Eur. Phys. J. Plus (2016) 131: 172
https://doi.org/10.1140/epjp/i2016-16172-9

Regular Article

Weyl geometry, anti-de Sitter space, and -theory

¹ Facultad de Ciencias, Universidad Nacional Autónoma de México Circuito Exterior, Ciudad Universitaria, 04510, México, Mexico
² Instituto de Ciencias, Universidad Nacional de General Sarmiento Juan Marí a Gutiérrez 1150 (B1613GSX), Los Polvorines, Pcia. de Buenos Aires, Argentina
³ Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México Circuito Exterior, Ciudad Universitaria, 04510, México, Mexico

^* e-mail: msocolov@ungs.edu.ar

Received: 21 April 2016
Accepted: 23 April 2016
Published online: 26 May 2016

Abstract

We study the Gaussian approximation to the quantum fluctuations of the metric of the four-dimensional anti-de Sitter spacetime. The associated massless scalar field has a quartic self-interaction, for which we construct the generating functional of the n-point correlation functions. The concomitant infrared divergence is cured by a mass renormalization provided by the cosmological constant, which is also responsible for the renormalization of the coupling constant of the field theory.