Journal of High Energy Physics

, Volume 2015, Issue 12, pp 1–22 | Cite as

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

Open Access
Regular Article - Theoretical Physics

Abstract

We analyze the pertubative contributions to the \( {D}^4{\mathrm{\mathcal{R}}}^4 \) and \( {D}^6{\mathrm{\mathcal{R}}}^4 \) couplings in the low-energy effective action of type II string theory compactified on a torus Td, 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 \( {D}^6{\mathrm{\mathcal{R}}}^4 \) contribution also probe essential properties of the Kawazumi-Zhang invariant.

Keywords

Superstrings and Heterotic Strings Supersymmetry and Duality String Duality 

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Copyright information

© The Author(s) 2015

Authors and Affiliations

  1. 1.CERN PH-TH, Case C01600, CERNGeneva 23Switzerland
  2. 2.Sorbonne Universités, UPMC Université Paris 6, UMR 7589ParisFrance
  3. 3.Laboratoire de Physique Théorique et Hautes Energies, CNRS UMR 7589Université Pierre et Marie CurieParis cedex 05France
  4. 4.Centre for Research in String Theory, School of Physics and AstronomyQueen Mary University of LondonLondonU.K.

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