Exact Solutions of 2d Supersymmetric Gauge Theories

TL;DR

This work analyzes two-dimensional ${\mathcal N}=(0,2)$ SQCD with gauge groups ${\rm SU}(N_c)$ or ${\rm U}(N_c)$ and matter content in Fermi and chiral multiplets. By combining 't Hooft anomaly matching, RG flow, level-rank duality, and modular invariance, the authors derive an exact IR solution: left-moving affine symmetry ${\mathfrak H}$ pairs with a right-moving ${\mathcal N}=2$ Kazama-Suzuki coset, yielding a finite sum of tensor-product modules that describe the IR spectrum. They demonstrate concrete IR structures via the ${\mathcal T}_{222}$ case, revealing an ${\rm E}_6$ enhancement and an index matching to UV data, and generalize to quivers, where fixed points are labeled by cyclically identified $(N_1,\dots,N_m)$ with complex-structure-dependent cosets, validating the construction through index gluing. In addition, they perform DLCQ-based meson spectroscopy, finding a finite-density spectrum with massless flavor-singlets and a Veneziano-like large-$N_c$ regime that favors screening over confinement. Overall, the paper provides a comprehensive exact framework for the IR dynamics of 2d ${\mathcal N}=(0,2)$ gauge theories, uncovering a rich landscape of SCFTs with potential heterotic-phenomenology applications and AdS$_3$ dual descriptions.

Abstract

We study dynamics of two-dimensional non-abelian gauge theories with N=(0,2) supersymmetry that include N=(0,2) supersymmetric QCD and its generalizations. In particular, we present the phase diagram of N=(0,2) SQCD and determine its massive and low-energy spectrum. We find that the theory has no mass gap, a nearly constant distribution of massive states, and lots of massless states that in general flow to an interacting CFT. For a range of parameters where supersymmetry is not dynamically broken at low energies, we give a complete description of the low-energy physics in terms of 2d N=(0,2) SCFTs using anomaly matching and modular invariance. Our construction provides a vast landscape of new N=(0,2) SCFTs which, for small values of the central charge, could be used for building novel heterotic models with no moduli and, for large values of the central charge, could be dual to AdS_3 string vacua.

Figures (16)

• Figure 1: The field content of $(0,2)$ SQCD with ${\rm SU}(N_c)$ gauge group, $N_f$ (resp. $N_b$) Fermi (resp. chiral) multiplets in the fundamental representation, and $2N_c - N_b + N_f$ chiral multiplets in the anti-fundamental representation. A similar theory with ${\rm U}(N_c)$ gauge group requires two extra Fermi multiplets in the determinant representation to cancel the abelian gauge anomaly.
• Figure 2: The phase diagram of ${\rm U}(N_c)$$(0,2)$ SQCD as a function of $N_c$ and $N_f$ (with $N_b$ kept fixed).
• Figure 3: The quiver diagram of ${\mathcal{N}}=(0,2)$ SQCD with ${\rm U}(N_c)$ gauge group. The solid lines denote bi-fundamental chiral multiplets and dotted lines denote bi-fundamental Fermi multiplets. We have explicitly depicted the two Fermi multiplets in the determinant representation of the gauge group with wiggly lines.
• Figure 4: Phases of gauge theories related by triality. Their parameter spaces can be glued to each other as shown.
• Figure 5: The oriented triangle represents the ${\mathcal{N}}=(0,2)$ SCFT labeled by $(N_1,N_2,N_3)$ modulo cyclic permutations.