M(atrix) Theory on the Negative Light-front

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 P11 = N/R11 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) ≈ U(N), SO(−2N) ≈ USp(2N) and USp(−2N) ≈ 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 T5/Z 2 and T9/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. 1 Work supported in part by the NSF-KOSEF Bilateral Grant, KOSEF SRC-Program, Ministry of Education Grant BSRI 97-2418 and The Korea Foundation for Advanced Studies Faculty Fellowship Motivation: M(atrix) theory [1] defines the light-front Hamiltonian description of Mtheory. By boosting Type IIA string theory along quantum, M-direction, parton content of M-theory is identified with D0-branes. Kinematical argument that leads to the identification of D0-partons is as follows. Consider, in M-theory, excitation of a particle of rest mass m and eleven-momentum (P0,P⊥, P11): P 2 0 − P 2 11 −P 2 ⊥ = m. (1) If the particle is boosted by P11 = N/R along S1 compactified M-coordinate of radius R while keeping P⊥ finite, P0 − |P11| = 1 P0 + |P11| (