Related papers: Eisenstein series for infinite-dimensional U-duali…
This paper is devoted to the study of the global existence of smooth solutions for the 3+1 dimensional Einstein-Klein-Gordon systems with a $U(1) \times \mathbb{R}$ isometry group for a class of regular Cauchy data. In our first paper…
We study families of metrics on automorphic vector bundles associated to representations of the modular group. These metrics are defined using an Eisenstein series construction. We show that in certain cases, the residue of these Eisenstein…
Explicit models for the restricted conformal group of the Einstein static universe of dimension greater than two and for its universal covering group are constructed. Based on these models, as an application we determine all oriented and…
We present a construction of complete self-dual Einstein metrics of negative scalar curvature on an uncountable family of manifolds of infinite topological type, which are enumerated by continued fraction expansions of irrational numbers.…
Based on Garland's work, in this paper we construct the Eisenstein series on the adelic loop groups over a number field, induced from either a cusp form or a quasi-character which is assumed to be unramified. We compute the constant terms,…
We discuss the relationship between target space modular invariance and discrete gauge symmetries in four-dimensional orbifold-like strings. First we derive the modular transformation properties of various string vertex operators of the…
We explicitly write down the Eisenstein elements inside the space of modular symbols for Eisenstein series with integer coefficients for the congruence subgroups $\Gamma_0(N)$ with $N$ odd square-free. We also compute the winding elements…
We continue our study of one-loop integrals associated to BPS-saturated amplitudes in $\mathcal{N}=2$ heterotic vacua. We compute their large-volume behaviour, and express them as Fourier series in the complexified volume, with Fourier…
In this paper we consider certain classes of generalized double Eisenstein series by simple differential calculations of trigonometric functions. In particular, we give four new transformation formula for some double Eisenstein series. We…
The moduli of N=1 compactifications of IIB string theory can be stabilized by a combination of fluxes (which freeze complex structure moduli and the dilaton) and nonperturbative superpotentials (which freeze Kahler moduli), typically…
We are presenting the basic ingredients of a stringy mechanism able to resolve both the Hagedorn instabilities of finite temperature superstrings as well as the initial singularity of the induced cosmology in arbitrary dimensions. These are…
We present a new approach for generating solutions in heterotic string theory compactified down to three dimensions on a torus with d+n>2, where d and n stand for the number of compactified space--time dimensions and Abelian gauge fields,…
The purpose of this of this paper is to develop the theory of Eisenstein series in the framework of geometric Langlands correspondence. Our construction is based on the study of certain relative compactification of the moduli stack of…
Exact non-perturbative results have been conjectured for R^4 couplings in type II maximally supersymmetric string theory. Strong evidence has already been obtained, but contributions of cusp forms, invisible in perturbation theory, have…
Caustics-envelopes formed by the trajectories of fluid particles-arise in proposed dynamical extensions for shell-crossing singularities occurring in the Einstein-dust system. In this study, a local existence result is established,…
We determine the spectrum of D-string bound states in various classes of generalized type I vacuum configurations with sixteen and eight supercharges. The precise matching of the BPS spectra confirms the duality between unconventional type…
It is shown that for a non-unitary twist of a Fuchsian group, which is unitary at the cusps, Eisenstein series converge in some half-plane. It is shown that invariant integral operators provide a spectral decomposition of the space of cusp…
We examine bounds on accelerated expansion in asymptotic regions of the moduli space in string theory compactifications to four spacetime dimensions. While there are conjectures that forbid or constrain accelerated expansion in such…
High-dimensional expanders are a generalization of the notion of expander graphs to simplicial complexes and give rise to a variety of applications in computer science and other fields. We provide a general tool to construct families of…
Scattering amplitudes of any four-dimensional theory with nonabelian gauge group $\mathcal G$ may be recast as two-dimensional correlation functions on the asymptotic two-sphere at null infinity. The soft gluon theorem is shown, for…