Related papers: Fermionic zero modes in self-dual vortex backgroun…
We study the propagation of massless fermionic fields in the background of a three-dimensional Lifshitz black hole, which is a solution of conformal gravity. The black hole solution is characterized by a null dynamical exponent. Then, we…
The response of isodoublet fermions to classical backgrounds of essentially 2-dimensional boson fields in SU(2) Yang-Mills-Higgs theory is investigated. In particular, the spectral flow of Dirac eigenvalues is calculated for a…
For the non-perturbative analysis of the topological content of Yang-Mills theories, it is essential to disentangle long-range structures from short-range fluctuations. Some time ago, one of us proposed to use the adjoint modes of the Dirac…
We propose the $2\pi$-periodic Aharonov-Bohm (AB) effect as a nonlocal probe of Majorana zero modes (MZMs) without the restriction of fermion parity. We demonstrate the enhancement of the AB effect, where the topological protection of MZMs…
We study non-Abelian solitons of the Bogomol'nyi type in N=2 (d=2+1) supersymmetric Chern-Simons (CS) and Yang-Mills (YM) theory with a generic gauge group. In CS theory, we find topological, non-topological and semi-local (non-)topological…
We study N=2 supersymmetric Chern-Simons Higgs models in $(2+1)$-dimensions. As we will demonstrate, an extended supersymmetric quantum mechanics algebras underlies the fermionic zero modes quantum system and the zero modes corresponding to…
We study free fermionic models that host Majorana zero modes using the Majorana orthogonal transformation, which is a type of transformation between different fermionic models under Majorana representation of complex fermions. Using…
We demonstrate that the number of fermionic zero modes of the static $2$-dimensional Dirac operator in the background of $SU(2)$ static gauge-Higgs field configurations is a topological invariant modulo four. Static configurations which are…
We show that for closed finite sized systems with an odd number of real fermionic modes, even in the presence of interactions, there are always at least two fermionic operators that commute with the Hamiltonian.There is a zero mode…
The dualities that map hard-to-solve, interacting theories to free, non-interacting ones often trigger a deeper understanding of the systems to which they apply. However, simplifying assumptions such as Lorentz invariance, low…
In 2+1 dimensions there exists a duality between a charged Dirac particle coupled minimally to a background vector potential and a neutral one coupled nonminimally to a background electromagnetic field strength. A constant uniform…
We study the relation between boundary conditions and categorical symmetries of two-dimensional fermionic conformal field theories. We determine all anomaly-free invertible global symmetries of two free complex Weyl fermions, which take the…
We show that the existence of a pair of zero-energy modes bound to a vortex carrying a pi-flux is a generic feature of the topologically non-trivial phase of the M-B model, which was introduced to describe the topological band insulator in…
We study a non-Hermitian (NH) $sl(2)$ affine Toda model coupled to fermions through soliton theory techniques and the realizations of the pseudo-chiral and pseudo-Hermitian symmetries. The interplay of non-Hermiticity, integrability,…
We demonstrate that the Higgs mechanism in three-dimensional topological superconductors exhibits unique features with experimentally observable consequences. The Higgs model we discuss has two superconducting components and an axion-like…
Fermion zero modes of Bogomol'nyi-Prasad-Sommerfield monopole-string-domain wall composites in three spatial dimensions are studied. We analytically solve the Dirac equation and prove the existence of one fermion zero mode. Depending on…
We study some consequences of dimensionally reducing systems with massless fermions and Abelian gauge fields from 3+1 to 2+1 dimensions. We first consider fermions in the presence of an external Abelian gauge field. In the reduced theory,…
We use canonical formalism to study the fermion determinant in different three dimensional abelian gauge field backgrounds that contain non-zero magnetic and electric flux in order to understand the non-perturbative contributions to the…
We find self-dual vortex solutions in a Maxwell-Chern-Simons model with anomalous magnetic moment. From a recently developed N=2-supersymmetric extension, we obtain the proper Bogomol'nyi equations together with a Higgs potential allowing…
The study of quantum mechanical bound states is as old as quantum theory itself. Yet, it took many years to realize that three-body borromean systems that are bound when any two-body subsystem is unbound are abundant in nature. Here we…