Superstring theories as low-energy limit of supergroup gauge theories

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.

13 pages, v2: a paragraph and 4 refs. added

References in corpus (3)

• Negative Branes, Supergroups and the Signature of Spacetime
• Non-Abelian Vortex in Four Dimensions as a Critical String on a Conifold
• Studying Critical String Emerging from Non-Abelian Vortex in Four Dimensions

Cited by in corpus (1)

• Superstring limit of Yang-Mills theories