# Supergravity limit of genus two modular graph functions in the worldline formalism

## TL;DR

This paper analyzes two-loop supergravity amplitudes up to D^{10} R^4 terms using the worldline formalism, providing detailed graph contributions without relying on explicit genus two string amplitude calculations.

## Contribution

It introduces a field-theoretic approach to compute individual graph contributions in two-loop supergravity, bypassing the need for explicit genus two string amplitude data.

## Key findings

- Derived explicit contributions from individual graphs in the two-loop supergravity amplitude.
- Connected low momentum expansion of string theory to supergravity via the worldline formalism.
- Enhanced understanding of the structure of two-loop amplitudes in supergravity.

## Abstract

We consider the contributions upto the $D^{10} \mathcal{R}^4$ terms in the low momentum expansion of the two loop four graviton amplitude in maximal supergravity that arise in the field theory limit of genus two modular graph functions that result from the low momentum expansion of the four graviton amplitude in toroidally compactified type II string theory, using the worldline formalism of the first quantized superparticle. The expression for the two loop supergravity amplitude in the worldline formalism allows us to obtain contributions from the individual graphs, unlike the expression for the same amplitude obtained using unitarity cuts which only gives the total contribution from the sum of all the graphs. Our two loop analysis is field theoretic, and does not make explicit use of the genus two string amplitude.