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While it has been pointed out that the chiral symmetry, which is important for the Dirac fermions in graphene, can be generalized to tilted Dirac fermions as in organic metals, such a generalized symmetry was so far defined only for a…
A conformally invariant theory of Majorana fermions in 2<d<4 with O(N) symmetry is studied using Operator Product Expansions and consistency relations based on the cancellation of shadow singularities. The critical coupling G_{*} of the…
We investigate the implications of the quantized vectorial and axial charges in the lattice Hamiltonian of multi-flavor staggered fermions in $(1+1)$ dimensions. These lattice charges coincide with those of the $U(1)_V$ and $U(1)_A$ global…
We discuss second quantization, discrete symmetry transformations and inner products in free non-Hermitian scalar quantum field theories with PT symmetry, focusing on a prototype model of two complex scalar fields with anti-Hermitian mass…
We consider chiral fermionic conformal field theories (CFTs) constructed from lattices and investigate their orbifolds under reflection and shift $\mathbb{Z}_2$ symmetries. For lattices based on binary error-correcting codes, we show the…
The commonly used pseudo-C symmetry $(\nu_{L})^{c}=C\overline{\nu_{L}}^{T}$ is not defined in Lagrangian field theory. In general, there exist two classes of Majorana fermions; the first is associated with the Dirac-type fermion with the…
The microscopic spectral eigenvalue correlations of QCD Dirac operators in the presence of dynamical fermions are calculated within the framework of Random Matrix Theory (RMT). Our approach treats the low--energy correlation functions of…
We show that the Dirac equation is separated into four differential equations for time-period Majarana fermions in Kerr-Newman, Kerr-Newman-(A)dS spacetimes. Although they can not be transformed into radial and angular equations, the four…
We study 2+1 dimensional gauge theories with a Chern-Simons term and a fermion in the adjoint representation. We apply general considerations of symmetries, anomalies, and renormalization group flows to determine the possible phases of the…
In this manuscript we describe a hidden conformal symmetry of the second Randall-Sundrum model (RS2). We show how this can be used to localize fermions of both chiralities. The conformal symmetry leaves few free dimensionless constants and…
We study K\"ahler-Dirac fermions on Euclidean dynamical triangulations. This fermion formulation furnishes a natural extension of staggered fermions to random geometries without requring vielbeins and spin connections. We work in the…
In the presence of boundaries, the quantum anomalies acquire additional boundary terms. In odd dimensions the integrated conformal anomaly, for which the bulk contribution is known to be absent, is non-trivial due to the boundary terms.…
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…
The possibility to distinguish Dirac from Majorana fermion by gravitational interaction and torsion coupling is discussed. The scattering of both Dirac and Majorana particles are the same in the spherically symmetric gravitational field up…
We discuss how the $1/N_c$ expansion and the chiral random matrix theory ($\chi$RMT) can be used in the study of large-$N_c$ gauge theories. We first clarify the parameter region in which each of these two approaches is valid: while the…
We classify two-dimensional purely chiral conformal field theories which are defined on two-dimensional surfaces equipped with spin structure and have central charge less than or equal to 16, and discuss their duality webs. This result can…
We explore a singlet Majorana fermion dark matter candidate using an effective field theory (EFT) framework, respecting the relations imposed by the standard model $SU(3)_C \times SU(2)_L \times U(1)_Y$ gauge invariance among different…
We discuss the fermionization of fusion category symmetries in two-dimensional topological quantum field theories (TQFTs). When the symmetry of a bosonic TQFT is described by the representation category $\mathrm{Rep}(H)$ of a semisimple…
Within five-dimensional compactified theories we discuss generalized periodicity and orbifold boundary conditions that allow for mixing between particles and anti-particles after a shift by the size of extra dimensions or after the orbifold…
Majorana fermions are the real (in a mathematical sense) counterparts of complex fermions like ordinary electrons. The promise of topological quantum computing has lead to substantial experimental progress in realizing these particles in…