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 electrodynamics that enjoys duality transformation invariance. These symmetries allow us to generalize the Eguchi-Hanson configuration while preserving its geometry. We then compute the Dirac index of the nonlinearly charged Eguchi-Hanson and Taub-NUT configurations. We find that there is an excess of positive chiral Dirac fermions over the negative ones which triggers the anomaly.
The gradient flow exact renormalization group (GFERG) is a formulation of the exact renormalization group that keeps exact gauge invariance. GFERG can keep also modified chiral invariance. We will show that this formulation reproduces the correct axial anomaly in four dimensions.
In this paper we study the axial anomaly in Very Special Relativity Electrodynamics using Pauli-Villars and dimensional regularization of ultraviolet divergences and Mandelstam-Leibbrandt regularization of infrared divergences. We compute the anomaly in 2 and 4 dimensional space-time. We find that this procedure preserves the vector Ward identity(charge conservation) and reproduce the standard axial anomaly in 2 and 4 dimensions without corrections from VSR. Finally, we show how to obtain the anomaly in the path integral approach.
We calculate the $U(1)$ axial-anomaly in two and four dimensions using a modified path integral method coupled to a Pauli-Villars regulator field in the noncommutative QED. Pauli-Villars regularization method provides us with unambiguous way to connect the modified path integral formalism with perturbative axial Ward identities at each step of calculations.
We generalize the dispersive approach to axial anomaly by A.D. Dolgov and V.I. Zakharov to a non-Abelian case with arbitrary photon virtualites. We derive the anomaly sum rule for the singlet current and obtain the $π^0,η,η'\rightarrowγγ^*$ transition form factors. Using them, we established the behavior of a nonperturbative gluon matrix element $\langle 0 |G\tilde{G} |γγ^*(q^2) \rangle$ in both spacelike and timelike regions. We found a significant contribution of the non-Abelian axial anomaly to the processes with one virtual photon, comparable to that of the electromagnetic anomaly. The dua…
In this note, we revise the problem of the axial anomaly in the framework of very special relativity following Fujikawa's path integral approach. We show nonperturbatively that no VSR contribution is present in the path integral measure in $(3+1)$-dimensional spacetime. Furthermore, we extend our results to $(1+1)$ dimensions, as well as to the two-dimesional curved spacetime.
Axial Anomaly from the BPHZ regularized BV master equation
De Jonghe，Paris和Troost最近提出了反场（或BV）量子化主方程的BPHZ重整化形式。这个框架被证明是非常强大的计算规范异常。我们在这里表明，这个方程也可以应用于计算全球异常（异常发散的经典保守的诺特电流），考虑的情况下QED。这样，在BPHZ正则化的BV框架中再现了标准QED（没有规范反常）中关于反常对轴向沃德恒等式贡献的基本结果。
In this paper, we examine the problem of anomalies of the fermionic currents in the context of the very special relativity (VSR). We consider the VSR contributions to the triangle amplitude $\left\langle J_{5}^λ J^μ J^ν \right\rangle $, which allows the evaluation of the vector and axial Ward identities. Actually, we observe that the VSR nonlocal effects respect the vector Ward identity, and it also contributes in a very interesting and unique way for the Adler-Bell-Jackiw anomaly.
We give a very simple derivation of the Atiyah-Patodi-Singer (APS) index theorem and its small generalization by using the path integral of massless Dirac fermions. It is based on the Fujikawa's argument for the relation between the axial anomaly and the Atiyah-Singer index theorem, and only a minor modification of that argument is sufficient to show the APS index theorem. The key ingredient is the identification of the APS boundary condition and its generalization as physical state vectors in the Hilbert space of the massless fermion theory. The APS $η$-invariant appears as the axial charge o…
In 3+1 dimensional spacetime, two vector gauge anomalies are known: The chiral anomaly and the mixed axial-gravitational anomaly. While the former is well documented and tied to the presence of a magnetic field, the latter instead requires a nonzero spacetime curvature, which has made it rather difficult to study. In this work, we show that a quantum anomaly arises in the second-order electrical response for zero magnetic field, which creates a dc-current that can be either longitudinal or transverse to electric field. Consequently, the continuity equation for the chiral current is not conserv…
