4d/3d reduction of dualities with O6

TL;DR

This paper investigates the circle reduction of 4d dualities involving U(N) gauge theories with tensor matter and brane engineering, comparing brane, field theory, and localization results, and addressing convergence issues in 3d reductions.

Contribution

It provides a detailed analysis of 4d/3d dualities with O6 planes via brane T-duality, matching results from multiple approaches, and clarifies the conditions for successful 3d superconformal index reduction.

Findings

Precise agreement between brane, field theory, and localization results.

Identification of convergence issues in 3d superconformal index reduction.

Necessity of double scaling limit for consistent 3d partition functions.

Abstract

We consider $\mathrm{U}(N)$ gauge theories with a pair of two-index tensors interacting through a quartic superpotential, in addition to fundamentals and antifundamentals. The models have a brane engineering in terms of NS, D4, D6 branes and an O6 plane. Depending on the representation of the tensorial matter we have either an O6$^{+}$ plane, an O6$^{-}$ plane or a combined state of O6$^{+}$ and O6$^{-}$, with the addition of 8 semi-infinite half-D6 branes, where the last case realizes a chiral theory. The 4d IR duality is realized through an HW transition in the brane description. Here we study the circle reduction of these dualities from the brane perspective by T-dualizing along the compact direction. We then compare the results against the one obtained from field theoretical considerations and from localization, finding a precise agreement. When we consider the reduction of the 4d superconformal index to the 3d squashed three sphere partition function we observe that it is not always possible to obtain convergent 3d result with the standard reduction prescription, and that the double scaling limit is necessary.