Dual infrared limits of 6d N=(2,0) theory

Abstract

Compactifying type AN−1 6d N=(2,0) supersymmetric CFT on a product manifold M4×Σ2=M3×S˜1×S1×I either over S1 or over S˜1 leads to maximally supersymmetric 5d gauge theories on M4×I or on M3×Σ2, respectively. Choosing the radii of S1 and S˜1 inversely proportional to each other, these 5d gauge theories are dual to one another since their coupling constants e2 and e˜2 are proportional to those radii respectively. We consider their non-Abelian but non-supersymmetric extensions, i.e. SU(N) Yang–Mills theories on M4×I and on M3×Σ2, where M4⊃M3=Rt×Tp2 with time t and a punctured 2-torus, and I⊂Σ2 is an interval. In the first case, shrinking I to a point reduces to Yang–Mills theory or to the Skyrme model on M4, depending on the method chosen for the low-energy reduction. In the second case, scaling down the metric on M3 and employing the adiabatic method, we derive in the infrared limit a non-linear SU(N) sigma model with a baby-Skyrme-type term on Σ2, which can be reduced further to AN−1 Toda theory.