Quiver Matrix Mechanics for IIB String Theory (II): Generic Dual Tori, Fractional Matrix Membrane and $SL(2,\integer)$ Duality

Details Quiver Matrix Mechanics for IIB String Theory (II): Generic Dual Tori, Fractional Matrix Membrane and $SL(2,\integer)$ Duality Quiver Matrix Mechanics for IIB String Theory (II): Generic Dual Tori, Fractional Matrix Membrane and $SL(2,\integer)$ Duality

2004-02-25

arxiv.org/abs/hep-th/0402201v2

Nucl.Phys. B708 (2005) 72-98

Physics

High Energy Physics

High Energy Physics - Theory

LaTeX2e file, 41 pages + 2 eps figures; v2: typos corrected, more clarifications added

Scientific paper

10.1016/j.nuclphysb.2004.11.043

With the deconstruction technique, the geometric information of a torus can be encoded in a sequence of orbifolds. By studying the Matrix Theory on these orbifolds as quiver mechanics, we present a formulation that (de)constructs the torus of {\em generic shape} on which Matrix Theory is ``compactified''. The continuum limit of the quiver mechanics gives rise to a $(1+2)$-dimensional SYM. A hidden (fourth) dimension, that was introduced before in the Matrix Theory literature to argue for the electric-magnetic duality, can be easily identified in our formalism. We construct membrane wrapping states rigorously in terms of Dunford calculus in the context of matrix regularization. Unwanted degeneracy in the spectrum of the wrapping states is eliminated by using $SL(2,\integer)$ symmetry and the relations to the FD-string bound states. The dual IIB circle emerges in the continuum limit, constituting a critical evidence for IIB/M duality.

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