Journal of Physics A Mathematical and General

General solutions to fundamental problems of SU(2)kWZW models

Bo-Yu Hou, Kang Li, Pei Wang

Published Aug 7, 1990• 0 citations

Abstract

The authors give solutions to fundamental problems of the Wess-Zumino-Witten model for general cases. They also find the explicit connection between the crossing matrices of the SU(2) k WZW model and the crossing matrices of the SL(2,q) quantum group; the latter are the quantum Racah coefficients.

DOI: 10.1088/0305-4470/23/15/018

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Journal of Physics A Mathematical and General

General solutions to fundamental problems of SU(2)kWZW models

Bo-Yu Hou, Kang Li, Pei Wang

Published Aug 7, 1990• 0 citations

Publisher

Abstract

DOI: 10.1088/0305-4470/23/15/018

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The authors have identified critical points in the Wess-Zumino-Witten (WZW) SU(2)

{}_{5}

universality class in the phase diagram of a spin-5/2 chain with frustrated next-nearest-neighbor and 3-site interactions, providing a concrete example of this universality class in a realistic, nonintegrable model. These points lie on a transition line to a dimerized phase and occur when the transition turns from first order into WZW SU(2)

{}_{3}

in agreement with the generic possibilities allowed by field theory arguments.

We suggest the possibility that the two-dimensional

\mathrm{SU}{(2)}_{k}

Wess-Zumino-Witten (WZW) theory, which has global

\mathrm{SO}(4)

symmetry, can be continued to $2+\ensuremath{\epsilon}$ dimensions by enlarging the symmetry to $\mathrm{SO}(4+\ensuremath{\epsilon})$. This is motivated by the three-dimensional sigma model with

\mathrm{SO}(5)

symmetry and a WZW term, which is relevant to deconfined criticality. If such a continuation exists, the structure of the renormalization group flows at small $\ensuremath{\epsilon}$ may be fixed by assuming analyticity in $\ensuremath{\epsilon}$. This leads to the conjecture that the WZW fixed point annihilates with a new, unstable fixed point at a critical dimensionality

{d}_{c}>2

. We suggest that

{d}_{c}<3

for all

k

, and we compute

{d}_{c}

in the limit of large

k

. The flows support the conjecture that the deconfined phase transition in

\mathrm{SU}(2)

magnets is a ``pseudocritical'' point with approximate

\mathrm{SO}(5)

, controlled by a fixed point slightly outside the physical parameter space.