15 research outputs found
Three-Point Functions of Quarter BPS Operators in N=4 SYM
In a recent paper hep-th/0109064, quarter-BPS chiral primaries were
constructed in the fully interacting four dimensional N=4 Super-Yang-Mills
theory with gauge group SU(N). These operators are annihilated by four
supercharges, and at order g^2 have protected scaling dimension and
normalization. Here, we compute three-point functions involving these
quarter-BPS operators along with half-BPS operators. The combinatorics of the
problem is rather involved, and we consider the following special cases: (1)
correlators of two half-BPS primaries with an arbitrary
chiral primary; (2) certain classes of and < quarter
quarter quarter > three-point functions; (3) three-point functions involving
the Delta
correlators with the special quarter-BPS operator made of single and double
trace operators only. The analysis in cases (1)-(3) is valid for general N,
while (4) is a large N approximation. Order g^2 corrections to all three-point
functions considered in this paper are found to vanish.
In the AdS/CFT correspondence, quarter-BPS chiral primaries are dual to
threshold bound states of elementary supergravity excitations. We present a
supergravity discussion of two- and three-point correlators involving these
bound states.Comment: 44 pages, Latex, eps figures, uses epsfig.sty; references adde
Large N Quantum Time Evolution Beyond Leading Order
For quantum theories with a classical limit (which includes the large N
limits of typical field theories), we derive a hierarchy of evolution equations
for equal time correlators which systematically incorporate corrections to the
limiting classical evolution. Explicit expressions are given for
next-to-leading order, and next-to-next-to-leading order time evolution. The
large N limit of N-component vector models, and the usual semiclassical limit
of point particle quantum mechanics are used as concrete examples. Our
formulation directly exploits the appropriate group structure which underlies
the construction of suitable coherent states and generates the classical phase
space. We discuss the growth of truncation error with time, and argue that
truncations of the large-N evolution equations are generically expected to be
useful only for times short compared to a ``decoherence'' time which scales
like N^{1/2}.Comment: 36 pages, 2 eps figures, latex, uses revtex, epsfig, float
On Low Rank Classical Groups in String Theory, Gauge Theory and Matrix Models
We consider N=1 supersymmetric U(N), SO(N), and Sp(N) gauge theories, with
two-index tensor matter and added tree-level superpotential, for general
breaking patterns of the gauge group. By considering the string theory
realization and geometric transitions, we clarify when glueball superfields
should be included and extremized, or rather set to zero; this issue arises for
unbroken group factors of low rank. The string theory results, which are
equivalent to those of the matrix model, refer to a particular UV completion of
the gauge theory, which could differ from conventional gauge theory results by
residual instanton effects. Often, however, these effects exhibit miraculous
cancellations, and the string theory or matrix model results end up agreeing
with standard gauge theory. In particular, these string theory considerations
explain and remove some apparent discrepancies between gauge theories and
matrix models in the literature.Comment: 41 pages, 1 table, harvmac. v2: minor corrections and references
adde