Supersymmetry constraints on the R^4 multiplet in type IIB on T^2

Abstract

We consider a class of eight derivative interactions in the effective action of type IIB string theory compactified on T^2. These 1/2 BPS interactions have moduli dependent couplings. We impose the constraints of supersymmetry to show that each of these couplings satisfy a first order differential equation on moduli space which relate it to other couplings in the same supermuliplet. These equations can be iterated to give second order differential equations for the various couplings. The couplings which only depend on the SO(2)\SL(2,R) moduli satisfy Laplace equation on moduli space, and are given by modular forms of SL(2,Z). On the other hand, the ones that only depend on the SO(3)\SL(3,R) moduli satisfy Poisson equation on moduli space, where the source terms are given by other couplings in the same supermultiplet. The couplings of the interactions which are charged under SU(2) are not automorphic forms of SL(3,Z). Among the interactions we consider, the R^4 coupling depends on all the moduli.

89 pages, LaTeX

References in corpus (4)

• Automorphic properties of low energy string amplitudes in various dimensions
• The D^4 R^4 term in type IIB string theory on T^2 and U-duality
• Explicit Action of E7(7) on N=8 Supergravity Fields
• The D^6 R^4 term in type IIB string theory on T^2 and U-duality

Cited by in corpus (14)

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• Modular Forms and $SL(2,\mathbb{Z})$-covariance of type IIB superstring theory
• Infrared divergences and harmonic anomalies in the two-loop superstring effective action
• Low momentum expansion of one loop amplitudes in heterotic string theory
• New Examples of Flux Vacua
• $D^6{R}^4$ curvature corrections, modular graph functions and Poincaré series
• Higher derivative type II string effective actions, automorphic forms and E11
• Discrete anomalies in supergravity and consistency of string backgrounds
• Parameters, limits and higher derivative type II string corrections
• Non--analytic terms from nested divergences in maximal supergravity