We revisit the evaluation of one-loop modular integrals in string theory, employing new methods that, unlike the traditional 'orbit method', keep T-duality manifest throughout. In particular, we apply the Rankin-Selberg-Zagier approach to cases where the integrand function grows at most polynomially in the IR. Furthermore, we introduce new techniques in the case where `unphysical tachyons' contribute to the one-loop couplings. These methods can be viewed as a modular invariant version of dimensional regularisation. As an example, we treat one-loop BPS-saturated couplings involving the d-dimensional Narain lattice and the invariant Klein j-function, and relate them to (shifted) constrained Epstein Zeta series of O(d,d;Z). In particular, we recover the well-known results for d=2 in a few easy steps.

A new look at one-loop integrals in string theory

ANGELANTONJ, Carlo;
2012

Abstract

We revisit the evaluation of one-loop modular integrals in string theory, employing new methods that, unlike the traditional 'orbit method', keep T-duality manifest throughout. In particular, we apply the Rankin-Selberg-Zagier approach to cases where the integrand function grows at most polynomially in the IR. Furthermore, we introduce new techniques in the case where `unphysical tachyons' contribute to the one-loop couplings. These methods can be viewed as a modular invariant version of dimensional regularisation. As an example, we treat one-loop BPS-saturated couplings involving the d-dimensional Narain lattice and the invariant Klein j-function, and relate them to (shifted) constrained Epstein Zeta series of O(d,d;Z). In particular, we recover the well-known results for d=2 in a few easy steps.
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http://arxiv.org/abs/1110.5318
Carlo Angelantonj; Ioannis Florakis; Boris Pioline
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2318/119198
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