M(atrix) Theory on the Negative Light-Front

Abstract

M(atrix) theory defines light-front description of M-theory boosted along positive direction of eleventh, M-coordinate. Rank of M(atrix) gauge group is directly related to M-momentum $P_{11} = N / R_{11}$ or, equivalently, to total number of D0-partons. Alternatively, M-theory may be boosted along opposite direction of M-coordinate, for which the theory consists only of anti-D0 partons. In M(atrix) theory description, we interpret this as analytic continuation of dimension of the gauge group: $U(-N) \sim U(N)$, $SO(-2N) \sim USp(2N)$ and $USp(-2N) \sim SO(2N)$. We check these reciprocity relations explicitly for uncompactified, heterotic, and CHL M(atrix) theories as well as effective M(atrix) gauge theories of $T_5/Z_2$ and $T_9/Z_2$ compactifications. In all cases, we show that absence of parity, gauge and supersymmetry anomalies require introduction of a twisted sector with negative numbers of matter multiplets. They are interpreted as massless open string excitations connected to anti-D-brane background.