A new look at one-loop integrals in string theory

作者：Angelantonj Carlo^*; Florakis Ioannis; Pioline Boris

来源：Communications in Number Theory and Physics, 2012, 6(1): 159-201.

We revisit the evaluation of one-loop modular integrals in string theory, employing new methods that, unlike the traditional %26apos;orbit method%26apos;, 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 infrared. Furthermore, we introduce new techniques in the case where %26quot;unphysical tachyons%26quot; contribute to the one-loop couplings. These methods can be viewed as a modular invariant version of dimensional regularization. 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.

• 出版日期2012