Duality walls and defects in 5d N=1 theories

TL;DR

This work constructs explicit duality walls for 5d N=1 gauge theories to capture UV symmetry enhancement in the IR, encoding Weyl reflections via Lagrangian 4d interfaces and Seiberg dualities. The authors validate the proposal through localization-based instanton partition-function identities, hemisphere/sphere index tests, and detailed Wilson loop analyses, revealing integral transform structures (elliptic Fourier transforms) as the action of walls on protected observables. They extend the framework to SQCD with flavors, linear quivers, and exceptional SU(2) cases, and further explore dualities between Sp(N) and exotic SU(N+1) theories, including codimension-2 defects and 2d-4d couplings. The results provide a coherent picture in which duality walls implement UV symmetry operations, constrain defect/operator behavior, and suggest a rich web of interrelated dualities across 5d gauge theories and their UV completions.

Abstract

We propose an explicit description of duality walls which encode at low energy the global symmetry enhancement expected in the UV completion of certain five-dimensional gauge theories. The proposal is supported by explicit localization computations and implies that the instanton partition function of these theories satisfies novel and unexpected integral equations.

Figures (16)

• Figure 1: The fivebrane web which engineers the UV completion of pure $SU(N)_N$ gauge theory. The gauge theory is supported on the bundle of $N$ parallel D5 branes. After removing the centre of mass, the only non-normalizable deformation is the separation $m$ between the NS5 branes
• Figure 2: Our schematic depiction of the duality wall. We denote 5d gauge groups on the two sides of an interface as open circles and the bi-fundamental matter as an arrow between them. The extra baryonic coupling is denoted as a black dot over the arrow.
• Figure 3: A schematic depiction of the composition of two duality walls. The resulting 4d $SU(N)$ gauge theory has $N$ flavors and at low energy it glues the two 5d gauge groups together.
• Figure 4: A schematic depiction of the duality-covariant interface $I_{N,M}$. We include a superpotential coupling for the closed loop of three arrows.
• Figure 5: The Seiberg duality transformation which implies the duality-covariance of $I_{N,M}$.