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Morita Equivalence and T-Duality (or Beta versus Theta)

机译：森田等价和T-对偶（或Beta与Theta）

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T-duality in M(atrix) theory has been argued to be realized as Morita equivalence211u001ein Yang-Mills theory on a non-commutative torus (NCSYM). ven though the two have 211u001ethe same structure group, they differ in their action since Morita equivalence 211u001emakes crucial use of an additional modulus on the NCSYM side, the constant 211u001eAbelian magnetic background. In this paper, we reanalyze and clarify the 211u001ecorrespondence between M(atrix) theory and NCSYM, and provide two resolutions of 211u001ethis puzzle. In the first of them, the standard map is kept and the extra modulus 211u001eis ignored, but the anomalous transformation is offset by the M(atrix) theory 211u001e'test term.' In the second, the standard map is modified so that the duality 211u001etransformations agree, and a SO(d) symmetry is found to eliminate the spurious 211u001emodulus. We argue that this is a true symmetry of supersymmetric Born-Infeld 211u001etheory on a non-commutative torus, which allows to freely trade a constant 211u001emagnetic background for non-commutativity of the base-space.

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