On 6d N=(2,0) theory compactified on a Riemann surface with finite area

TL;DR

This paper investigates the compactification of 6d N=(2,0) SU(N) theory on Riemann surfaces with finite area, revealing how the zero-area limit leads to 4d theories with contracted symmetries and novel defect operator products.

Contribution

It provides a detailed analysis of the Higgs branch metric dependence on surface area and explains symmetry contraction and subgroup emergence in the 4d limit.

Findings

Higgs branch metric inversely proportional to surface area

Zero-area limit involves Wigner-Inonu contraction of symmetries

Defects have operator product expansions with 4d field theory coefficients

Abstract

We study 6d N=(2,0) theory of type SU(N) compactified on Riemann surfaces with finite area, including spheres with fewer than three punctures. The Higgs branch, whose metric is inversely proportional to the total area of the Riemann surface, is discussed in detail. We show that the zero-area limit, which gives us a genuine 4d theory, can involve a Wigner-Inonu contraction of global symmetries of the six-dimensional theory. We show how this explains why subgroups of SU(N) can appear as the gauge group in the 4d limit. As a by-product we suggest that half-BPS codimension-two defects in the six-dimensional (2,0) theory have an operator product expansion whose operator product coefficients are four-dimensional field theories.