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

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.
Document type :
Journal articles
Domain :

https://hal.archives-ouvertes.fr/hal-00639799
Contributor : Boris Pioline <>
Submitted on : Thursday, November 10, 2011 - 8:54:53 AM
Last modification on : Friday, January 4, 2019 - 5:32:28 PM

### Citation

Carlo Angelantonj, Ioannis Florakis, Boris Pioline. A new look at one-loop integrals in string theory. Communications in Number Theory and Physics, International Press, 2012, 6, pp.159 - 201. ⟨10.4310/CNTP.2012.v6.n1.a4⟩. ⟨hal-00639799⟩

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