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We consider the contributions upto the $D^{10} \mathcal{R}^4$ terms in thelow momentum expansion of the two loop four graviton amplitude in maximalsupergravity that arise in the field theory limit of genus two modular graphfunctions that result from the low momentum expansion of the four gravitonamplitude in toroidally compactified type II string theory, using the worldlineformalism of the first quantized superparticle. The expression for the two loopsupergravity amplitude in the worldline formalism allows us to obtaincontributions from the individual graphs, unlike the expression for the sameamplitude obtained using unitarity cuts which only gives the total contributionfrom the sum of all the graphs. Our two loop analysis is field theoretic, anddoes not make explicit use of the genus two string amplitude.

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