Dual infrared limits of 6d $\mathcal{N}$=(2,0) theory

Abstract

Compactifying type $A_{N-1}$ 6d $\mathcal{N}=(2,0)$ supersymmetric CFT on a product manifold $M^4\times {\Sigma }^2=M^3\times {\tilde{S}}^1\times S^1\times \mathcal{I}$ either over $S^1$ or over ${\tilde{S}}^1$ leads to maximally supersymmetric 5d gauge theories on $M^4\times \mathcal{I}$ or on $M^3\times {\Sigma }^2$, respectively. Choosing the radii of $S^1$ and ${\tilde{S}}^1$ inversely proportional to each other, these 5d gauge theories are dual to one another since their coupling constants $e^2$ and ${\tilde{e}}^2$ are proportional to those radii respectively. We consider their non-Abelian but non-supersymmetric extensions, i.e. SU($N$) Yang-Mills theories on $M^4\times \mathcal{I}$ and on $M^3\times {\Sigma }^2$, where $M^4\supset M^3={\mathbb{R}}_t\times T_p^2$ with time $t$ and a punctured 2-torus, and $\mathcal{I}\subset {\Sigma }^2$ is an interval. In the first case, shrinking $\mathcal{I}$ to a point reduces to Yang-Mills theory or to the Skyrme model on $M^4$, depending on the method chosen for the low-energy reduction. In the second case, scaling down the metric on $M^3$ 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 ${\Sigma }^2$, which can be reduced further to $A_{N-1}$ Toda theory.

1+10 pages; v2: minor corrections, one reference added

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Cited by in corpus (1)

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