Thermodynamics of SU(2) $$ \mathcal{N} $$ =2 supersymmetric Yang-Mills theory

Abstract

The thermodynamics of four-dimensional SU (2) N = 2 super-Yang-Mills theory is examined in both high and low temperature regimes. At low temperatures, compelling evidence is found for two distinct equilibrium states related by a spontaneously broken discrete R-symmetry. These equilibrium states exist because the quantum moduli space of the theory has two singular points where extra massless states appear. At high temperature, a unique R-symmetry-preserving equilibrium state is found. Discrepancies with previous results in the literature are explained. Contents 1 To obtain a Minkowski space Lagrange density, L (Mink.) , from the Euclidean version, one performs the rotation x 0 = −ix 0 E and identifies L (Mink.) = −L (Eucl.) .7 Here a is understood to mean a . Future usage should be clear from context.

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

“…the behavior of the theory; see the finite-T study of N = 2 SYM theory [42]. Here, however, there is a more interesting story to tell, thanks to the existence of nonperturbative saddle points to the Yang-Mills equations, which lift the Coulomb branch of N = 1 SYM theory.…”

“…At T > 0, supersymmetry is broken by the boundary conditions on S 1 β and we expect that the potentials (3.28) will receive T -dependent contributions. Our goal is not a full calculation of the finite-T loop corrections to (3.24) (see [42] for a calculation in Seiberg-Witten theory, where the finite-T contributions are the leading ones lifting the moduli space and are thus crucial), but rather an estimate of these corrections. The one-loop thermal correction to the potential 15 of φ, the second term in L φ ,β→∞ , has relative strength ∼ 16πT L g 2 compared to the term already present in the Lagrangian L φ ,β→∞ .…”

Microscopic structure of magnetic bions

“…where we use the notation of [20] for the Euclidean space quantities (throughout the rest of the paper all quantities are understood to be in Euclidean space).…”

“…However, one should keep the full expression of F 2 (r) in (3.21) and (3.25) if we want to avoid singularities at the locations of the monopoles. Using the change of variables x− x BPS = y, going to the spherical coordinates, and performing the integrations in the θ and φ coordinates we obtain: 19) where r = | x BPS − x KK |, and I(x) is given by: 20) where Li n (x) is defined by the infinite sum Li n (x) = ∞ k=1 x k k n . We can calculate I numerically to find that I → 2 as r L, as expected.…”

Searching for Fermi surfaces in super-QED

“…Ref. [44] studied N = 4 SYM theory with R-charge chemical potentials compactified on a 3-sphere, with a focus mostly on the high-T limit, while [45] studied the finite-T properties of N = 2 super-Yang-Mills (SYM) theory. Ref.…”