String theory integrands and supergravity divergences

TL;DR

This paper analyzes how string theory integrands relate to supergravity divergences, revealing the role of UV divergences and string interactions in the low-energy effective action and clarifying the appearance of odd zeta values.

Contribution

It determines the dependence of higher-derivative interaction coefficients on the cutoff and links logarithmic terms to supergravity UV divergences, enhancing understanding of string and supergravity interplay.

Findings

Logarithmic terms relate to supergravity UV divergences and string interactions.

The boundary behavior of integrands explains odd zeta values in expansions.

Low-energy string amplitudes reflect non-analytic terms tied to divergences.

Abstract

At low energies, interactions of massless particles in type II strings compactified on a torus $T^d$ are described by an effective Wilsonian action $\mathcal{S}(\Lambda)$, consisting of the usual supergravity Lagrangian supplemented by an infinite series of higher-derivative vertices, including the much studied $\nabla^{4p+6q} \mathcal{R}^4$ gravitational interactions. Using recent results on the asymptotics of the integrands governing four-graviton scattering at genus one and two, I determine the $\Lambda$-dependence of the coefficient of the above interaction, and show that the logarithmic terms appearing in the limit $\Lambda\to 0$ are related to UV divergences in supergravity amplitudes, augmented by stringy interactions. This provides a strong consistency check on the expansion of the integrand near the boundaries of moduli space, in particular it elucidates the appearance of odd zeta values in these expansions. I briefly discuss how these logarithms are reflected in non-analytic terms in the low energy expansion of the string scattering amplitude.