The One-Loop Five-Graviton Amplitude and the Effective Action

TL;DR

This paper analyzes the one-loop five-graviton amplitude in type II string theory, deriving the structure of low-energy effective action terms and revealing specific coefficient relations and absence of certain higher-order terms.

Contribution

It provides the first detailed low-energy expansion of the one-loop five-graviton amplitude in light-cone gauge, identifying the structure and coefficients of D^4R^5 terms and confirming the absence of R^5 and D^2R^5 terms.

Findings

Absence of one-loop R^5 and D^2R^5 terms.

Exact structure and coefficient of D^4R^5 terms.

Coefficient of D^4R^5 matches that of D^6R^4.

Abstract

We consider the one-loop five-graviton amplitude in type II string theory calculated in the light-cone gauge. Although it is not possible to explicitly evaluate the integrals over the positions of the vertex operators, a low-energy expansion can be obtained, which can then be used to infer terms in the low-energy effective action. After subtracting diagrams due to known D^{2n}R^4 terms, we show the absence of one-loop R^5 and D^2R^5 terms and determine the exact structure of the one-loop D^4R^5 terms where, interestingly, the coefficient in front of the D^4R^5 terms is identical to the coefficient in front of the D^6R^4 term. Finally, we show that, up to D^6R^4 ~ D^4R^5, the \epsilon_{10} terms package together with the t_8 terms in the usual combination (t_8t_8\pm{1/8}\epsilon_{10}\epsilon_{10}).