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)∼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
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.