Superstring theories as low-energy limit of supergroup gauge theories

TL;DR

This paper demonstrates how supergroup gauge theories in certain limits can reproduce superstring actions, establishing a duality between gauge fields and superstrings, including for the AdS$_5$×S$^5$ background.

Contribution

It shows that superstring actions emerge as low-energy limits of supergroup gauge theories on specific manifolds, extending gauge-string duality.

Findings

Yang-Mills theory with super translation group flows to superstring action in the infrared limit.

The $d=5$ Chern-Simons term corresponds to the Wess-Zumino part of the superstring.

Duality is established for type IIB superstring on AdS$_5$×S$^5$ and supergroup gauge theory.

Abstract

We consider Yang-Mills theory with $N=2$ super translation group in $d=10$ auxiliary dimensions as the structure group. The gauge theory is defined on a direct product manifold $\Sigma_2\times H^2$, where $\Sigma_2$ is a two-dimensional Lorentzian manifold and $H^2$ is the open disc in $\mathbb{R}^2$ with the boundary $S^1=\partial H^2$. We show that in the adiabatic limit, when the metric on $H^2$ is scaled down, the Yang-Mills action supplemented by the $d=5$ Chern-Simons term becomes the Green-Schwarz superstring action. More concretely, the Yang-Mills action in the infrared limit flows to the kinetic part of the superstring action and the $d=5$ Chern-Simons action, defined on a 5-manifold with the boundary $\Sigma_2\times H^2$, flows to the Wess-Zumino part of the superstring action. The same kind of duality between gauge fields and strings is established for type IIB superstring on AdS$_5\times S^5$ background and a supergroup gauge theory with PSU(2,2$|$4) as the structure group.