  We study finite-temperature N=1 SU(2) super Yang-Mills theory, compactified
on a spatial circle of size L with supersymmetric boundary conditions. In the
semiclassical 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) arXiv:1112.6389, 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 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 Z_2^{beta} thermal and 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 Z_2^{L}
remaining unbroken at the transition. Thus, the SYM transition appears similar
to the one in SU(2) QCD(adj) arXiv:1112.6389 and is also likely to be
characterized by continuously varying critical exponents.

High Energy Physics - Theory;Statistical Mechanics;High Energy Physics - Lattice;High Energy Physics - Phenomenology