Publication : t14/009

SL(2,Z)-invariance and D-instanton contributions to the D^6R^4 interaction

Vanhove P. (CEA, IPhT (Institut de Physique Théorique), F-91191 Gif-sur-Yvette, France)
Green M.B. (Department of Applied Mathematics and Theoretical Physics (DAMTP), Center for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, England UNITED KINGDOM (UK))
Miller, S.D. (Department of Mathematics Hill Center-Busch Campus Rutgers, The State University of New Jersey 110 Frelinghuysen Rd Piscataway, NJ 08854-8019)
The modular invariant coefficient of the $D^6R^4$ interaction in the low energy expansion of type IIB string theory has been conjectured to be a solution of an inhomogeneous Laplace eigenvalue equation, obtained by considering the toroidal compactification of two-loop Feynman diagrams of eleven-dimensional supergravity. In this paper we determine its exact $SL(2,mathbb Z)$-invariant solution $f(Omega)$ as a function of the complex modulus, $Omega=x+iy$, satisfying an appropriate moderate growth condition as $yto infty$ (the weak coupling limit). The solution is presented as a Fourier series with modes $widehat{f}_n(y) e^{2pi i n x}$, where the mode coefficients, $widehat{f}_n(y)$ are bilinear in $K$-Bessel functions. Invariance under $SL(2,mathbb Z)$ requires these modes to satisfy the nontrivial boundary condition $ widehat{f}_n(y) =O(y^{-2})$ for small $y$, which uniquely determines the solution. The large-$y$ expansion of $f(Omega)$ contains the known perturbative (power-behaved) terms, together with precisely-determined exponentially decreasing contributions that have the form expected of D-instantons, anti-D-instantons and D-instanton/anti-D-instanton pairs.
Année de publication : 2015
Revue : Commun. Numb. Theor. Phys. 9-2 307-344 (2015)
DOI : 10.4310/CNTP.2015.v9.n2.a3
Preprint : arXiv:1404.2192
Langue : Anglais


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