Electromagnetic quantum effects in anti-de Sitter spacetime
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ELEMENTARY PARTICLES AND FIELDS Theory
Electromagnetic Quantum Effects in Anti-De Sitter Spacetime∗ A. S. Kotanjyan** and A. A. Saharian*** Department of Physics, Yerevan State University, Armenia Received May 18, 2016
Abstract—The two-point functions of the vector potential and of the field tensor for the electromagnetic field in the background of anti-de Sitter (AdS) spacetime are evaluated in an arbitrary number of spatial dimensions. First, we consider the two-point functions in the boundary-free geometry and then generalize the results in the presence of a reflecting boundary parallel to the AdS horizon. By using the expressions for the two-point functions of the field tensor, we investigate the vacuum expectation values of the electric field squared and of the energy–momentum tensor. Simple asymptotic expressions are provided near the AdS boundary and horizon. DOI: 10.1134/S1063778817030152
1. INTRODUCTION Among the most interesting directions in quantum field theory on curved spacetimes is the investigation of the influence of the gravitational field on the properties of the quantum vacuum. The corresponding problems are exactly solvable for highly symmetric background geometries only. In particular, the investigations of quantum effects in anti-de Sitter (AdS) spacetime have attracted a great deal of attention. There are several reasons for that. Much of early interest to AdS spacetime was motivated by the questions of principle nature related to the quantization of fields propagating on curved backgrounds. The lack of global hyperbolicity and the presence of both regular and irregular modes give rise to a number of new features which have no analogs in quantum field theory on the Minkowski bulk. The importance of this theoretical work increased when it was realized that AdS spacetime emerges as a stable ground state solution in extended supergravity and Kaluza–Klein models and in string theories. The appearance of the AdS/CFT correspondence and braneworld models of Randall–Sundrum type has revived interest in this subject considerably. The AdS/CFT correspondence (for reviews see [1]) represents a realization of the holographic principle and relates string theories or supergravity in the AdS bulk with a conformal field theory living on its boundary. It has many interesting consequences ∗
The text was submitted by the authors in English. E-mail: [email protected] *** E-mail: E-mail:[email protected] **
and provides a powerful tool for the investigation of gauge field theories. Among the recent developments of the AdS/CFT correspondence is the application to strong-coupling problems in condensed matter physics. The braneworld scenario (for reviews see [2]) offers a new perspective on the hierarchy problem between the gravitational and electroweak mass scales. The main idea to resolve the large hierarchy is that the small coupling of four-dimensional gravity is generated by the large physical volume of extra dimensions. Braneworlds naturally appear in string/M-theory context and present intriguing possibilities to solve
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