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
2001
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.
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Published date: 2001
Additional Information:
UMI-30-24721
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Local EPrints ID: 57605
URI: http://eprints.soton.ac.uk/id/eprint/57605
PURE UUID: 20a9f94e-fca8-43c4-8ecf-ff21868057df
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Date deposited: 07 Aug 2008
Last modified: 11 Dec 2021 17:53
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Author:
A.O. Starinets
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