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Superstring theory on \(\text{AdS}_2\times S^2\) as a coset supermanifold. (English) Zbl 0951.81040

Summary: We quantize the superstring on the \(\text{AdS}_2\times S^2\) background with Ramond-Ramond flux using a PSU\((1,1|2)/U(1)\times U(1)\) sigma model with a WZ term. One-loop conformal invariance of the model is guaranteed by a general mechanism which holds for coset spaces \(G/H\) where \(G\) is Ricci-flat and \(H\) is the invariant locus of a \(\mathbb{Z}_4\) automorphism of \(G\). This mechanism gives conformal theories for the PSU\((1,1|2)\times\) PSU\((2|2)/\text{SU}(2)\times\text{SU}(2)\) and PSU\((2,2|4)/\text{SO}(4,1)\times\) SO(5) coset spaces, suggesting our results might be useful for quantizing the superstring on \(\text{AdS}_3\times S^3\) and \(\text{AdS}_5\times S^5\) backgrounds.

MSC:

81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
83E30 String and superstring theories in gravitational theory
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