1,581 research outputs found
Minimal Models of CFT on Z_N-Surfaces
The conformal field theory on a Z_N-surface is studied by mapping it on the
branched sphere. Using a coulomb gas formalism we construct the minimal models
of the theory.Comment: 16 pages, latex, no figures; two important early references on the
coset construction have been included; to appear in Mod. Phys. Let
Lie superalgebras and irreducibility of A_1^(1)-modules at the critical level
We introduce the infinite-dimensional Lie superalgebra and
construct a family of mappings from certain category of -modules
to the category of A_1^(1)-modules of critical level. Using this approach, we
prove the irreducibility of a family of A_1^(1)-modules at the critical level.
As a consequence, we present a new proof of irreducibility of certain
Wakimoto modules. We also give a natural realizations of irreducible quotients
of relaxed Verma modules and calculate characters of these representations.Comment: 21 pages, Late
On a class of representations of the Yangian and moduli space of monopoles
A new class of infinite dimensional representations of the Yangians
and corresponding to a complex semisimple algebra
and its Borel subalgebra is constructed.
It is based on the generalization of the Drinfeld realization of ,
in terms of quantum minors to the case of an arbitrary
semisimple Lie algebra . The Poisson geometry associated with the
constructed representations is described. In particular it is shown that the
underlying symplectic leaves are isomorphic to the moduli spaces of
-monopoles defined as the components of the space of based maps of
into the generalized flag manifold . Thus the constructed
representations of the Yangian may be considered as a quantization of the
moduli space of the monopoles.Comment: 16 pages, LaTex2e, some misprints are fixe
Density of States for a Specified Correlation Function and the Energy Landscape
The degeneracy of two-phase disordered microstructures consistent with a
specified correlation function is analyzed by mapping it to a ground-state
degeneracy. We determine for the first time the associated density of states
via a Monte Carlo algorithm. Our results are described in terms of the
roughness of the energy landscape, defined on a hypercubic configuration space.
The use of a Hamming distance in this space enables us to define a roughness
metric, which is calculated from the correlation function alone and related
quantitatively to the structural degeneracy. This relation is validated for a
wide variety of disordered systems.Comment: Accepted for publication in Physical Review Letter
Jack superpolynomials with negative fractional parameter: clustering properties and super-Virasoro ideals
The Jack polynomials P_\lambda^{(\alpha)} at \alpha=-(k+1)/(r-1) indexed by
certain (k,r,N)-admissible partitions are known to span an ideal I^{(k,r)}_N of
the space of symmetric functions in N variables. The ideal I^{(k,r)}_N is
invariant under the action of certain differential operators which include half
the Virasoro algebra. Moreover, the Jack polynomials in I^{(k,r)}_N admit
clusters of size at most k: they vanish when k+1 of their variables are
identified, and they do not vanish when only k of them are identified. We
generalize most of these properties to superspace using orthogonal
eigenfunctions of the supersymmetric extension of the trigonometric
Calogero-Moser-Sutherland model known as Jack superpolynomials. In particular,
we show that the Jack superpolynomials P_{\Lambda}^{(\alpha)} at
\alpha=-(k+1)/(r-1) indexed by certain (k,r,N)-admissible superpartitions span
an ideal {\mathcal I}^{(k,r)}_N of the space of symmetric polynomials in N
commuting variables and N anticommuting variables. We prove that the ideal
{\mathcal I}^{(k,r)}_N is stable with respect to the action of the
negative-half of the super-Virasoro algebra. In addition, we show that the Jack
superpolynomials in {\mathcal I}^{(k,r)}_N vanish when k+1 of their commuting
variables are equal, and conjecture that they do not vanish when only k of them
are identified. This allows us to conclude that the standard Jack polynomials
with prescribed symmetry should satisfy similar clustering properties. Finally,
we conjecture that the elements of {\mathcal I}^{(k,2)}_N provide a basis for
the subspace of symmetric superpolynomials in N variables that vanish when k+1
commuting variables are set equal to each other.Comment: 36 pages; the main changes in v2 are : 1) in the introduction, we
present exceptions to an often made statement concerning the clustering
property of the ordinary Jack polynomials for (k,r,N)-admissible partitions
(see Footnote 2); 2) Conjecture 14 is substantiated with the extensive
computational evidence presented in the new appendix C; 3) the various tests
supporting Conjecture 16 are reporte
Mirror symmetry in two steps: A-I-B
We suggest an interpretation of mirror symmetry for toric varieties via an
equivalence of two conformal field theories. The first theory is the twisted
sigma model of a toric variety in the infinite volume limit (the A-model). The
second theory is an intermediate model, which we call the I-model. The
equivalence between the A-model and the I-model is achieved by realizing the
former as a deformation of a linear sigma model with a complex torus as the
target and then applying to it a version of the T-duality. On the other hand,
the I-model is closely related to the twisted Landau-Ginzburg model (the
B-model) that is mirror dual to the A-model. Thus, the mirror symmetry is
realized in two steps, via the I-model. In particular, we obtain a natural
interpretation of the superpotential of the Landau-Ginzburg model as the sum of
terms corresponding to the components of a divisor in the toric variety. We
also relate the cohomology of the supercharges of the I-model to the chiral de
Rham complex and the quantum cohomology of the underlying toric variety.Comment: 50 pages; revised versio
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
A braided Yang-Baxter Algebra in a Theory of two coupled Lattice Quantum KdV: algebraic properties and ABA representations
A generalization of the Yang-Baxter algebra is found in quantizing the
monodromy matrix of two (m)KdV equations discretized on a space lattice. This
braided Yang-Baxter equation still ensures that the transfer matrix generates
operators in involution which form the Cartan sub-algebra of the braided
quantum group. Representations diagonalizing these operators are described
through relying on an easy generalization of Algebraic Bethe Ansatz techniques.
The conjecture that this monodromy matrix algebra leads, {\it in the cylinder
continuum limit}, to a Perturbed Minimal Conformal Field Theory description is
analysed and supported.Comment: Latex file, 46 page
Fock space resolutions of the Virasoro highest weight modules with c<=1
We extend Felder's construction of Fock space resolutions for the Virasoro
minimal models to all irreducible modules with . In particular, we
provide resolutions for the representations corresponding to the boundary and
exterior of the Kac table.Comment: 14 pages, revised versio
Fermionic formulas for eigenfunctions of the difference Toda Hamiltonian
We use the Whittaker vectors and the Drinfeld Casimir element to show that
eigenfunctions of the difference Toda Hamiltonian can be expressed via
fermionic formulas. Motivated by the combinatorics of the fermionic formulas we
use the representation theory of the quantum groups to prove a number of
identities for the coefficients of the eigenfunctions.Comment: 33 pages, Late
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