Superstring limit of Yang-Mills theories

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• 作者：Olaf Lechtenfeld^a ; ^b ; ^{lechtenf@itp.uni-hannover.de" class="auth_mail" title="E-mail the corresponding author} ; Alexander D. Popov^a ; ^b ; ^{popov@itp.uni-hannover.de" class="auth_mail" title="E-mail the corresponding author}
• 刊名：Physics Letters B
• 出版年：2016
• 出版时间：10 November 2016
• 年：2016
• 卷：762
• 期：Complete
• 页码：309-314
• 全文大小：326 K

文摘

It was pointed out by Shifman and Yung that the critical superstring on X¹⁰=R⁴×Y⁶$X^{10}={\mathbb{R}}^4\times Y^6$, where Y⁶$Y^6$ is the resolved conifold, appears as an effective theory for a U(2) Yang–Mills–Higgs system with four fundamental Higgs scalars defined on Σ₂×R²${\mathrm{\Sigma }}_2\times {\mathbb{R}}^2$, where Σ₂${\mathrm{\Sigma }}_2$ is a two-dimensional Lorentzian manifold. Their Yang–Mills model supports semilocal vortices on R²⊂Σ₂×R²${\mathbb{R}}^2\subset {\mathrm{\Sigma }}_2\times {\mathbb{R}}^2$ with a moduli space X¹⁰$X^{10}$. When the moduli of slowly moving thin vortices depend on the coordinates of Σ₂${\mathrm{\Sigma }}_2$, 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 ${\mathrm{\Sigma }}_2\times T_p^2$, 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.