From Large N Matrices to the Noncommutative
Torus |
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Authors: | G Landi F Lizzi R J Szabo |
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Institution: | Dipartimento di Scienze Matematiche, Università di Trieste, P.le Europa 1, 34127 Trieste, Italy.?E-mail: landi@mathsun1.univ.trieste.it, IT Dipartimento di Scienze Fisiche, Università di Napoli Federico II, Mostra d'Oltremare Pad.~20,?80125 Napoli, Italy. E-mail: fedele.lizzi@na.infn.it, IT The Niels Bohr Institute, Blegdamsvej 17, 2100 Copenhagen ?, Denmark. E-mail: szabo@nbi.dk, DK
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Abstract: | We describe how and to what extent the noncommutative two-torus can be approximated by a tower of finite-dimensional matrix
geometries. The approximation is carried out for both irrational and rational deformation parameters by embedding the C
*-algebra of the noncommutative torus into an approximately finite algebra. The construction is a rigorous derivation of the
recent discretizations of noncommutative gauge theories using finite dimensional matrix models, and it shows precisely how
the continuum limits of these models must be taken. We clarify various aspects of Morita equivalence using this formalism
and describe some applications to noncommutative Yang–Mills theory.
Received: 24 December 1999 / Accepted: 7 October 2000 |
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