19 research outputs found
Unitary minimal models of SW(3/2,3/2,2) superconformal algebra and manifolds of G_2 holonomy
The SW(3/2,3/2,2) superconformal algebra is a W algebra with two free
parameters. It consists of 3 superconformal currents of spins 3/2, 3/2 and 2.
The algebra is proved to be the symmetry algebra of the coset
(su(2)+su(2)+su(2))/su(2). At the central charge c=21/2 the algebra coincides
with the superconformal algebra associated to manifolds of G_2 holonomy. The
unitary minimal models of the SW(3/2,3/2,2) algebra and their fusion structure
are found. The spectrum of unitary representations of the G_2 holonomy algebra
is obtained.Comment: 34 pages, 2 figures, latex; v2: added examples in appendix D; v3:
published version, corrected typo
Integrable Model of Boundary Interaction: The Paperclip
We consider a model of 2D quantum field theory on a disk, whose bulk dynamics
is that of a two-component free massless Bose field (X,Y), and interaction
occurs at the boundary, where the boundary values (X_B, Y_B) are constrained to
special curve - the ``paperclip brane''. The interaction breaks conformal
invariance, but we argue that it preserves integrability. We propose exact
expression for the disk partition function (and more general overlap amplitudes
of the boundary state with all primary states) in terms of solutions
of certain ordinary linear differential equations.Comment: 41 pages, 2 figure
Dirichlet sigma models and mean curvature flow
The mean curvature flow describes the parabolic deformation of embedded
branes in Riemannian geometry driven by their extrinsic mean curvature vector,
which is typically associated to surface tension forces. It is the gradient
flow of the area functional, and, as such, it is naturally identified with the
boundary renormalization group equation of Dirichlet sigma models away from
conformality, to lowest order in perturbation theory. D-branes appear as fixed
points of this flow having conformally invariant boundary conditions. Simple
running solutions include the paper-clip and the hair-pin (or grim-reaper)
models on the plane, as well as scaling solutions associated to rational (p, q)
closed curves and the decay of two intersecting lines. Stability analysis is
performed in several cases while searching for transitions among different
brane configurations. The combination of Ricci with the mean curvature flow is
examined in detail together with several explicit examples of deforming curves
on curved backgrounds. Some general aspects of the mean curvature flow in
higher dimensional ambient spaces are also discussed and obtain consistent
truncations to lower dimensional systems. Selected physical applications are
mentioned in the text, including tachyon condensation in open string theory and
the resistive diffusion of force-free fields in magneto-hydrodynamics.Comment: 77 pages, 21 figure
The phase diagram of the extended anisotropic ferromagnetic-antiferromagnetic Heisenberg chain
By using Density Matrix Renormalization Group (DMRG) technique we study the
phase diagram of 1D extended anisotropic Heisenberg model with ferromagnetic
nearest-neighbor and antiferromagnetic next-nearest-neighbor interactions. We
analyze the static correlation functions for the spin operators both in- and
out-of-plane and classify the zero-temperature phases by the range of their
correlations. On clusters of sites with open boundary
conditions we isolate the boundary effects and make finite-size scaling of our
results. Apart from the ferromagnetic phase, we identify two gapless spin-fluid
phases and two ones with massive excitations. Based on our phase diagram and on
estimates for the coupling constants known from literature, we classify the
ground states of several edge-sharing materials.Comment: 12 pages, 13 figure
Generalized Drinfeld-Sokolov Reductions and KdV Type Hierarchies
Generalized Drinfeld-Sokolov (DS) hierarchies are constructed through local
reductions of Hamiltonian flows generated by monodromy invariants on the dual
of a loop algebra. Following earlier work of De Groot et al, reductions based
upon graded regular elements of arbitrary Heisenberg subalgebras are
considered. We show that, in the case of the nontwisted loop algebra
, graded regular elements exist only in those Heisenberg
subalgebras which correspond either to the partitions of into the sum of
equal numbers or to equal numbers plus one . We prove that the
reduction belonging to the grade regular elements in the case yields
the matrix version of the Gelfand-Dickey -KdV hierarchy,
generalizing the scalar case considered by DS. The methods of DS are
utilized throughout the analysis, but formulating the reduction entirely within
the Hamiltonian framework provided by the classical r-matrix approach leads to
some simplifications even for .Comment: 43 page
On the Completeness of the Set of Classical W-Algebras Obtained from DS Reductions
We clarify the notion of the DS --- generalized Drinfeld-Sokolov ---
reduction approach to classical -algebras. We first strengthen an
earlier theorem which showed that an embedding can be associated to every DS reduction. We then use the fact that a
\W-algebra must have a quasi-primary basis to derive severe restrictions on
the possible reductions corresponding to a given embedding. In the
known DS reductions found to date, for which the \W-algebras are denoted by
-algebras and are called canonical, the
quasi-primary basis corresponds to the highest weights of the . Here we
find some examples of noncanonical DS reductions leading to \W-algebras which
are direct products of -algebras and `free field'
algebras with conformal weights . We also show
that if the conformal weights of the generators of a -algebra
obtained from DS reduction are nonnegative (which isComment: 48 pages, plain TeX, BONN-HE-93-14, DIAS-STP-93-0
Elliptic hypergeometry of supersymmetric dualities II. Orthogonal groups, knots, and vortices
We consider Seiberg electric-magnetic dualities for 4d SYM
theories with SO(N) gauge group. For all such known theories we construct
superconformal indices (SCIs) in terms of elliptic hypergeometric integrals.
Equalities of these indices for dual theories lead both to proven earlier
special function identities and new conjectural relations for integrals. In
particular, we describe a number of new elliptic beta integrals associated with
the s-confining theories with the spinor matter fields. Reductions of some
dualities from SP(2N) to SO(2N) or SO(2N+1) gauge groups are described.
Interrelation of SCIs and the Witten anomaly is briefly discussed. Possible
applications of the elliptic hypergeometric integrals to a two-parameter
deformation of 2d conformal field theory and related matrix models are
indicated. Connections of the reduced SCIs with the state integrals of the knot
theory, generalized AGT duality for (3+3)d theories, and a 2d vortex partition
function are described.Comment: Latex, 58 pages; paper shortened, to appear in Commun. Math. Phy