Eisenstein series and string thresholds.
type: Item
instance of: scholarly article
title: Eisenstein series and string thresholds.
zbMATH Open document ID: 1043.81059
author: Niels A. Obers
author: Boris Pioline
published in: Communications in Mathematical Physics
publication date: 2000-05-11T00:00:00Z
full work available at URL: https://arxiv.org/abs/hep-th/9903113
review text: Let \(G(\mathbb Z)\) be the mapping class group \(S\ell(d,\mathbb Z)\), the \(T\)-duality group \(SO(d,d,\mathbb Z)\), or the non-perturbative \(U\)-duality group \(E_{d+ 1(d+1)} (\mathbb Z)\). The authors investigate the relevance of Eisenstein series for representing certain \(G(\mathbb Z)\)-invariant string theory amplitudes which receive corrections from BPS states only. Using \(G(\mathbb Z)\)-invariant mass formulae, they construct invariant modular functions on the symmetric space \(K \backslash G(\mathbb R)\) associated to a maximal compact subgroup \(K\) of \(G(\mathbb R)\), which generalize the standard nonholomorphic Eisenstein series arising in harmonic analysis on the fundamental domain of the Poincaré upper half plane. By comparing the asymptotics and eigenvalues of the Eisenstein series under second order differential operators with quantities arising in one-loop and \(g\)-loop string amplitudes, the authors also obtain a \(T\)-duality invariant representation of the latter, conjecture their non-perturbative \(U\)-duality invariant extension, and analyze the resulting non-perturbative effects.
reviewed by: Min Ho Lee
Mathematics Subject Classification ID: 81T30
Mathematics Subject Classification ID: 11F11
Mathematics Subject Classification ID: 11M36
Mathematics Subject Classification ID: 11Z05
zbMATH DE Number: 1422923
zbMATH Keywords: Eisenstein series
zbMATH Keywords: automorphic forms
zbMATH Keywords: string theory
MaRDI profile type: Publication
OpenAlex ID: W2949200361
Wikidata QID: Q57726811
arXiv ID: hep-th/9903113
DOI: 10.1007/S002200050022
description: scientific article