Zhang-Kawazumi invariants and superstring amplitudes
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Volume
144
Pagination
111 - 150
DOI
10.1016/j.jnt.2014.03.021
Journal
Journal of Number Theory
ISSN
0022-314X
Metadata
Show full item recordAbstract
The four-graviton amplitude in Type IIB superstring theory is invariant under the S-duality group SL(2,Z) acting on the complex coupling T. This amplitude contains a sum of effective interactions D2pR4 with coefficients that are modular functions of T whose form has been conjectured when p≤. 3. The weak coupling expansion of these coefficients can be calculated in superstring perturbation theory. We here show that the two-loop D6R4 term is proportional to the integral of an invariant introduced by Zhang and Kawazumi that is related to the Faltings invariant. The conjectured value of the two-loop superstring contribution to D6R4 leads us to a prediction for the integral of the Zhang-Kawazumi invariant over the moduli space of genus-two surfaces. We propose invariants corresponding to p>. 3, which generalize Zhang-Kawazumi invariants. © 2014.
Authors
D'Hoker, E; Green, MBCollections
- Physics and Astronomy [1280]