Superstring limit of Yang-Mills theories

TL;DR

This paper explores how certain low-energy limits of pure Yang-Mills theories on specific 2D manifolds lead to moduli spaces that resemble superstring target spaces, connecting gauge theories with string theory.

Contribution

It extends previous work by showing that pure Yang-Mills theories on punctured tori can produce superstring target spaces via moduli of flat connections, without requiring Higgs fields.

Findings

Moduli spaces of flat connections on punctured tori can serve as superstring target spaces.

Superstring models can be derived from pure Yang-Mills theories without Higgs fields.

Different gauge groups yield various ten-dimensional superstring target spaces.

Abstract

It was pointed out by Shifman and Yung that the critical superstring on $X^{10}={\mathbb R}^4\times Y^6$, where $Y^6$ is the resolved conifold, appears as an effective theory for a U(2) Yang-Mills-Higgs system with four fundamental Higgs scalars defined on $\Sigma_2\times{\mathbb R}^2$, where $\Sigma_2$ is a two-dimensional Lorentzian manifold. Their Yang-Mills model supports semilocal vortices on ${\mathbb R}^2\subset\Sigma_2\times{\mathbb R}^2$ with a moduli space $X^{10}$. When the moduli of slowly moving thin vortices depend on the coordinates of $\Sigma_2$, the vortex strings can be identified with critical fundamental strings. We show that similar results can be obtained for the low-energy limit of pure Yang-Mills theory on $\Sigma_2\times T^2_p$, where $T^2_p$ is a two-dimensional torus with a puncture $p$. The solitonic vortices of Shifman and Yung then get replaced by flat connections. Various ten-dimensional superstring target spaces can be obtained as moduli spaces of flat connections on $T^2_p$, depending on the choice of the gauge group. The full Green-Schwarz sigma model requires extending the gauge group to a supergroup and augmenting the action with a topological term.