Deconfinement in $ \mathcal{N}=1 $ super Yang-Mills theory on $ {{\mathbb{R}}^3}\times {{\mathbb{S}}^1} $ via dual-Coulomb gas and 'affine' XY-model

Autor: Erich Poppitz, Mohamed M. Anber, Seth Strimas-Mackey, Scott Collier, Brett Teeple
Rok vydání: 2013
Předmět:
Zdroj: Journal of High Energy Physics. 2013
ISSN: 1029-8479
DOI: 10.1007/jhep11(2013)142
Popis: We study finite-temperature $ \mathcal{N}=1 $ SU(2) super Yang-Mills theory, compactified on a spatial circle of size L with supersymmetric boundary conditions. In the semi-classical small-L regime, a deconfinement transition occurs at T c ≪ 1/L. The transition is due to a competition between non-perturbative topological “molecules” — magnetic and neutral bion-instantons — and electrically charged W -bosons and superpartners. Compared to deconfinement in non-supersymmetric QCD(adj) [1], the novelty is the relevance of the light modulus scalar field. It mediates interactions between neutral bions (and W -bosons), serves as an order parameter for the $ \mathbb{Z}_2^{(L) } $ center symmetry associated with the non-thermal circle, and explicitly breaks the electric-magnetic (Kramers-Wannier) duality enjoyed by non-supersymmetric QCD(adj) near T c . We show that deconfinement can be studied using an effective two-dimensional gas of electric and magnetic charges with (dual) Coulomb and Aharonov-Bohm interactions, or, equivalently, via an XY-spin model with a symmetry-breaking perturbation, where each system couples to the scalar field. To study the realization of the discrete R-symmetry and the $ \mathbb{Z}_2^{{\left( \beta \right)}} $ thermal and $ \mathbb{Z}_2^{(L) } $ non-thermal center symmetries, we perform Monte Carlo simulations of both systems. The dual-Coulomb gas simulations are a novel way to analyze deconfinement and provide a new venue to study the phase structure of a class of two-dimensional condensed matter models that can be mapped into dual-Coulomb gases. Our results indicate a continuous deconfinement transition, with $ \mathbb{Z}_2^{(L) } $ remaining unbroken at the transition. Thus, the SYM transition appears similar to the one in SU(2) QCD(adj) [1] and is also likely to be characterized by continuously varying critical exponents.
Databáze: OpenAIRE
Externí odkaz: