Related papers: Weyl-Dirac zero-mode for calorons
We consider properties of zero and near-zero modes for overlap fermion operator in SU(2) lattice gluodynamics. The density of the states is of the order of Lambda(QCD) while the localization volume of the modes tends to zero in physical…
Quenched studies of a global U(1) symmetric Wilson-Yukawa model in two dimensions show no evidence of a charged fermion in the vortex phase at strong Wilson-Yukawa coupling while there is strong indication of a massive neutral fermion.…
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…
The color excitations of interacting fermions carrying an $SU(3)$ color and $U(N_f)$ flavor index in one spatial dimension are studied in the framework of a perturbed $SU(3)_{N_f}$ Wess-Zumino-Novikov-Witten model. Using Bethe ansatz…
In this paper we study massless fermions coupled to spherically symmetric $SU(N)$ monopoles without Yukawa couplings between the Higgs and fermion fields. The corresponding Dirac operator is not Fredholm and the associated eigenfunctions…
Zero modes of massive standard model fermions have been found on electroweak Z-strings. A zero mode solution for a massless left-handed neutrino is also known, but was thought to be non-normalizable. Here we show that although this mode is…
We study soliton solutions in supersymmetric scalar field theory with a class of potentials. We study both bosonic and fermionic zero-modes around the soliton solution. We study two possible couplings of gauge fields to these models. While…
We show how to generalize the previous result of the monopole condensation in SU(2) QCD to SU(3) QCD. We present the gauge independent Weyl symmetric Abelian decomposition of the SU(3) QCD which decomposes the gluons to the color neutral…
A self-consistent Ansatz for a new sphaleron of SU(3) Yang-Mills-Higgs theory is presented. With a single triplet of Weyl fermions added, there exists, most likely, one pair of fermion zero modes, which is known to give rise to the…
In this note we study fermionic zero modes in gauge and gravity backgrounds taking a two dimensional compact manifold $T^2$ as extra dimensions. The result is that there exist massless Dirac fermions which have normalizable zero modes under…
We study fermionic zero modes in the domain wall background. The fermions have Dirac and left- and right-handed Majorana mass terms. The source of the Dirac mass term is the coupling to a scalar field $\Phi$. The source of the Majorana mass…
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 present the detailed derivation of the charge one periodic instantons - or calorons - with non-trivial holonomy for SU(2). We use a suitable combination of the Nahm transformation and ADHM techniques. Our results rely on our ability to…
In this work we consider fermionic zero modes in the external scalar and electromagnetic field forming the vortex on a sphere. We find the correspondence between the equations for the fermions in different dimensions, find their explicit…
We consider fermions in a zero-temperature superconducting anti-de Sitter domain wall solution and find continuous bands of normal modes. These bands can be either partially filled or totally empty and gapped. We present a semi-classical…
Fermion zero modes for abelian BPS monopoles are considered. In the spherically symmetric case the normalisable zero modes are determined for arbitrary monopole charge N. If N>1 the zero modes are zero along $N-1$ half-lines emanating from…
In presence of string solitons, index theorems for the generalised Dirac operators have to be revisited. We show that in supersymmetric configurations the fermionic operators decouple, so that there are no mixing effects between different…
We characterise a class of SU(2) gluonic field configurations in the modified axial gauge where a zero mode component vanishes at some space point but the global Haar measure remains non-zero. The consequence of this is that gluonic…
Motivated by the recent Kitaev's K-theory analysis of topological insulators and superconductors, we adopt the same framework to study the topological phase structure of Jackiw-Rebbi model in 3+1 dimensions. According to the K-theory…
The adjoint 2-dimensional $QCD$ with the gauge group $SU(N)/Z_N$ admits topologically nontrivial gauge field configurations associated with nontrivial $\pi_1[SU(N)/Z_N] = Z_N$. The topological sectors are labelled by an integer $k=0,\ldots,…