G/G gauged WZW model and Bethe Ansatz for the phase model

Abstract

We investigate the G/G gauged Wess-Zumino-Witten model on a Riemann surface from the point of view of the algebraic Bethe Ansatz for the phase model. After localization procedure is applied to the G/G gauged Wess-Zumino-Witten model, the diagonal components for group elements satisfy Bethe Ansatz equations for the phase model. We show that the partition function of the G/G gauged Wess-Zumino-Witten model is identified as the summation of norms with respect to all the eigenstates of the Hamiltonian with the fixed number of particles in the phase model. We also consider relations between the Chern-Simons theory on $S^1\times {\Sigma }_h$ and the phase model.

arXiv comment15 pages.v2: published version

References in corpus (20)

• Quantum Inverse Scattering Method and Correlation Functions
• Two Dimensional Gauge Theories Revisited
• Supersymmetric vacua and Bethe ansatz
• Integrating Over Higgs Branches
• Partition functions of N=(2,2) gauge theories on S^2 and vortices
• Exact Results in D=2 Supersymmetric Gauge Theories
• Quantum integrability and supersymmetric vacua
• Derivation of the Verlinde Formula from Chern-Simons Theory and the G/G model
• Correlation functions for a strongly correlated boson system
• Chern-Simons Theory on S^1-Bundles: Abelianisation and q-deformed Yang-Mills Theory
• Cohomological localization of Chern-Simons theory
• The sl(n)-WZNW Fusion Ring: a combinatorial construction and a realisation as quotient of quantum cohomology
• Higgs Bundles, Gauge Theories and Quantum Groups
• Non-Abelian Localization for Supersymmetric Yang-Mills-Chern-Simons Theories on Seifert Manifold
• Level-rank duality of the U(N) WZW model, Chern-Simons theory, and 2d qYM theory
• $G/G$--Topological Field Theories by Cosetting $G_k$
• Localization in GWZW and Verlinde formula
• Volume of Moduli Space of Vortex Equations and Localization
• Correlators of the phase model
• On Affine Fusion and the Phase Model

Cited by in corpus (15)

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• K-theoretic boson-fermion correspondence and melting crystals
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• Higgs and Coulomb Branch Descriptions of the Volume of the Vortex Moduli Space
• Gauge/Bethe correspondence on $S^1\times {\Sigma }_h$ and index over moduli space
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