Infrared divergences and harmonic anomalies in the two-loop superstring effective action

2015/10/08 by Boris Pioline, Rodolfo Russo · 1 citation
Physics and Astronomy · #hep-th

paper · pdf · doi:10.1007/jhep12(2015)102

23 pages

arxiv created 2015/10/08 · arxiv updated 2016/01/27

Abstract

We analyze the pertubative contributions to the D⁴ R⁴ and D⁶ R⁴ couplings in the low-energy effective action of type II string theory compactified on a torus T^d, with particular emphasis on two-loop corrections. In general, it is necessary to introduce an infrared cut-off Λ to separate local interactions from non-local effects due to the exchange of massless states. We identify the degenerations of the genus-two Riemann surface which are responsible for power-like dependence on Λ, and give an explicit prescription for extracting the Λ-independent effective couplings. These renormalized couplings are then shown to be eigenmodes of the Laplace operator with respect to the torus moduli, up to computable anomalous source terms arising in the presence of logarithmic divergences, in precise agreement with predictions from U-duality. Our results for the two-loop D⁶ R⁴ contribution also probe essential properties of the Kawazumi-Zhang invariant

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