Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Redeeming Bad Theories

Itamar Yaakov

TL;DR

We address the problem of describing IR fixed points of 3d $\mathcal{N}=4$ gauge theories at zero Chern-Simons level in the presence of a 'bad' monopole spectrum, proposing a Seiberg-like dual where the interacting sector is dual to a $U(N_f-N_c)$ theory with $N_f$ flavors and a decoupled free hypermultiplet sector consisting of $2N_c-N_f$ hypermultiplets. The authors test the proposal with global-symmetry matching, moduli-space structure, and a regularized squashed-$S^3$ partition function computed via localization and hyperbolic gamma integrals, showing partition-function equality under analytic continuation of IR R-charges. They further develop a controlled procedure to integrate out flavors in the matrix model, demonstrating vacuum matching between original and dual theories and interpreting an ambiguous prefactor as the decoupled free sector. These results provide a practical handle on IR observables such as entanglement entropy and supersymmetric Wilson loops in bad theories, and pave the way for broader checks and generalizations of 3d Seiberg-like dualities.

Abstract

We give a Seiberg-like dual description of the interacting superconformal infrared fixed point of $\mathcal{N}=4$ gauge theory in three dimensions with vanishing Chern Simons level and $N_c\le N_f<2N_c$ fundamental flavors. These theories are known as "bad" theories due to the existence of unitarity violating monopole operators. We show that, in a dual description, all such operators are realized by free fields and the remainder theory is the Seiberg-like dual previously identified using the type IIB brane construction.

Redeeming Bad Theories

TL;DR

We address the problem of describing IR fixed points of 3d gauge theories at zero Chern-Simons level in the presence of a 'bad' monopole spectrum, proposing a Seiberg-like dual where the interacting sector is dual to a theory with flavors and a decoupled free hypermultiplet sector consisting of hypermultiplets. The authors test the proposal with global-symmetry matching, moduli-space structure, and a regularized squashed- partition function computed via localization and hyperbolic gamma integrals, showing partition-function equality under analytic continuation of IR R-charges. They further develop a controlled procedure to integrate out flavors in the matrix model, demonstrating vacuum matching between original and dual theories and interpreting an ambiguous prefactor as the decoupled free sector. These results provide a practical handle on IR observables such as entanglement entropy and supersymmetric Wilson loops in bad theories, and pave the way for broader checks and generalizations of 3d Seiberg-like dualities.

Abstract

We give a Seiberg-like dual description of the interacting superconformal infrared fixed point of gauge theory in three dimensions with vanishing Chern Simons level and fundamental flavors. These theories are known as "bad" theories due to the existence of unitarity violating monopole operators. We show that, in a dual description, all such operators are realized by free fields and the remainder theory is the Seiberg-like dual previously identified using the type IIB brane construction.

Paper Structure

This paper contains 13 sections, 40 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Proposal and preliminary checks
  3. A Seiberg-like duality
  4. Global symmetries
  5. Moduli space
  6. Flowing from "ugly" to "bad"
  7. The $S_{b}^{3}$ partition function
  8. The matrix model
  9. Seiberg-like duality
  10. Integrating out flavors
  11. Matching
  12. Interpretation
  13. Discussion and conclusions

Figures (1)

  • Figure 1: Brane manipulations in type IIB string theory which yield a possible Seiberg-like dual Hanany:1996ie. Solid vertical lines are NS5 branes. Horizontal lines are coincident D3 branes. Dashed lines are D5 branes. The legend indicates the compactification direction (t or $x_{6}$) and the directions of possible triplet mass (m) terms (3,4,5), and possible triplet FI (w) terms (7 8 9). Directions (0 1 2) are common to the world volume of all branes and are suppressed. We first move $N_{f}$ D5 branes through the right NS5 brane, creating $N_{f}$ D3 branes in the process. We then exchange the two NS5 branes, changing the number of suspended D3 branes in the interval.