1,296 research outputs found
Baxter Equation for Quantum Discrete Boussinesq Equation
Studied is the Baxter equation for the quantum discrete Boussinesq equation.
We explicitly construct the Baxter operator from a generating
function of the local integrals of motion of the affine Toda lattice field
theory, and show that it solves the third order operator-valued difference
equation.Comment: 25 page
Difference equation of the colored Jones polynomial for torus knot
We prove that the N-colored Jones polynomial for the torus knot T_{s,t}
satisfies the second order difference equation, which reduces to the first
order difference equation for a case of T_{2,2m+1}. We show that the
A-polynomial of the torus knot can be derived from this difference equation.
Also constructed is a q-hypergeometric type expression of the colored Jones
polynomial for T_{2,2m+1}.Comment: 7 page
Supersymmetric Polychronakos Spin Chain: Motif, Distribution Function, and Character
Degeneracy patterns and hyper-multiplet structure in the spectrum of the
su() supersymmetric Polychronakos spin chain are studied by use of the
"motif''. Using the recursion relation of the supersymmetric Rogers-Szeg{\"o}
polynomials which are closely related to the partition function of the spin
chain, we give the representation for motif in terms of the supersymmetric skew
Young diagrams. We also study the distribution function for quasi-particles.
The character formulae for are briefly discussed.Comment: 24 pages + 1 figure, to appear in Nucl. Phys.
Dimensional Reduction by Conformal Bootstrap
The dimensional reductions in the branched polymer and the random field Ising
model (RFIM) are discussed by a conformal bootstrap method. The small size
minors are applied for the evaluations of the scale dimensions of these two
models and the results are compared to D'=D-2 dimensional Yang-Lee edge
singularity and to pure D'=D-2 dimensional Ising model, respectively. For the
former case, the dimensional reduction is shown to be valid for , and for the latter case, the deviation from the dimensional reduction can
be seen below five dimensions.Comment: 23 page, 13 figure
Hyperbolicity of Partition Function and Quantum Gravity
We study a geometry of the partition function which is defined in terms of a
solution of the five-term relation. It is shown that the 3-dimensional
hyperbolic structure or Euclidean AdS_3 naturally arises in the classical limit
of this invariant. We discuss that the oriented ideal tetrahedron can be
assigned to the partition function of string.Comment: 16 pages, 4 figure
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