The Cat's Cradle: Deforming the higher rank $E_1$ and $\tilde{E}_1$ theories

TL;DR

This paper investigates the space of supersymmetric mass deformations in higher rank 5d $E_1$ and $ ilde{E}_1$ theories using 5-brane webs, revealing diverse IR phases and symmetry enhancements.

Contribution

It provides a detailed analysis of the deformation space and IR phases of higher rank $E_1$ and $ ilde{E}_1$ theories, highlighting differences between even and odd ranks and predicting symmetry enhancements.

Findings

Identification of IR free and interacting fixed point phases.

Discovery of rank-dependent differences in deformation spaces.

Prediction of symmetry enhancement in certain $SU(N)$ theories.

Abstract

We use 5-brane webs to study the two-dimensional space of supersymmetric mass deformations of higher rank generalizations of the 5d $E_1$ and $\tilde{E}_1$ theories. Some of the resulting IR phases are described by IR free supersymmetric gauge theories, while others correspond to interacting fixed points. The number of different phases appears to grow with the rank. The space of deformations is qualitatively different for the even and odd rank cases, but that of the even (odd) rank $E_1$ theory is similar to that of the odd (even) rank $\tilde{E}_1$ theory. One result of our analysis predicts that the supersymmetric $SU(N)$ theory with CS level $k=\frac{N}{2} + 4$ and a single massless antisymmetric hypermultiplet exhibits an enhanced global symmetry at the UV fixed point, given by $SU(2)\times SU(2)$ if $N$ is even, and $SU(2)\times U(1)$ if $N$ is odd.