Aspects of U-Duality in Matrix Theory

Abstract

We explore various aspects of implementing the full M-theory U-duality group E_{d+1}, and thus Lorentz invariance, in the finite N matrix theory (DLCQ of M-theory) on d-tori: (1) We generalize the analysis of U-duality orbits of BPS states by Elitzur et al. (hep-th/9707217) from E_{d} to E_{d+1}. (2) We identify the new E_{d+1}-symmetries with Nahm-duality-like symmetries (N-duality) exchanging the rank N of the matrix theory gauge group with other quantum numbers. (3) We describe the action of N-duality on BPS bound states, thus making testable predictions for the Lorentz invariance of matrix theory. (4) We discuss the problems that arise in the matrix theory limit for BPS states with no top-dimensional branes, i.e. configurations with N=0. (5) We show that N-duality maps the matrix theory SYM picture to the matrix string picture and argue that, for d even, the latter should be thought of as an M-theory membrane description (which appears to be well defined even for d>5). (6) We find a compact and unified expression for a U-duality invariant of E_{d+1} for all d and show that in d=5,6 it reduces to the black hole entropy cubic E_{6}- and quartic E_{7}-invariants respectively. (7) We describe some of the solitonic states in d=6,7 and give an example (a `rolled-up' Taub-NUT 6-brane) of a configuration exhibiting the unusual 1/g_{s}^{3}-behaviour.

40 pages, LaTeX

References in corpus (13)

• Matrix String Theory
• Why is the Matrix Model Correct?
• Matrix Description of M-theory on $T^5$ and $T^5/Z_2$
• Matrix Description of M-theory on $T^4$ and $T^5$
• M-Theory and U-duality on T^d with Gauge Backgrounds
• Algebraic Aspects of Matrix Theory on T^d
• Matrix Theory and U-Duality in Seven Dimensions
• Torons and D-Brane Bound States
• Matrix Description of M-theory on $T^6$
• M-branes and N=2 Strings
• Duality symmetry of N=4 Yang-Mills theory on T^3
• On the Moduli Spaces of M(atrix)-Theory Compactifications
• BPS states in Matrix Strings

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