RG Domain Walls and Hybrid Triangulations

TL;DR

This paper explores the construction and analysis of 3d domain walls in N=2 gauge theories derived from 6d SCFTs, focusing on their geometric and duality properties, including S-duality and RG flows, using triangulation-based quantization methods.

Contribution

It introduces a unified framework for constructing 3d domain walls associated with 4d dualities and RG flows, employing geometric parametrization and quantization of flat connections.

Findings

Constructed 3d theories representing domain walls in various duality frames.

Connected Janus domain walls to S-duality and RG flow phenomena.

Validated geometric models through field theory and quantum Teichmuller theory comparisons.

Abstract

This paper studies the interplay between the N=2 gauge theories in three and four dimensions that have a geometric description in terms of twisted compactification of the six-dimensional (2,0) SCFT. Our main goal is to construct the three-dimensional domain walls associated to any three-dimensional cobordism. We find that we can build a variety of 3d theories that represent the local degrees of freedom at a given domain wall in various 4d duality frames, including both UV S-dual frames and IR Seiberg-Witten electric-magnetic dual frames. We pay special attention to Janus domain walls, defined by four-dimensional Lagrangians with position-dependent couplings. If the couplings on either side of the wall are weak in different UV duality frames, Janus domain walls reduce to S-duality walls, i.e. domain walls that encode the properties of UV dualities. If the couplings on one side are weak in the IR and on the other weak in the UV, Janus domain walls reduce to RG walls, i.e. domain walls that encode the properties of RG flows. We derive the 3d geometries associated to both types of domain wall, and test their properties in simple examples, both through basic field-theoretic considerations and via comparison with quantum Teichmuller theory. Our main mathematical tool is a parametrization and quantization of framed flat SL(K) connections on these geometries based on ideal triangulations.