930 research outputs found
Lagrangian subcategories and braided tensor equivalences of twisted quantum doubles of finite groups
We classify Lagrangian subcategories of the representation category of a
twisted quantum double of a finite group. In view of results of 0704.0195v2
this gives a complete description of all braided tensor equivalent pairs of
twisted quantum doubles of finite groups. We also establish a canonical
bijection between Lagrangian subcategories of the representation category of a
twisted quantum double of a finite group G and module categories over the
category of twisted G-graded vector spaces such that the dual tensor category
is pointed. This can be viewed as a quantum version of V. Drinfeld's
characterization of homogeneous spaces of a Poisson-Lie group in terms of
Lagrangian subalgebras of the double of its Lie bialgebra. As a consequence, we
obtain that two group-theoretical fusion categories are weakly Morita
equivalent if and only if their centers are equivalent as braided tensor
categories.Comment: 26 pages; several comments and references adde
Properties of Chiral Wilson Loops
We study a class of Wilson Loops in N =4, D=4 Yang-Mills theory belonging to
the chiral ring of a N=2, d=1 subalgebra. We show that the expectation value of
these loops is independent of their shape. Using properties of the chiral ring,
we also show that the expectation value is identically 1. We find the same
result for chiral loops in maximally supersymmetric Yang-Mills theory in three,
five and six dimensions. In seven dimensions, a generalized Konishi anomaly
gives an equation for chiral loops which closely resembles the loop equations
of the three dimensional Chern-Simons theory.Comment: 15 pages, two pictures, some references adde
Chiral rings, anomalies and loop equations in N=1* gauge theories
We examine the equivalence between the Konishi anomaly equations and the
matrix model loop equations in N=1* gauge theories, the mass deformation of N=4
supersymmetric Yang-Mills. We perform the superfunctional integral of two
adjoint chiral superfields to obtain an effective N=1 theory of the third
adjoint chiral superfield. By choosing an appropriate holomorphic variation,
the Konishi anomaly equations correctly reproduce the loop equations in the
corresponding three-matrix model. We write down the field theory loop equations
explicitly by using a noncommutative product of resolvents peculiar to N=1*
theories. The field theory resolvents are identified with those in the matrix
model in the same manner as for the generic N=1 gauge theories. We cover all
the classical gauge groups. In SO/Sp cases, both the one-loop holomorphic
potential and the Konishi anomaly term involve twisting of index loops to
change a one-loop oriented diagram to an unoriented diagram. The field theory
loop equations for these cases show certain inhomogeneous terms suggesting the
matrix model loop equations for the RP2 resolvent.Comment: 23 pages, 3 figures, latex2e, v4: minor changes in introduction and
conclusions, 4 references are added, version to appear in JHE
Simple Current Actions of Cyclic Groups
Permutation actions of simple currents on the primaries of a Rational
Conformal Field Theory are considered in the framework of admissible weighted
permutation actions. The solution of admissibility conditions is presented for
cyclic quadratic groups: an irreducible WPA corresponds to each subgroup of the
quadratic group. As a consequence, the primaries of a RCFT with an order n
integral or half-integral spin simple current may be arranged into multiplets
of length k^2 (where k is a divisor of n) or 3k^2 if the spin of the simple
current is half-integral and k is odd.Comment: Added reference, minor change
Supersymmetric Gauge Theories, Intersecting Branes and Free Fermions
We show that various holomorphic quantities in supersymmetric gauge theories
can be conveniently computed by configurations of D4-branes and D6-branes.
These D-branes intersect along a Riemann surface that is described by a
holomorphic curve in a complex surface. The resulting I-brane carries
two-dimensional chiral fermions on its world-volume. This system can be mapped
directly to the topological string on a large class of non-compact Calabi-Yau
manifolds. Inclusion of the string coupling constant corresponds to turning on
a constant B-field on the complex surface, which makes this space
non-commutative. Including all string loop corrections the free fermion theory
is elegantly formulated in terms of holonomic D-modules that replace the
classical holomorphic curve in the quantum case.Comment: 67 pages, 6 figure
Radiation from Accelerated Branes
The radiation emitted by accelerated fundamental strings and D-branes is
studied within the linear approximation to the supergravity limit of string
theory. We show that scalar, gauge field and gravitational radiation is
generically emitted by such branes. In the case where an external scalar field
accelerates the branes, we derive a Larmor-type formula for the emitted scalar
radiation and study the angular distribution of the outgoing energy flux. The
classical radii of the branes are calculated by means of the corresponding
Thompson scattering cross sections. Within the linear approximation, the
interaction of the external scalar field with the velocity fields of the branes
gives a contribution to the observed gauge field and gravitational radiation.Comment: LaTeX, 25 pages, 2 figures; v2: added comments on the validity of the
linear approximation, minor changes; version to appear in Physical Review
Necessary and sufficient conditions for non-perturbative equivalences of large N orbifold gauge theories
Large N coherent state methods are used to study the relation between U(N)
gauge theories containing adjoint representation matter fields and their
orbifold projections. The classical dynamical systems which reproduce the large
N limits of the quantum dynamics in parent and daughter orbifold theories are
compared. We demonstrate that the large N dynamics of the parent theory,
restricted to the subspace invariant under the orbifold projection symmetry,
and the large N dynamics of the daughter theory, restricted to the untwisted
sector invariant under "theory space'' permutations, coincide. This implies
equality, in the large N limit, between appropriately identified connected
correlation functions in parent and daughter theories, provided the orbifold
projection symmetry is not spontaneously broken in the parent theory and the
theory space permutation symmetry is not spontaneously broken in the daughter.
The necessity of these symmetry realization conditions for the validity of the
large N equivalence is unsurprising, but demonstrating the sufficiency of these
conditions is new. This work extends an earlier proof of non-perturbative large
N equivalence which was only valid in the phase of the (lattice regularized)
theories continuously connected to large mass and strong coupling.Comment: 21 page, JHEP styl
Complex Curve of the Two Matrix Model and its Tau-function
We study the hermitean and normal two matrix models in planar approximation
for an arbitrary number of eigenvalue supports. Its planar graph interpretation
is given. The study reveals a general structure of the underlying analytic
complex curve, different from the hyperelliptic curve of the one matrix model.
The matrix model quantities are expressed through the periods of meromorphic
generating differential on this curve and the partition function of the
multiple support solution, as a function of filling numbers and coefficients of
the matrix potential, is shown to be the quasiclassical tau-function. The
relation to softly broken N=1 supersymmetric Yang-Mills theories is discussed.
A general class of solvable multimatrix models with tree-like interactions is
considered.Comment: 36 pages, 10 figures, TeX; final version appeared in special issue of
J.Phys. A on Random Matrix Theor
Vortices on Higher Genus Surfaces
We consider the topological interactions of vortices on general surfaces. If
the genus of the surface is greater than zero, the handles can carry magnetic
flux. The classical state of the vortices and the handles can be described by a
mapping from the fundamental group to the unbroken gauge group. The allowed
configurations must satisfy a relation induced by the fundamental group. Upon
quantization, the handles can carry ``Cheshire charge.'' The motion of the
vortices can be described by the braid group of the surface. How the motion of
the vortices affects the state is analyzed in detail.Comment: 28 pages with 10 figures; uses phyzzx and psfig; Caltech preprint
CALT-68-187
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