Deconfinement on $\mathbb R^2\times S^1_L\times S^1_{\beta}$ for all gauge groups and duality to double Coulomb Gas

TL;DR

This paper investigates the deconfinement transition in finite-temperature super Yang-Mills theories with various gauge groups, revealing a duality to a double Coulomb gas of topological objects and W-bosons, with potential for lattice studies.

Contribution

It introduces a duality between the gauge theory and a double Coulomb gas model for all gauge groups, extending previous work to a broader class of theories.

Findings

Identifies a deconfinement transition at low temperature regimes.

Establishes a duality to a Coulomb gas involving monopole-instantons and W-bosons.

Describes interactions including Aharonov-Bohm effects and charge attraction/repulsion.

Abstract

I study finite-temperature $\mathcal N=1$ super Yang-Mills for any gauge group $G=A_N, B_N, C_N, D_N, E_{6,7,8},F_4,G_2$, compactified from four dimensions on a torus, $\mathbb R^2\times S^1_L\times S^1_{\beta}$. I examine in particular the low temperature regime $L\ll\beta=1/T$, where $L$ is the length of the spatial circle with periodic boundary conditions and with anti-periodic boundary conditions for the adjoint gauginos along the thermal cycle $S^1_{\beta}$. For small such $L$ we are in a regime were semiclassical calculations can be performed and a transition occurs at $T_c$ much smaller than $1/NL$. The transition is mediated by the competition between non-perturbative objects including 'exotic' topological molecules: neutral and magnetic bions composed of BPS and KK monopole constituents, with $r=rank(G)$ different charges in the co-root lattice of the gauge group $G$, and the perturbative electrically charged W-bosons (along with their wino superpartners). I determine a duality to a double Coulomb gas of neutral and magnetic bions of different charges of their constituent monopole-instantons, and W-bosons of both scalar and electric charges. Aharanov-Bohm interactions exist between magnetic bions and W-bosons, and scalar charges of W-bosons and neutral bions attract like charges, as opposed to the magnetic and electric charges where like charges repel. It is hoped in the future that lattice studies of this Coulomb gas can be done as in [1] for all gauge groups. It is hoped that a dual lattice 'affine' XY model with symmetry breaking perturbations can also be found in future studies of general gauge group as done in [1] for $SU(2)$.