Chiral sine-Gordon model

Abstract

We investigate the chiral sine-Gordon model using the renormalization group method. The chiral sine-Gordon model is a model for $G$-valued fields and describes a new class of phase transitions, where $G$ is a compact Lie group. We show that the model is renormalizable by means of a perturbation expansion and we derive beta functions of the renormalization group theory. The coefficients of beta functions are represented by the Casimir invariants. The model contains both asymptotically free and ultraviolet strong coupling regions. The beta functions have a zero which is a bifurcation point that divides the parameter space into two regions; they are the weak coupling region and the strong coupling region. A large-$N$ model is also considered. This model is reduced to the conventional sine-Gordon model that describes the Kosterlitz-Thouless transition near the fixed point. In the strong-coupling limit, the model is reduced to a $U(N)$ matrix model.

6 pages; dimension d=2-epsilon

References in corpus (3)

• Non-Abelian Sine-Gordon Solitons
• Experimental observation of a first-order phase transition below the superconducting transition temperature in the multilayer cuprate superconductor HgBa${}_2$Ca${}_4$Cu${}_5$O${}_y$
• Fluctuation-induced Nambu-Goldstone bosons in a Higgs-Josephson model

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• Field theoretical model of multi-layered Josephson junction and dynamics of Josephson vortices
• Nambu-Goldstone bosons characterized by the order parameter in spontaneous symmetry breaking
• Exact Renormalization Group and Sine Gordon Theory
• Holographic Beta functions for the Generalized Sine Gordon Theory
• Renormalization group analysis of the hyperbolic sine-Gordon model -- Asymptotic freedom from cosh interaction --
• Renormalization group theory of generalized multi-vertex sine-Gordon model