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Evidence for a Non-Supersymmetric 5d CFT from Deformations of 5d $SU(2)$ SYM

Pietro Benetti Genolini, Masazumi Honda, Hee-Cheol Kim, David Tong, Cumrun Vafa

TL;DR

Addresses whether non-supersymmetric, interacting fixed points can arise from SUSY-breaking deformations of the 5d E1 fixed point (UV completion of SU(2) N=1 SYM). Uses background U(1) Chern-Simons terms and anomaly inflow arguments to classify phases and locate a strong-coupling phase transition. Finds that the CS levels jump across quadrants in the deformation parameter space and, at h=0 with tilde m≠0, massless modes emerge carrying charges of both U(1)_R and U(1)_I, consistent with a non-supersymmetric fixed point in 4+1 dimensions. Suggests that these massless non-perturbative states hint at a genuine interacting 5d CFT and proposes bootstrap and anomaly-based avenues for further verification.

Abstract

We study supersymmetry breaking deformations of the $\mathcal{N}=1$ 5d fixed point known as $E_1$, the UV completion of $SU(2)$ super-Yang-Mills. The phases of the non-supersymmetric theory can be characterized by Chern-Simons terms involving background $U(1)$ gauge fields, allowing us to identify a phase transition at strong coupling. We propose that this may signify the emergence of a non-trivial, non-supersymmetric CFT in $d=4+1$ dimensions.

Evidence for a Non-Supersymmetric 5d CFT from Deformations of 5d $SU(2)$ SYM

TL;DR

Addresses whether non-supersymmetric, interacting fixed points can arise from SUSY-breaking deformations of the 5d E1 fixed point (UV completion of SU(2) N=1 SYM). Uses background U(1) Chern-Simons terms and anomaly inflow arguments to classify phases and locate a strong-coupling phase transition. Finds that the CS levels jump across quadrants in the deformation parameter space and, at h=0 with tilde m≠0, massless modes emerge carrying charges of both U(1)_R and U(1)_I, consistent with a non-supersymmetric fixed point in 4+1 dimensions. Suggests that these massless non-perturbative states hint at a genuine interacting 5d CFT and proposes bootstrap and anomaly-based avenues for further verification.

Abstract

We study supersymmetry breaking deformations of the 5d fixed point known as , the UV completion of super-Yang-Mills. The phases of the non-supersymmetric theory can be characterized by Chern-Simons terms involving background gauge fields, allowing us to identify a phase transition at strong coupling. We propose that this may signify the emergence of a non-trivial, non-supersymmetric CFT in dimensions.

Paper Structure

This paper contains 6 sections, 42 equations, 2 figures.

Table of Contents

  1. Introduction
  2. The E1 Critical Point
  3. Breaking Supersymmetry
  4. Topological Phases
  5. Appendix: Majorana Spinors and Zero Modes
  6. An Alternative Non-Supersymmetric Deformation

Figures (2)

  • Figure 1: Brane configurations corresponding to the pure $SU(2)$ gauge theory on the Coulomb branch. Horizontal lines represent D5-branes and vertical lines NS5-branes. A fundamental string stretched between D5-branes corresponds to a W-boson in the field theory on the left-diagram, while it appears as an instanton of the dual $\widehat{SU(2)}$ gauge theory on the right. The supersymmetric CFT arises when the rectangle shrinks to a point.
  • Figure 2: Phase diagram for 5d $SU(2)$ SYM; the subscripts denote the levels $(k_I,k_R)$ of the background Chern--Simons terms. The dark blue point at the origin is the strongly-coupled UV fixed point with enhanced global symmetry. Turning on relevant deformations triggers RG flows with different endpoints which, at weak coupling, coincide with pure Yang--Mills. (Strictly speaking, the labels YM and SYM tell us about the physics close to the fixed point; the fixed point itself is free.) The $\mathbb{Z}_2\times \mathbb{Z}_2$ symmetry of the diagram is due to the "UV duality."