Topological zero modes at nonzero chemical potential

Abstract

We give analytical and numerical solutions for the zero modes of the Dirac operator in topological SU(2) gauge backgrounds at nonzero chemical potential. Continuation from imaginary to real chemical potential is used to systematically derive analytical zero modes for calorons at arbitrary holonomy and, in particular limits, for instantons and dyons (magnetic monopoles). For the latter a spherical ansatz is explored as well. All the zero mode exhibit stronger peaks at the core and negative regions in their densities. We discuss the structure of the corresponding overlap matrix elements. For discretized calorons on the lattice we consider the staggered operator and show that it does possess (quartet quasi-)zero modes, whose eigenmodes agree very well with the continuum profiles, also for nonzero chemical potential.

Instanton-dyon liquid model. III. Finite chemical potential

“…For µ = 0, we recover the zero modes in [2,11]. We have checked that the periodic M-dyon zero modes are in agreement with those obtained in [23]. The restriction to the lowest Matsubara frequencies makes the mean-field analysis to follow reliable in the range µ/3ω 0 < 1 and for temperatures in the range of the critical temperature.…”

Phases of circle-compactified QCD with adjoint fermions at finite density

“…9 For the index theorem at finite µ, see Refs. [29,40,61]. 10 The fermionic zero modes of monopoles are absent if one starts from a genuine compact U(1) theory rather than breaking a non-Abelian group with a Higgs mechanism.…”

“…It should be noted that S 1 in this paper is a compactified spatial direction along which fermions obey the periodic boundary condition (PBC); the imaginary-time direction is infinite and the system is at zero temperature. This setup must not be confused with previous studies of a holonomy potential for thermal S 1 at µ ≠ 0 [26][27][28][29][30].…”

Electric charge catalysis by magnetic fields and a nontrivial holonomy

“…1 Theories such as softly broken SYM, and QCD(adj) in confined phase, are believed to be continuously connected to their non-supersymmetric counterpart. 2 Because of self-duality E E E = B B B, these monopoles are sometimes referred to as dyons [13,14,20,15]. This name is however somewhat misleading because these objects do not interact with the A 0 field like an electrically charged particle would (see discussions in [10,21] as well as in the original reference [7]).…”