Related papers: Fermion Zero Modes in Odd Dimensions
We define a scale-dependent effective mass anomalous dimension from the scaling of the mode number of the massless Dirac operator, which connects the perturbative $\gamma_m$ of an asymptotically-free system to the universal…
Fermion bound states in the background of the electroweak SU(2) monopole are investigated for various values of gauge coupling constant $g$, the Higgs self-coupling constant $\lambda$, and the Yukawa coupling constant $y_q$. Numerical…
A study of the zero modes of the Faddeev-Popov operator in the maximal Abelian gauge is presented in the case of the gauge group SU(2) and for different Euclidean space-time dimensions. Explicit examples of classes of normalizable zero…
Boundary conditions for a massless Dirac fermion in 2+1 dimensions where the space is a half-plane are discussed in detail. It is argued that linear boundary conditions that leave the Hamiltonian Hermitian generically break $C$ $P$ and $T$…
A self-consisting gauge-theory approach to describe Dirac fermions on flexible surfaces with a disclination is formulated. The elastic surfaces are considered as embeddings into R^3 and a disclination is incorporated through a topologically…
The axially symmetric $U(1)$ gauged self-interacting Q-balls are shown to support normalizable fermionic bound state, minimally coupled to the electromagnetic field of the Q-ball. It is shown that the effects of the backreaction of the…
The paper analyses the decay of any zero modes that might exist for a massless Dirac operator $H:= \ba \cdot (1/i) \bgrad + Q, $ where $Q$ is $4 \times 4$-matrix-valued and of order $O(|\x|^{-1})$ at infinity. The approach is based on…
We find explicitly a zero mode of the Kraichnan operator at two dimensions.
We study dimensional reduction of M5 branes on a circle bundle when the supersymmetry parameter is not constant along the circle. When the gauge group is Abelian and the fields appear quadratically in the Lagrangian, we can always obtain a…
We show how strongly interacting two-dimensional Dirac fermions can be realized with ultracold atoms in a two-dimensional optical square lattice with an experimentally realistic, inherent gauge field, which breaks time-reversal and…
We calculate all symmetries of the Dirac-Pauli equation in two-dimensional and three-dimensional Euclidean space. Further, we use our results for an investigation of the issue of zero mode degeneracy. We construct explicitly a class of…
We consider a generic time-reversal invariant model of fermions hopping randomly on a square lattice. By means of the conventional replica-trick within the fermionic path-integral formalism, the model is mapped onto a non-linear sigma-model…
The Osp(2|2) current algebra at level k=-2 is known to describe the IR fixed point of 2D Dirac fermions, subject to a random SU(2) gauge potential. We show that this theory has a simple free-field representation in terms of a compact, and a…
The classical part of the QCD partition function (the integrand) has, ignoring irrelevant exact zero modes of the Dirac operator, a local SU(2N_F) \supset SU(N_F)_L \times SU(N_F)_R \times U(1)_A symmetry which is absent at the Lagrangian…
We study two well-known $SU(N)$ chiral gauge theories with fermions in the symmetric, anti-symmetric and fundamental representations. We give a detailed description of the global symmetry, including various discrete quotients. Recent work…
We show that the local gauge-invariance of the quantum geometric tensor (QGT) defined in the Block-momentum space of a generic $N$-level (sublattice degrees of freedom) band insulator implies the existence of zero modes of non-abelian Dirac…
We study continuum quantum field theories in 2+1 dimensions with time-reversal symmetry $\cal T$. The standard relation ${\cal T}^2=(-1)^F$ is satisfied on all the "perturbative operators" i.e. polynomials in the fundamental fields and…
We study zero modes of Laplacians on compact and non-compact metric graphs with general self-adjoint vertex conditions. In the first part of the paper the number of zero modes is expressed in terms of the trace of a unitary matrix…
Quantum study of supersymmetric theories on Euclidean two dimensional anti-de Sitter space (EAdS$_2$) requires complexified spectrum. For a chiral multiplet, we showed that the spectrum of the Dirac operator acquires a universal shift of…
We present exact analytical solutions for the zero-energy modes of two-dimensional massless Dirac fermions fully confined within a smooth one-dimensional potential V(x)= - {\alpha}/cosh({\beta}x), which provides a good fit for potential…