Rankin-Selberg methods for closed strings on orbifolds

Abstract : In recent work we have developed a new unfolding method for computing one-loop modular integrals in string theory involving the Narain partition function and, possibly, a weak almost holomorphic elliptic genus. Unlike the traditional approach, the Narain lattice does not play any role in the unfolding procedure, T-duality is kept manifest at all steps, a choice of Weyl chamber is not required and the analytic structure of the amplitude is transparent. In the present paper, we generalise this procedure to the case of Abelian Z_N orbifolds, where the integrand decomposes into a sum of orbifold blocks that can be organised into orbits of the Hecke congruence subgroup {\Gamma}_0(N). As a result, the original modular integral reduces to an integral over the fundamental domain of {\Gamma}_0(N), which we then evaluate by extending our previous techniques. Our method is applicable, for instance, to the evaluation of one-loop corrections to BPS-saturated couplings in the low energy effective action of closed string models, of quantum corrections to the Kähler metric and, in principle, of the free-energy of superstring vacua.
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Contributor : Boris Pioline <>
Submitted on : Wednesday, April 17, 2013 - 8:00:23 AM
Last modification on : Sunday, March 31, 2019 - 1:31:09 AM

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Carlo Angelantonj, Ioannis Florakis, Boris Pioline. Rankin-Selberg methods for closed strings on orbifolds. Journal of High Energy Physics, Springer Verlag (Germany), 2013, 2013 (1037), pp.181. 〈10.1007/JHEP07(2013)181〉. 〈hal-00814356〉

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