Massive Theta Lifts

TL;DR

This paper introduces a new 'massive theta lift' using Poincare series for Maass-Jacobi forms, which deforms known string theory integrals and converges rapidly, avoiding the need for renormalization.

Contribution

It defines a novel massive theta lift for Maass-Jacobi forms and applies it to classical functions, providing a new perspective on string threshold corrections.

Findings

Massive theta lifts decay exponentially, ensuring finiteness of certain integrals.

Application to the j-function demonstrates the lift's effectiveness.

Deformation of known string integrals offers new analytical tools.

Abstract

We use Poincare series for massive Maass-Jacobi forms to define a "massive theta lift", and apply it to the examples of the constant function and the modular invariant j-function, with the Siegel-Narain theta function as integration kernel. These theta integrals are deformations of known one-loop string threshold corrections. Our massive theta lifts fall off exponentially, so some Rankin-Selberg integrals are finite without Zagier renormalization.