Low energy expansion of the four-particle genus-one amplitude in type II superstring theory
By M. Green, Jorge G. Russo, Pierre Vanhove. 2008
179 citations recorded by the source corpus.
A diagrammatic expansion of coefficients in the low-momentum expansion of the genus-one four-particle amplitude in type II superstring theory is developed. This is applied to determine coefficients up to order s6 R4 (where s is a Mandelstam invariant and R the linearized super-curvature), and partial results are obtained beyond that order. This involves integrating powers of the scalar propagator on a toroidal world-sheet, as well as integrating over the modulus of the torus. At any given order in s the coefficients of these terms are given by rational numbers multiplying multiple zeta values (or Euler-Zagier sums) that, up to the order studied here, reduce to products of Riemann zeta values. We are careful to disentangle the analytic pieces from logarithmic threshold terms, which involves a discussion of the conditions imposed by unitarity. We further consider the compactification of the amplitude on a circle of radius r, which results in a plethora of terms that are power-behaved in r. These coefficients provide boundary `data' that must be matched by any non-perturbative expression for the low-energy expansion of the four-graviton amplitude. The paper includes an appendix by Don Zagier.
Subfields: Applied Mathematics, Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/1315d881f61d387f4fc39f8161f9f10ae4c809ee
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In Applied Mathematics
In Atomic and Molecular Physics, and Optics
- Tim Adamo
- Eduardo Casali
- David Skinner
- Jorge G. Russo
- M. Green
- Pierre Vanhove
- F. Cachazo
- N. Berkovits
In Nuclear and High Energy Physics
Citations in the corpus
- Automorphic properties of low energy string amplitudes in various dimensions (2010, methodology): “Genus-one integrals in string theory In this appendix we evaluate the one-loop integrals arising in the derivative expansion of the genus-one four-graviton amplitude in 10− d dimensions, which was discussed in [4].”
- Ambitwistor strings and the scattering equations at one loop (2013, methodology): “It may be possible to make this connection already at the worldsheet level, perhaps using techniques introduced in [33] and extended in [34, 35].”