Free particles from Brauer algebras in complex matrix models
Free particles from Brauer algebras in complex matrix models
The gauge invariant degrees of freedom of matrix models based on an N x N complex matrix, with U(N) gauge symmetry, contain hidden free particle structures. These are exhibited using triangular matrix variables via the Schur decomposition. The Brauer algebra basis for complex matrix models developed earlier is useful in projecting to a sector which matches the state counting of N free fermions on a circle. The Brauer algebra projection is characterized by the vanishing of a scale invariant laplacian constructed from the complex matrix. The special case of N=2 is studied in detail: the ring of gauge invariant functions as well as a ring of scale and gauge invariant differential operators are characterized completely. The orthonormal basis of wavefunctions in this special case is completely characterized by a set of five commuting Hamiltonians, which display free particle structures. Applications to the reduced matrix quantum mechanics coming from radial quantization in N=4 SYM are described. We propose that the string dual of the complex matrix harmonic oscillator quantum mechanics has an interpretation in terms of strings and branes in 2+1 dimensions.
Kimura, Yusuke
da6cd9eb-3298-4a0d-8c50-c054e80d0534
Ramgoolam, Sanjaye
3a80b8b6-419e-456d-8449-b9216c386568
Turton, David
6ce84b30-3cc0-42aa-ace5-f298d4260e9b
14 May 2010
Kimura, Yusuke
da6cd9eb-3298-4a0d-8c50-c054e80d0534
Ramgoolam, Sanjaye
3a80b8b6-419e-456d-8449-b9216c386568
Turton, David
6ce84b30-3cc0-42aa-ace5-f298d4260e9b
Kimura, Yusuke, Ramgoolam, Sanjaye and Turton, David
(2010)
Free particles from Brauer algebras in complex matrix models.
JHEP, 2010, [52].
(doi:10.1007/JHEP05(2010)052).
Abstract
The gauge invariant degrees of freedom of matrix models based on an N x N complex matrix, with U(N) gauge symmetry, contain hidden free particle structures. These are exhibited using triangular matrix variables via the Schur decomposition. The Brauer algebra basis for complex matrix models developed earlier is useful in projecting to a sector which matches the state counting of N free fermions on a circle. The Brauer algebra projection is characterized by the vanishing of a scale invariant laplacian constructed from the complex matrix. The special case of N=2 is studied in detail: the ring of gauge invariant functions as well as a ring of scale and gauge invariant differential operators are characterized completely. The orthonormal basis of wavefunctions in this special case is completely characterized by a set of five commuting Hamiltonians, which display free particle structures. Applications to the reduced matrix quantum mechanics coming from radial quantization in N=4 SYM are described. We propose that the string dual of the complex matrix harmonic oscillator quantum mechanics has an interpretation in terms of strings and branes in 2+1 dimensions.
Text
0911.4408v3
- Accepted Manuscript
More information
Accepted/In Press date: 24 April 2010
Published date: 14 May 2010
Identifiers
Local EPrints ID: 469761
URI: http://eprints.soton.ac.uk/id/eprint/469761
ISSN: 1126-6708
PURE UUID: 8bc3b4e5-8ed9-42c3-896d-9c50e44319b4
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Date deposited: 23 Sep 2022 17:29
Last modified: 17 Mar 2024 03:48
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Author:
Yusuke Kimura
Author:
Sanjaye Ramgoolam
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