Phase transitions and Wilson loops in antisymmetric representations in Chern–Simons-matter theory

Abstract

We study the phase transitions of three-dimensional N = 2 U (N ) Chern-Simons theory on S 3 with a varied number of massive fundamental hypermultiplets and with a Fayet-Iliopoulos parameter. We characterize the various phase diagrams in the decompactification limit, according to the number of different mass scales in the theory. For this, we extend the known solution of the saddle-point equations to the setting where the one cut solution is characterized by asymmetric intervals. We then study the large N limit of Wilson loops in antisymmetric representations, with the additional scaling corresponding to the variation of the size of the representation. We give explicit expressions, both with and without FI terms, and study 1/R corrections for the different phases. These corrections break the perimeter law behavior, as they introduce a scaling with the size of the representation. We show how the phase transitions of the Wilson loops can either be of first or second order and determine the underlying mechanism in terms of the eventual asymmetry of the support of the solution of the saddle-point equation, at the critical points. arXiv:1808.02855v2 [hep-th] 28 Aug 2018 7 Outlook 46 A Free energy second derivatives 47 A.0.1 ζ < m 1 with two mass scales 47 A.0.2 ζ < m 1 with one mass scale 47 A.0.3 ζ > m 1 with two mass scales 48 B Regions with no saddle point 48 B.0.1 Re (z) > 1 or Re (z) < −1 48 B.0.2 Re (z) around ±1

SQED3 and SQCD3 : Phase transitions and integrability

“…In turn, these seemingly simple representations, in general of the matrix model type, contain a wealth of information of different type. First, they are very useful for asymptotic analysis and, in suitable large N double scaling limits, have predicted phase transitions in the theory [3][4][5][6]. Secondly, in many cases, especially for three dimensional theories, they are amenable to exact analytical solutions, even for finite N [4,7].…”

“…See Fig. 1 for the match of expressions (5) and (6). The exact evaluation (3) of the partition function, or its equivalent representation as a conical function, relies on the hypothesis coshðmÞ ≥ 1, thus on reality of the mass.…”

Multiple phases in a generalized Gross-Witten-Wadia matrix model

“…In some unitary models the underlying mechanism triggering some phase transitions may be different. See for example a discussion in appendix (B.1) in [24].…”

Aspects of massive gauge theories on three sphere in infinite mass limit

“…The resolvent is determined from the analyticity and the one-cut solution of the resolvent is given by (A. 14) as…”

“…Then, we can approach the non-trivial dynamics triggered using these real mass parameter with the localization methods. In [4][5][6][7][8][9][10][11][12][13][14][15], the phase structure of mass-deformed gauge theories on S 3 is investigated.…”