Related papers: Modular Forms and $SL(2, {\mathbb Z})$-covariance …

We present an action for $N=1$ supergravity in $10+2$ dimensions, containing the gauge fields of the $OSp(1|64)$ superalgebra, i.e. one-forms $B^{(n)}$ with $n$=1,2,5,6,9,10 antisymmetric D=12 Lorentz indices and a Majorana gravitino…

This paper concerns a special class of $n$-point correlation functions of operators in the stress tensor supermultiplet of $\mathcal{N}=4$ supersymmetric $SU(N)$ Yang-Mills theory. These are "maximal $U(1)_Y$-violating" correlators that…

We define L-functions for meromorphic modular forms that are regular at cusps, and use them to: (i) find new relationships between Hurwitz class numbers and traces of singular moduli, (ii) establish predictions from the physics of…

We propose a manifestly U-duality invariant modular form for the D^4 R^4 interaction in type IIB string theory compactified on T^2. It receives perturbative contributions upto two loops, and non-perturbative contributions from D-instantons…

We obtain T--duality invariant second order differential equations satisfied by the $D^8\mathcal{R}^4$ and $D^{10} \mathcal{R}^4$ interactions from the low energy expansion of the one loop four graviton amplitude in toroidally compactified…

We study maximally symmetric cosmological solutions of type II supersymmetric strings in the presence of the exact, SL(2,Z)-invariant, higher-curvature corrections to the lowest order effective action. We find that, unlike the case of type…

The low-momentum expansion of the two-loop four-graviton scattering amplitude in eleven-dimensional supergravity compactified on a circle and a two-torus is considered up to terms of order S^6R^4 (where S is a Mandelstam invariant and R is…

We study freely acting orbifolds of type IIB string theory on $T^5$ that spontaneously break supersymmetry from $\mathcal{N}=8$ to $\mathcal{N}=6,4,2$ or 0 in five dimensions. We focus on orbifolds that are a $\mathbb{Z}_p$ quotient by a…

We investigate the old problem of determining the exact bulk moduli of generic $\mathrm{SU}(3)$-structure flux backgrounds of type II string theory. Using techniques from generalised geometry, we show that the infinitesimal deformations are…

We review recent developments in the context of two-dimensional conformally invariant sigma-models. These quantum field theories play a prominent role in the covariant superstring quantization in flux backgrounds and in the analysis of…

We study the instanton partition functions of two well-known superconformal field theories with mass deformations. Two types of anomaly equations, namely, the modular anomaly and holomorphic anomaly, have been discovered in the literature.…

We investigate a higher-form symmetry in type IIB superstring theory, which possesses an ${\rm SL}(2,\mathbb{Z})$ symmetry. From the point of view of the low-energy effective field theory, the ${\rm SL}(2,\mathbb{Z})$ symmetry is treated as…

The "superconformal index" is a character-valued invariant attached by theoretical physics to unitary representations of Lie superalgebras, such as $\mathfrak{su}(2,2\vert n)$, that govern certain quantum field theories. The index can be…

We present a manifestly Sl(2;Z)-covariant action for the type IIB superstring, and prove kappa-symmetry for on-shell IIB supergravity backgrounds.

Following Feigin and Fuchs, we compute the first cohomology of the Lie superalgebra $\mathcal{K}(1)$ of contact vector fields on the (1,1)-dimensional real superspace with coefficients in the superspace of linear differential operators…

We review the structure of the moduli space of particular N = (2,2) superconformal field theories. We restrict attention to those of particular use in superstring compactification, namely those with central charge c = 3d for some integer d…

To every $k$-dimensional modular invariant vector space we associate a modular form on $SL(2,\mathbb{Z})$ of weight $2k$. We explore number theoretic properties of this form and find a sufficient condition for its vanishing which yields…

We consider the long range forces between two BPS particles on the Coulomb branch of N=2 and N=4 supersymmetric gauge theories. The 1/r potential is unambiguously fixed, even at strong coupling, by the moduli dependence of central charges…

This introductory paper studies a class of real analytic functions on the upper half plane satisfying a certain modular transformation property. They are not eigenfunctions of the Laplacian and are quite distinct from Maass forms. These…

We describe a method for obtaining relations between higher derivative interactions in supersymmetric effective actions. The method extends to all orders in the momentum expansion. As an application, we consider the string coupling…