A new look at one-loop integrals in string theory

Details A new look at one-loop integrals in string theory A new look at one-loop integrals in string theory

2011-10-24

arxiv.org/abs/1110.5318v2

Physics

High Energy Physics

High Energy Physics - Theory

32 pages. V2: refs added, misprints corrected, in section 4 explicit expressions for integrals with non trivial Hecke operator

Scientific paper

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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