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

Abstract : We analyze the pertubative contributions to the $D^4 R^4$ and $D^6 R^4$ 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 $\Lambda$ 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 $\Lambda$, and give an explicit prescription for extracting the $\Lambda$-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 $D^6 R^4$ contribution also probe essential properties of the Kawazumi-Zhang invariant.
Document type :
Journal articles

https://hal.archives-ouvertes.fr/hal-01214250
Contributor : Boris Pioline Connect in order to contact the contributor
Submitted on : Sunday, October 11, 2015 - 10:14:09 AM
Last modification on : Saturday, December 4, 2021 - 4:05:42 AM

### Citation

Boris Pioline, Rodolfo Russo. Infrared divergences and harmonic anomalies in the two-loop superstring effective action. Journal of High Energy Physics, Springer Verlag (Germany), In press, 1512, pp.102. ⟨10.1007/JHEP12(2015)102⟩. ⟨hal-01214250⟩

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