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Cyclic products of Szego kernels and spin structure sums. Part I. Hyper-elliptic formulation
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- D'Hoker, Eric (author)
- Univ Calif Los Angeles, Mani L Bhaumik Inst Theoret Phys, Dept Phys & Astron, Los Angeles, CA 90095 USA.
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- Hidding, Martijn (author)
- Uppsala universitet,Teoretisk fysik
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- Schlotterer, Oliver (author)
- Uppsala universitet,Teoretisk fysik
- Univ Calif Los Angeles, Mani L Bhaumik Inst Theoret Phys, Dept Phys & Astron, Los Angeles, CA 90095 USA Teoretisk fysik (creator_code:org_t)
- Springer Nature, 2023
- 2023
- English.
- In: Journal of High Energy Physics (JHEP). - : Springer Nature. - 1126-6708 .- 1029-8479. ; :5
- Journal article (peer-reviewed)
Abstract
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- The summation over spin structures, which is required to implement the GSO projection in the RNS formulation of superstring theories, often presents a significant impediment to the explicit evaluation of superstring amplitudes. In this paper we discover that, for Riemann surfaces of genus two and even spin structures, a collection of novel identities leads to a dramatic simplification of the spin structure sum. Explicit formulas for an arbitrary number of vertex points are obtained in two steps. First, we show that the spin structure dependence of a cyclic product of Szego kernels (i.e. Dirac propagators for worldsheet fermions) may be reduced to the spin structure dependence of the four-point function. Of particular importance are certain trilinear relations that we shall define and prove. In a second step, the known expressions for the genus-two even spin structure measure are used to perform the remaining spin structure sums. The dependence of the spin summand on the vertex points is reduced to simple building blocks that can already be identified from the two-point function. The hyper-elliptic formulation of genus-two Riemann surfaces is used to derive these results, and its SL(2, DOUBLE-STRUCK CAPITAL C) covariance is employed to organize the calculations and the structure of the final formulas. The translation of these results into the language of Riemann & thetasym;-functions, and applications to the evaluation of higher-point string amplitudes, are relegated to subsequent companion papers.
Subject headings
- NATURVETENSKAP -- Fysik -- Annan fysik (hsv//swe)
- NATURAL SCIENCES -- Physical Sciences -- Other Physics Topics (hsv//eng)
Keyword
- Conformal Field Models in String Theory
- Superstrings and Heterotic Strings
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- ref (subject category)
- art (subject category)
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