The University of Southampton
University of Southampton Institutional Repository

Etudes on 1/N

Etudes on 1/N
Etudes on 1/N
A number of problems in string theory and lattice statistical mechanics is studied using the large N approximation, with N being the dimension of the fundamental representation of the underlying symmetry algebra. As the first problem, the absorption of a minimally coupled massless scalar in the gravitational background created by a stack of near-extremal black three-branes is considered. The low-temperature asymptotic expansion and the high-temperature perturbative expansion are obtained. A field-theoretical calculation of the absorption cross section in the brane's world-volume theory is also performed. As an application, the shear viscosity of a strongly coupled Yang-Mills plasma is computed. In the second problem, we study supergravity solutions with two asymptotically Anti de Sitter regions which are conjectured to describe the renormalization group flow of a four-dimensional field theory from a UV fixed point to an interacting IR fixed point. We show that, in the UV (IR) limit, the two-point function of a minimally-coupled scalar field depends only on the UV (IR) region of the metric, asymptotic to AdS(5) thus lending a support to the conjecture. In the third problem, monotonicity and other properties of the canonical c-function in some holographic duals of 4-d quantum field theories are investigated. The canonical c-function and its derivatives are related to the 5-d Green's function of the dual supergravity theory. In the fourth problem, we study solutions of the equations (Delta; minus; lambda;)phis; = 0 and (Delta; minus; lambda;)2phis = 0 C AdS(d) of the d-dimensional Anti de-Sitter space subject to various boundary conditions, and we analyze their connection to the unitary irreducible representations of SO d15; (- 1, 2). Finally, as the fifth problem, we compute the phase diagram in the N RP(N)-(1) CP(N)-1 QP(N)-1(sigma) - models with the quartic action, and more generally for mixed isovector/isotensor models. We show that the N; limit exhibits phase transitions that are forbidden for any finite N. We clarify the origin of these pathologies by examining the exact solution of the one- dimensional model. We conjecture the correct phase diagram for finite N as a function of the spatial dimension d. We also obtain new results concerning the complex zeros of confluent hypergeometric functions.
Starinets, A.O.
c38a7047-d3e8-46f0-877e-a7a23534a246
Starinets, A.O.
c38a7047-d3e8-46f0-877e-a7a23534a246

Starinets, A.O. (2001) Etudes on 1/N. New York University, Doctoral Thesis, 353pp.

Record type: Thesis (Doctoral)

Abstract

A number of problems in string theory and lattice statistical mechanics is studied using the large N approximation, with N being the dimension of the fundamental representation of the underlying symmetry algebra. As the first problem, the absorption of a minimally coupled massless scalar in the gravitational background created by a stack of near-extremal black three-branes is considered. The low-temperature asymptotic expansion and the high-temperature perturbative expansion are obtained. A field-theoretical calculation of the absorption cross section in the brane's world-volume theory is also performed. As an application, the shear viscosity of a strongly coupled Yang-Mills plasma is computed. In the second problem, we study supergravity solutions with two asymptotically Anti de Sitter regions which are conjectured to describe the renormalization group flow of a four-dimensional field theory from a UV fixed point to an interacting IR fixed point. We show that, in the UV (IR) limit, the two-point function of a minimally-coupled scalar field depends only on the UV (IR) region of the metric, asymptotic to AdS(5) thus lending a support to the conjecture. In the third problem, monotonicity and other properties of the canonical c-function in some holographic duals of 4-d quantum field theories are investigated. The canonical c-function and its derivatives are related to the 5-d Green's function of the dual supergravity theory. In the fourth problem, we study solutions of the equations (Delta; minus; lambda;)phis; = 0 and (Delta; minus; lambda;)2phis = 0 C AdS(d) of the d-dimensional Anti de-Sitter space subject to various boundary conditions, and we analyze their connection to the unitary irreducible representations of SO d15; (- 1, 2). Finally, as the fifth problem, we compute the phase diagram in the N RP(N)-(1) CP(N)-1 QP(N)-1(sigma) - models with the quartic action, and more generally for mixed isovector/isotensor models. We show that the N; limit exhibits phase transitions that are forbidden for any finite N. We clarify the origin of these pathologies by examining the exact solution of the one- dimensional model. We conjecture the correct phase diagram for finite N as a function of the spatial dimension d. We also obtain new results concerning the complex zeros of confluent hypergeometric functions.

This record has no associated files available for download.

More information

Published date: 2001
Additional Information: UMI-30-24721

Identifiers

Local EPrints ID: 57605
URI: http://eprints.soton.ac.uk/id/eprint/57605
PURE UUID: 20a9f94e-fca8-43c4-8ecf-ff21868057df

Catalogue record

Date deposited: 07 Aug 2008
Last modified: 11 Dec 2021 17:53

Export record

Contributors

Author: A.O. Starinets

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×