From Exact Results to Gauge Dynamics on ${\mathbb{R}}^3\times S^1$

Abstract

We revisit the vacuum structure of the $\mathcal{N}=1$ Intriligator-Seiberg-Shenker model on ${\mathbb{R}}^3\times S^1$. Guided by the Cardy-like asymptotics of its Romelsberger index, and building on earlier semi-classical results by Poppitz and Ünsal, we argue that previously overlooked non-perturbative effects generate a Higgs-type potential on the classical Coulomb branch of the low-energy effective 3d $\mathcal{N}=2$ theory. In particular, on part of the Coulomb branch we encounter the first instance of a dynamically-generated quintic monopole superpotential.

arXiv commentv3: Major revision with a more cogent presentation and several clarifications added. Mention of a preliminary investigation indicating a potential mismatch between the index perspective and the semi-classical approach in the case of the BCI model removed, as we now deem that investigation too crude. 20 pages, 2 figures

References in corpus (31)

• Reading between the lines of four-dimensional gauge theories
• Counting chiral primaries in N=1 d=4 superconformal field theories
• Aspects of N=2 Supersymmetric Gauge Theories in Three Dimensions
• Periodic Instantons with non-trivial Holonomy
• 3d dualities from 4d dualities
• Monopoles and Instantons on Partially Compactified D-Branes
• Cardy Formulae for SUSY Theories in d=4 and d=6
• Aspects of 3d N=2 Chern-Simons-Matter Theories
• Localization on Hopf surfaces
• Proposal for a Simple Model of Dynamical SUSY Breaking
• An Elliptic Superpotential for Softly Broken N=4 Supersymmetric Yang-Mills Theory
• Index theorem for topological excitations on R^3 * S^1 and Chern-Simons theory
• Instantons, Three-Dimensional Gauge Theory, and the Atiyah-Hitchin Manifold
• Chiral Duals of Non-Chiral SUSY Gauge Theories
• SUSY monopole potentials in 2+1 dimensions
• RG Fixed Points and Flows in SQCD with Adjoints
• High-temperature asymptotics of supersymmetric partition functions
• S-Duality and the Dyon Spectrum in N=2 Super Yang-Mills Theory
• Instanton Effects in Three-Dimensional Supersymmetric Gauge Theories with Matter
• Modular invariance on $S^1\times S^3$ and circle fibrations
• Cardy Formula for 4d SUSY Theories and Localization
• Chiral gauge dynamics and dynamical supersymmetry breaking
• Misleading Anomaly Matchings?
• IR Free or Interacting? A Proposed Diagnostic
• On the ISS model of dynamical SUSY breaking
• Chern-Simons and RG Flows: Contact with Dualities
• 3-manifold topology and the Donaldson-Witten partition function
• The character of the supersymmetric Casimir energy
• 't Hooft anomalies and the holomorphy of supersymmetric partition functions
• New 3d $\mathcal{N}=2$ Dualities from Quadratic Monopoles
• Branes, partition functions and quadratic monopole superpotentials

Cited by in corpus (4)

• EFT and the SUSY Index on the 2nd Sheet
• Decomposition of BPS Moduli Spaces and Asymptotics of Supersymmetric Partition Functions
• 3d SUSY enhancement and non-semisimple TQFTs from four dimensions
• Bridging 4D QFTs and 2D VOAs via 3D high-temperature EFTs