Superstring limit of Yang-Mills theories

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 ${\Sigma }_2\times T_p^2$, where $T_p^2$ 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 $T_p^2$, 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.

arXiv comment1+11 pages, v2: minor corrections

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• Strolling along gauge theory vacua