Construction of SL(2,Z) invariant amplitudes in type IIB superstring theory

Abstract

The construction of $SL(2,Z)$ invariant amplitudes that generalizethe Virasoro amplitude is investigated in detail. We describe a number of mathematical properties that characterize the simplest example, and present pieces of evidence that it represents the tree-level four-graviton scattering amplitude in membrane theory on ${\mathbf{R}}^9\times T^2$ in the limit that the torus area goes to zero. In particular, we show that the poles of the $S$-dual amplitude are in precise correspondence with the states of membrane theory that survive in the type IIB limit. These are shown to be the states that span the Cartan subspaces of area preserving diffeomorphisms of the 2-torus; all other states become infinitely massive, and membrane world-volume theory acquires the structure of a free theory.

new section on effective action, small corrections. 23 pages, harvmac

References in corpus (5)

• Effects of D-instantons
• One loop in eleven dimensions
• D-instantons, Strings and M-theory
• An ansatz for a non-perturbative four-graviton amplitude in type IIB superstring theory
• T-duality in M-theory and supermembranes

Cited by in corpus (20)

• Duality and higher derivative terms in M theory
• The low energy expansion of the one-loop type II superstring amplitude
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• Normalization of Type IIB D-instanton Amplitudes
• The ${\hat{G}}^4{\lambda }^{16}$ Term in IIB Supergravity
• On a supersymmetric completion of the $R^4$ term in type IIB supergravity
• On the supersymmetric completion of the $R^4$ term in M-theory
• 4-point effective actions in open and closed superstring theory
• S and U-duality Constraints on IIB S-matrices
• Cosmological string models from Milne spaces and SL(2,Z) orbifold
• Dual expansions of N=4 super Yang-Mills theory via IIB superstring theory
• Free energy and critical temperature in eleven dimensions
• Higher derivative type II string effective actions, automorphic forms and E11
• Parameters, limits and higher derivative type II string corrections
• Poisson equations, higher derivative automorphic forms and string parameter limits
• Effects of D-instantons in string amplitudes
• Quantum State Density and Critical Temperature in M-theory
• Quantum States, Thermodynamic Limits and Entropy in M-Theory