The one-loop five-graviton amplitude and the effective action

We consider the one-loop five-graviton amplitude in type II string theory calculated in the light-cone gauge. Although it is not possible explicitly to 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 D2nR4 terms, we show the absence of one-loop R5 and D2R5 terms and determine the exact structure of the one-loop D4R5 terms where, interestingly, the coefficient in front of the D4R5 terms is identical to the coefficient in front of the D6R4 term. Finally, we show that, up to D6R4 ~ D4R5, the 10 terms package together with the t8 terms in the usual combination (t8t8 ± (1/8)1010).