1,442 research outputs found
A New Supersymmetric Extension of Conformal Mechanics
In this paper a new supersymmetric extension of conformal mechanics is put
forward. The beauty of this extension is that all variables have a clear
geometrical meaning and the super-Hamiltonian turns out to be the
Lie-derivative of the Hamiltonian flow of standard conformal mechanics. In this
paper we also provide a supersymmetric extension of the other conformal
generators of the theory and find their "square-roots". The whole superalgebra
of these charges is then analyzed in details. We conclude the paper by showing
that, using superfields, a constraint can be built which provides the exact
solution of the system.Comment: 11 pages, no figure
Wavefunctions and counting formulas for quasiholes of clustered quantum Hall states on a sphere
The quasiholes of the Read-Rezayi clustered quantum Hall states are
considered, for any number of particles and quasiholes on a sphere, and for any
degree k of clustering. A set of trial wavefunctions, that are zero-energy
eigenstates of a k+1-body interaction, and so are symmetric polynomials that
vanish when any k+1 particle coordinates are equal, is obtained explicitly and
proved to be both complete and linearly independent. Formulas for the number of
states are obtained, without the use of (but in agreement with) conformal field
theory, and extended to give the number of states for each angular momentum. An
interesting recursive structure emerges in the states that relates those for k
to those for k-1. It is pointed out that the same numbers of zero-energy states
can be proved to occur in certain one-dimensional models that have recently
been obtained as limits of the two-dimensional k+1-body interaction
Hamiltonians, using results from the combinatorial literature.Comment: 9 pages. v2: minor corrections; additional references; note added on
connection with one-dimensional Hamiltonians of recent interes
Embedding of the Lie superalgebra into the Lie superalgebra of pseudodifferential symbols on
We obtain an embedding of a one-parameter family of exceptional simple Lie
superalgebras into the Lie superalgebra of
pseudodifferential symbols on the supercircle . Correspondingly, there
is an embedding of into a nontrivial central extension of
the derived contact superconformal algebra realized in terms of
matrices over a Weyl algebra.Comment: 19 pages, LaTex, to be published in J.Math. Phy
Highest weight representations of the quantum algebra U_h(gl_\infty)
A class of highest weight irreducible representations of the quantum algebra
U_h(gl_\infty) is constructed. Within each module a basis is introduced and the
transformation relations of the basis under the action of the Chevalley
generators are explicitly written.Comment: 7 pages, PlainTe
Rigorous Proof of a Liquid-Vapor Phase Transition in a Continuum Particle System
We consider particles in , interacting via attractive
pair and repulsive four-body potentials of the Kac type. Perturbing about mean
field theory, valid when the interaction range becomes infinite, we prove
rigorously the existence of a liquid-gas phase transition when the interaction
range is finite but long compared to the interparticle spacing.Comment: 11 pages, in ReVTeX, e-mail addresses: [email protected],
[email protected], [email protected]
Weight Vectors of the Basic A_1^(1)-Module and the Littlewood-Richardson Rule
The basic representation of \A is studied. The weight vectors are
represented in terms of Schur functions. A suitable base of any weight space is
given. Littlewood-Richardson rule appears in the linear relations among weight
vectors.Comment: February 1995, 7pages, Using AMS-Te
Finite energy shifts in SU(n) supersymmetric Yang-Mills theory on T^3xR at weak coupling
We consider a semi-classical treatment, in the regime of weak gauge coupling,
of supersymmetric Yang-Mills theory in a space-time of the form T^3xR with
SU(n)/Z_n gauge group and a non-trivial gauge bundle. More specifically, we
consider the theories obtained as power series expansions around a certain
class of normalizable vacua of the classical theory, corresponding to isolated
points in the moduli space of flat connections, and the perturbative
corrections to the free energy eigenstates and eigenvalues in the weakly
interacting theory. The perturbation theory construction of the interacting
Hilbert space is complicated by the divergence of the norm of the interacting
states. Consequently, the free and interacting Hilbert furnish unitarily
inequivalent representation of the algebra of creation and annihilation
operators of the quantum theory. We discuss a consistent redefinition of the
Hilbert space norm to obtain the interacting Hilbert space and the properties
of the interacting representation. In particular, we consider the lowest
non-vanishing corrections to the free energy spectrum and discuss the crucial
importance of supersymmetry for these corrections to be finite.Comment: 31 pages, 1 figure, v4 Minor changes, references correcte
Quantum R-matrix and Intertwiners for the Kashiwara Algebra
We study the algebra presented by Kashiwara and introduce
intertwiners similar to -vertex operators. We show that a matrix determined
by 2-point functions of the intertwiners coincides with a quantum R-matrix (up
to a diagonal matrix) and give the commutation relations of the intertwiners.
We also introduce an analogue of the universal R-matrix for the Kashiwara
algebra.Comment: 21 page
Instantons, supersymmetric vacua, and emergent geometries
We study instanton solutions and superpotentials for the large number of
vacua of the plane-wave matrix model and a 2+1 dimensional Super Yang-Mills
theory on with sixteen supercharges. We get the superpotential in
the weak coupling limit from the gauge theory description. We study the gravity
description of these instantons. Perturbatively with respect to a background,
they are Euclidean branes wrapping cycles in the dual gravity background.
Moreover, the superpotential can be given by the energy of the electric charge
system characterizing each vacuum. These charges are interpreted as the
eigenvalues of matrices from a reduction for the 1/8 BPS sector of the gauge
theories. We also discuss qualitatively the emergence of the extra spatial
dimensions appeared on the gravity side.Comment: 29 pages, 3 figures, latex. v2: references added, comments added. v3:
accepted version in PR
- …