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Classical integrability and quantum aspects of the AdS 3 × S 3 × S 3 × S 1 superstring

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Abstract

In this paper we continue the investigation of aspects of integrability of the type IIA AdS 3 × S 3 × S 3 × S 1 and AdS 3 × S 3 × T 4 superstrings. By constructing a one parameter family of flat connections we prove that the Green-Schwarz string is classically integrable, at least to quadratic order in fermions, without fixing the kappa-symmetry. We then compare the quantum dispersion relation, fixed by integrability up to an unknown interpolating function h(λ), to explicit one-loop calculations on the string worldsheet. For AdS 3 × S 3 × S 3 × S 1 the spectrum contains heavy, as well as light and massless modes, and we find that the one-loop contribution differs depending on how we treat these modes showing that similar regularization ambiguities as appeared in AdS4/CFT3 occur also here.

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  1. The Laboratory for Quantum Gravity & Strings, Department of Mathematics and Applied Mathematics, University of Cape Town, Private Bag, Rondebosch, 7700, South Africa

    Per Sundin

  2. George P. & Cynthia Woods Mitchell Institute for Fundamental Physics and Astronomy, Texas A&M University, College Station, TX, 77843, U.S.A

    Linus Wulff

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  1. Per Sundin
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ArXiv ePrint: 1207.5531

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Sundin, P., Wulff, L. Classical integrability and quantum aspects of the AdS 3 × S 3 × S 3 × S 1 superstring. J. High Energ. Phys. 2012, 109 (2012). https://doi.org/10.1007/JHEP10(2012)109

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