2011/10/24 by Carlo Angelantonj, Angelantonj, Carlo, Ioannis Florakis +3
Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Number Theory (math.NT) #hep-th #math.NT
paper · pdf · doi:10.48550/arxiv.1110.5318
32 pages. V2: refs added, misprints corrected, in section 4 explicit expressions for integrals with non trivial Hecke operators given
arxiv created 2011/11/09 · arxiv updated 2011/11/10
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.