and $n_-$ negative chirality…

We calculate the exact parity odd part of the effective action ($\Gamma_{odd}^{2d+1}$) for massive Dirac fermions in 2d+1 dimensions at finite temperature, for a certain class of gauge field configurations. We consider first Abelian…

We find a large class of quantum gauge models with massless fermions where the coupling to the gauge fields is not chirally symmetric and which nevertheless do not suffer from gauge anomalies. To be specific we study two dimensional Abelian…

We compute the parity-odd part of the Weyl anomaly for chiral fermions in a background gravitational field. We start from a manifestly real form of the Lagrangian (that is, not only real up to a total derivative), and we regularize it by…

Chiral defect fermions in the background of an external, $2n$ dimensional gauge field are considered. Assuming first a finite extra dimension, we calculate the axial anomaly in a vector-like, gauge invariant model for arbitrary $n$, and the…

We consider the chiral anomaly for systems with a wide class of Hermitian Dirac operators ${Q}$ in 4D Euclidean spacetime. We suppose that $ Q$ is not necessarily linear in derivatives and also that it contains a coordinate inhomogeneity…

We consider N Dirac fermions on a 4-dimensional Euclidean space with a quadratic interaction given by arbitrary external Clifford-valued fields. The divergence of the axial current satisfies on the classical level a relation that is…