Gravity, strings, modular and quasimodular forms

P. Marios Petropoulos[1]; Pierre Vanhove[2]

  • [1] Centre de Physique Théorique École Polytechnique, CNRS UMR 7644 91128 Palaiseau Cedex France
  • [2] IHÉS Le Bois-Marie 91440 Bures-sur-Yvette, France and Institut de Physique Théorique CEA, CNRS URA 2306 91191 Gif-sur-Yvette France

Annales mathématiques Blaise Pascal (2012)

  • Volume: 19, Issue: 2, page 379-430
  • ISSN: 1259-1734

Abstract

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Modular and quasimodular forms have played an important role in gravity and string theory. Eisenstein series have appeared systematically in the determination of spectrums and partition functions, in the description of non-perturbative effects, in higher-order corrections of scalar-field spaces, ...The latter often appear as gravitational instantons i.e. as special solutions of Einstein’s equations. In the present lecture notes we present a class of such solutions in four dimensions, obtained by requiring (conformal) self-duality and Bianchi IX homogeneity. In this case, a vast range of configurations exist, which exhibit interesting modular properties. Examples of other Einstein spaces, without Bianchi IX symmetry, but with similar features are also given. Finally we discuss the emergence and the role of Eisenstein series in the framework of field and string theory perturbative expansions, and motivate the need for unravelling novel modular structures.

How to cite

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Petropoulos, P. Marios, and Vanhove, Pierre. "Gravity, strings, modular and quasimodular forms." Annales mathématiques Blaise Pascal 19.2 (2012): 379-430. <http://eudml.org/doc/251060>.

@article{Petropoulos2012,
abstract = {Modular and quasimodular forms have played an important role in gravity and string theory. Eisenstein series have appeared systematically in the determination of spectrums and partition functions, in the description of non-perturbative effects, in higher-order corrections of scalar-field spaces, ...The latter often appear as gravitational instantons i.e. as special solutions of Einstein’s equations. In the present lecture notes we present a class of such solutions in four dimensions, obtained by requiring (conformal) self-duality and Bianchi IX homogeneity. In this case, a vast range of configurations exist, which exhibit interesting modular properties. Examples of other Einstein spaces, without Bianchi IX symmetry, but with similar features are also given. Finally we discuss the emergence and the role of Eisenstein series in the framework of field and string theory perturbative expansions, and motivate the need for unravelling novel modular structures.},
affiliation = {Centre de Physique Théorique École Polytechnique, CNRS UMR 7644 91128 Palaiseau Cedex France; IHÉS Le Bois-Marie 91440 Bures-sur-Yvette, France and Institut de Physique Théorique CEA, CNRS URA 2306 91191 Gif-sur-Yvette France},
author = {Petropoulos, P. Marios, Vanhove, Pierre},
journal = {Annales mathématiques Blaise Pascal},
keywords = {Eisenstein series; gravitational instantons; string moduli spaces},
language = {eng},
month = {7},
number = {2},
pages = {379-430},
publisher = {Annales mathématiques Blaise Pascal},
title = {Gravity, strings, modular and quasimodular forms},
url = {http://eudml.org/doc/251060},
volume = {19},
year = {2012},
}

TY - JOUR
AU - Petropoulos, P. Marios
AU - Vanhove, Pierre
TI - Gravity, strings, modular and quasimodular forms
JO - Annales mathématiques Blaise Pascal
DA - 2012/7//
PB - Annales mathématiques Blaise Pascal
VL - 19
IS - 2
SP - 379
EP - 430
AB - Modular and quasimodular forms have played an important role in gravity and string theory. Eisenstein series have appeared systematically in the determination of spectrums and partition functions, in the description of non-perturbative effects, in higher-order corrections of scalar-field spaces, ...The latter often appear as gravitational instantons i.e. as special solutions of Einstein’s equations. In the present lecture notes we present a class of such solutions in four dimensions, obtained by requiring (conformal) self-duality and Bianchi IX homogeneity. In this case, a vast range of configurations exist, which exhibit interesting modular properties. Examples of other Einstein spaces, without Bianchi IX symmetry, but with similar features are also given. Finally we discuss the emergence and the role of Eisenstein series in the framework of field and string theory perturbative expansions, and motivate the need for unravelling novel modular structures.
LA - eng
KW - Eisenstein series; gravitational instantons; string moduli spaces
UR - http://eudml.org/doc/251060
ER -

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