Abstract
We study what we call the all-loop anisotropic bosonized Thirring σ-model. This interpolates between the WZW model and the non-Abelian T-dual of the principal chiral model for a simple group. It has an invariance involving the inversion of the matrix parameterizing the coupling constants. We compute the general renormalization group flow equations which assume a remarkably simple form and derive its properties. For symmetric couplings, they consistently truncate to previous results in the literature. One of the examples we provide gives rise to a first order system of differential equations interpolating between the Lagrange and the Darboux–Halphen integrable systems.
Highlights
Given the above comments it is always exciting if we can obtain the exact RG flow equations for the couplings of a theory. We expect that this could be feasible if the perturbed theory is highly symmetric. Such cases arise when the starting point is a two-dimensional conformal field theory (CFT) with infinitely dimensional current algebra symmetries for the left and the right movers
In a recent development a large family of σ-models was constructed in [8] by a gauging procedure. It interpolates between the Wess–Zumino–Witten (WZW) model and the non-Abelian T-dual of the principal chiral model (PCM) model for a simple group G
The main result of the present paper is the proof of the one-loop renormalizability and the computation of the RG flow equations for the coupling matrix λab of the action (2.6)
Summary
We present the two-dimensional σ-models of interest to us, in a way suitable for studying their behaviour under RG flow in subsequent sections. The form of the general σ-model action is given by [8]. Where E is a real matrix parametrizing the coupling constants of the theory. ∂+Xμ∂−Xν k 12π fabcLa ∧ Lb ∧ Lc. Tr(g1−1∂− g1∂+ g2g2−1) , which is very practical in evaluating the action for specific parametrizations of g ∈ G. If the matrix λ is proportional to the identity, the corresponding σ-model is of special interest since it is integrable. This was proven in [8] by showing that the corresponding metric and antisymmetric tensor fields satisfy the algebraic constraints for integrability of [9] and [15]. A form of the action similar to (2.6) has appeared before in [16], along with related to this action discussion
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