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Holomorphic curves and their matrix ...

Cornalba, Lorenzo.

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Holomorphic curves and their matrix representations.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Holomorphic curves and their matrix representations./
Author:	Cornalba, Lorenzo.
Description:	122 p.
Notes:	Source: Dissertation Abstracts International, Volume: 60-06, Section: B, page: 2760.
Contained By:	Dissertation Abstracts International60-06B.
Subject:	Physics, Elementary Particles and High Energy. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=9933635
ISBN:	0599344032

Holomorphic curves and their matrix representations.
Cornalba, Lorenzo.

Holomorphic curves and their matrix representations. - 122 p.

Source: Dissertation Abstracts International, Volume: 60-06, Section: B, page: 2760.

Thesis (Ph.D.)--Princeton University, 1999.

This thesis is devoted to the problem of representing, within the matrix formulation of M-theory, states with a prescribed membrane configuration. In particular we focus our attention on static membranes which preserve part of the super-symmetry of the theory, and which are represented classically by holomorphically embedded curves. These branes are constructed in terms of the fundamental degrees of freedom of a collection of D0 branes, and are represented by infinite-dimensional matrices, which are static solutions to the matrix theory equations of motion. When the branes are embedded in compact tori, the infinite matrices can be reinterpreted as U(N) gauge fields on the dual torus, with almost-self-dual field strength and with non-vanishing first Chern class. This fact leads us to conjecture a relation between the space of curves on a torus and the space of almost-self-dual U(N) fields on the dual torus, and we give initial evidence supporting the conjecture.

ISBN: 0599344032Subjects--Topical Terms:

1019488
Physics, Elementary Particles and High Energy.

Holomorphic curves and their matrix representations.
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100 1 $a Cornalba, Lorenzo. $3 1905352
245 1 0 $a Holomorphic curves and their matrix representations.
300 $a 122 p.
500 $a Source: Dissertation Abstracts International, Volume: 60-06, Section: B, page: 2760.
502 $a Thesis (Ph.D.)--Princeton University, 1999.
520 $a This thesis is devoted to the problem of representing, within the matrix formulation of M-theory, states with a prescribed membrane configuration. In particular we focus our attention on static membranes which preserve part of the super-symmetry of the theory, and which are represented classically by holomorphically embedded curves. These branes are constructed in terms of the fundamental degrees of freedom of a collection of D0 branes, and are represented by infinite-dimensional matrices, which are static solutions to the matrix theory equations of motion. When the branes are embedded in compact tori, the infinite matrices can be reinterpreted as U(N) gauge fields on the dual torus, with almost-self-dual field strength and with non-vanishing first Chern class. This fact leads us to conjecture a relation between the space of curves on a torus and the space of almost-self-dual U(N) fields on the dual torus, and we give initial evidence supporting the conjecture.
520 $a The representation problem can be phrased as a problem in geometric quantization, where e&sim;l3P/R plays the role of the Planck constant. The concept of Bergman projection is used as a basic tool and a local expansion for the action of the projection in inverse powers of curvature is derived. This expansion is then used to compute the required matrices asymptotically in e . Moreover, the proposed quantization scheme naturally provides an associative star-product over the space of functions on the surface, for which we give an explicit and coordinate-invariant expression. This product can, in turn, be used to quantize, in the sense of deformation quantization, any symplectic manifold of dimension two.
590 $a School code: 0181.
650 4 $a Physics, Elementary Particles and High Energy. $3 1019488
690 $a 0798
710 2 0 $a Princeton University. $3 645579
773 0 $t Dissertation Abstracts International $g 60-06B.
790 $a 0181
791 $a Ph.D.
792 $a 1999
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=9933635