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

摘要

Compactifying typeAN?16dN=(2,0)supersymmetric CFT on a product manifoldM4×Σ2=M3×S?1×S1×Ieither overS1or overS?1leads to maximally supersymmetric 5d gauge theories onM4×Ior onM3×Σ2, respectively. Choosing the radii ofS1andS?1inversely proportional to each other, these 5d gauge theories are dual to one another since their coupling constantse2ande?2are proportional to those radii respectively. We consider their non-Abelian but non-supersymmetric extensions, i.e. SU(N) Yang–Mills theories onM4×Iand onM3×Σ2, whereM4?M3=Rt×Tp2with timetand a punctured 2-torus, andI?Σ2is an interval. In the first case, shrinkingIto a point reduces to Yang–Mills theory or to the Skyrme model onM4, depending on the method chosen for the low-energy reduction. In the second case, scaling down the metric onM3and employing the adiabatic method, we derive in the infrared limit a non-linear SU(N) sigma model with a baby-Skyrme-type term onΣ2, which can be reduced further toAN?1Toda theory.