Related papers: Scale-invariance of parity-invariant three-dimensi…
Two-dimensional QCD with $N_c$ colors and $N_f$ flavors of massless fermions in the fundamental representation is expected to exhibit conformal behavior in the infrared governed by a $u(N_f)$ WZW model with level $N_c$. Using numerical…
We formulate lattice perturbation theory for gauge theories in noncommutative geometry. We apply it to three-dimensional noncommutative QED and calculate the effective action induced by Dirac fermions. In particular "parity invariance" of a…
We consider the parity-invariant Dirac operator with a mass term in three-dimensional QCD for $N_c=2$ and quarks in the fundamental representation. We show that there exists a basis in which the matrix elements of the Euclidean Dirac…
We present the results of studies [1,2] of the gauge covariance of the massless fermion propagator in three-dimensional quenched quantum electrodynamics in the framework of dimensional regularization in d=3-2\ep. Assuming the finiteness of…
In odd dimensions the lattice overlap formalism is simpler than in even dimensions. Masslessness of fermions can still be preserved without fine tuning and gauge invariance without gauge averaging can be maintained, although, sometimes,…
Following Feynman's successful treatment of the polaron problem we apply the same variational principle to quenched QED in the worldline formulation. New features arise from the description of fermions by Grassmann trajectories, the…
The overlap fermion offers the tremendous advantage of exact chiral symmetry on the lattice, but is numerically intensive. This can be made affordable while still providing large lattice volumes, by using coarse lattice spacing, given that…
Monopole operators are studied in a large family of quantum critical points between Dirac and topological quantum spin liquids (QSLs): chiral and Z$_{2}$ QSLs. These quantum phase transitions are described by conformal field theories…
The chiral symmetry relation and scaling of the overlap fermions are studied numerically on the quenched lattices at 3 couplings with about the same physical volume. We find that the generalized Gell-Mann-Oakes-Renner relation is satisfied…
We review the parity anomaly and a duality web in 2+1 dimensions. An odd dimensional non-interacting Dirac fermion theory is not parity invariant at quantum level. We demonstrate the parity anomaly in a three dimensional non-interacting…
A conformal invariant QED-inspired model is solved for a general covariant linear gauge using the Dyson-Schwinger equations for the propagators assuming a pure vector like interaction. The leading corrections to the asymptotic solutions and…
I discuss the 2-flavor Schwinger model with $\theta=0$ and small equal and opposite fermion masses (or $\theta=\pi$ with equal masses). The massless model has an unparticle sector with unbroken conformal symmetry. I argue that this special…
Quantum anomalies arise when symmetries of a classical theory cannot be preserved upon quantization, leading to unconventional topological responses. A prominent example is the parity anomaly of a single two-dimensional Dirac fermion, which…
SU(3) gauge theory with overlap fermions in the 2-index symmetric (sextet) and fundamental representations is considered. A priori it is not known what the pattern of chiral symmetry breaking is in a higher dimensional representation…
We show that a system of three species of one-dimensional fermions, with an attractive three-body contact interaction, features a scale anomaly directly related to the anomaly of two-dimensional fermions with two-body forces. We show,…
The results of calculation of the three-loop radiative correction to the renormalization constant of fermion masses for non-abelian gauge theory interacting with fermions are presented. Dimensional regularization and the 't Hooft minimal…
We investigate whether it is possible to extract the quark mass anomalous dimension and its scale dependence from the spectrum of the twisted mass Dirac operator in Lattice QCD. The answer to this question appears to be positive, provided…
The equivalence of domain wall and overlap fermion formulations is demonstrated for lattice gauge theories in 2+1 spacetime dimensions with parity-invariant mass terms. Even though the domain wall approach distinguishes propagation along a…
We study the fixed point that controls the IR dynamics of QED in $d = 4 - 2\epsilon$. We derive the scaling dimensions of four-fermion and bilinear operators beyond leading order in $\epsilon$-expansion. For the four-fermion operators, this…
We study by non perturbative techniques a vector, axial--vector theory characterized by a parameter which interpolates between pure vector and chiral Schwinger models. Main results are two windows in the space of parameters which exhibit…