Related papers: Abelian Zero Modes in Odd Dimensions
The procedure of null reduction provides a concrete way of constructing field theories with Galilean invariance. We use this to examine Galilean gauge theories, viz. Galilean electrodynamics and Yang-Mills theories in spacetime dimensions 3…
We study a four-dimensional low-energy effective field theory derived from extra dimensional field theories with general gauge backgrounds. We find that products among fermionic zero-modes and lightest scalar modes are expanded by other…
While it has been well-known that the chirality is an important symmetry for Dirac-fermion systems that gives rise to the zero-mode Landau level in graphene, here we explore whether this notion can be extended to tilted Dirac cones as…
Dynamical localization of non-Abelian gauge fields in non-compact flat $D$ dimensions is worked out. The localization takes place via a field-dependent gauge kinetic term when a field condenses in a finite region of spacetime. Such a…
It is shown that $\Vert A \Vert_{L^d}^2 \ge \frac{d}{d-2}\, S_d$ is a necessary condition for the existence of a nontrivial solution of the Dirac equation $\gamma \cdot (-i\nabla -A)\psi = 0$ in $d$ dimensions. Here, $S_d$ is the sharp…
Recently, in an attempt to study disordered criticality in Quantum Hall systems and $d$-wave superconductivity, it was found that two dimensional random Dirac fermion systems contain a line of critical points which is connected to the pure…
We consider a Dirac field in 2+1 dimensions with a domain wall like defect in its mass, minimally coupled to a dynamical Abelian vector field. The mass of the fermionic field is assumed to have just one linear domain wall, which is…
We analyze general zero mode properties of the parent Hamiltonian of the unprojected Jain-2/5 state. We characterize the zero mode condition associated to this Hamiltonian via projection onto a four-dimensional two-particle subspace for…
At zero energy the Dirac equation has interesting behaviour. The asymmetry in the number of spin up and spin down modes is determined by the topology of both space and the gauge field in which the system sits. An analogous phenomenon also…
In the three-dimensional ${\cal N}=6$ Chern-Simons matter (ABJM) theory, the integrand for the logarithm of the scattering amplitude admits a decomposition in terms of negative geometries, which implies that all the infrared divergences…
A simple derivation of the free energy and expectation values of Polyakov-loops in $QCD_2$ via path integral methods is given. In the chosen gauge (which can be generalized to 4 dimensions) without Gribov-copies the Fadeev-Popov determinant…
We consider minimally supersymmetric Yang-Mills theory with a Chern-Simons term on a flat spatial two-torus in the limit when the torus becomes small. The zero-modes of the fields then decouple from the non-zero modes and give rise to a…
Consider the massless Dirac operator on a 3-torus equipped with Euclidean metric and standard spin structure. It is known that the eigenvalues can be calculated explicitly: the spectrum is symmetric about zero and zero itself is a double…
We analyse holographic field theory dual to Lovelock Chern-Simons AdS Gravity in higher dimensions using first order formalism. We first find asymptotic symmetries in the AdS sector showing that they consist of local translations, local…
Three-dimensional Dirac semimetals, a three-dimensional analogue of graphene, are unusual quantum materials with massless Dirac fermions, which can be further converted to Weyl fermions by breaking time reversal or inversion symmetry.…
We discuss the discrete as well as the continuous symmetry transformations for a three $(2+1)$-dimensional $(3D)$ combined system of the free Abelian 1-form and 2-form gauge theories within the framework of Becchi-Rouet-Stora-Tyutin (BRST)…
At the interface between two massless Dirac models with opposite helicity a paradoxical situation arises: A transversally impinging electron can seemingly neither be transmitted nor reflected, due to the locking between spin and momentum.…
We evaluate the eigenvalues of Dirac operator in the background of instanton-anti-instanton configuration (I-$\bar{{\rm I}}$), in a simple (1+0)-dimensional model, and find that quasi-zero-mode disappears for the closely localized…
We study the twist defects in the toric code model introduced by Bombin [Phys. Rev. Lett. 105, 030403 (2010)]. Using a generalized 2D Jordan-Wigner transformation, we show explicitly the twist defects carry unpaired Majorana zero modes. We…
The anomalous scaling behavior of the n-th order correlation functions ${\cal F}_n$ of the Kraichnan model of turbulent passive scalar advection is believed to be dominated by the homogeneous solutions (zero-modes) of the Kraichnan equation…