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Integrable interpolations: From exact CFTs to non-Abelian T-duals (1312.4560v3)

Published 16 Dec 2013 in hep-th, math-ph, and math.MP

Abstract: We derive two new classes of integrable theories interpolating between exact CFT WZW or gauged WZW models and non-Abelian T-duals of principal chiral models or geometric coset models. They are naturally constructed by gauging symmetries of integrable models. Our analysis implies that non-Abelian T-duality preserves integrability and suggests a novel way to understand the global properties of the corresponding backgrounds.

Citations (306)

Summary

  • The paper introduces new integrable models that interpolate between exact CFT WZW models and their non-Abelian T-duals using refined algebraic methods.
  • It extends the interpolation technique to coset models through parafermionic perturbations while maintaining classical integrability with Poisson bracket algebras.
  • The findings offer potential advances in understanding duality symmetries, renormalization group flows, and their applications in string theory.

Integrable Interpolations: From Exact CFTs to Non-Abelian T-duals

The paper "Integrable interpolations: From exact CFTs to non-Abelian T-duals" presents an intricate paper of integrable models that connect exact Conformal Field Theories (CFTs) and non-Abelian T-dualities. It achieves this through innovative extensions of the well-established frameworks of Wess–Zumino–Witten (WZW) models and Principal Chiral Models (PCMs). The authors successfully construct new classes of integrable theories in two dimensions by interpolating between these known regimes, thereby broadening the utility of integrable models in theoretical physics.

Core Contributions

The paper's primary contribution is twofold. Firstly, it proposes new integrable models that interpolate between exact CFT WZW models and their non-Abelian T-duals, demonstrating integrability through a refined algebraic approach. This is achieved by leveraging gauged symmetries, particularly focusing on the symmetry structure inherent within these theories.

Secondly, the research extends the interpolation method to include coset models, hence presenting a more comprehensive family of integrable models. By using parafermionic perturbations, these models navigate from gauged WZW formulations of coset CFTs to their non-Abelian T-duals.

Methodology and Analytic Derivations

The paper systematically derives integrable conditions by examining Hamiltonian equations derived from current algebras associated with different symmetry groups. For instance, the integrable models are explicitly solved for the SU(2) group, where existing methods previously relied on brute force. The solutions were generalized to any group G with non-singular σ-model fields, demonstrated through thorough analytic derivations, ensuring these theories retain integrability across transitions.

Additionally, by exploring the algebraic structures, the work employs Poisson bracket algebras to enhance the canonical and algebraic structures needed to uphold integrability. The derivations make extensive use of frames, spin connections, and anisotropic tensors, facilitating clear conditions under which classical integrability is maintained.

Theoretical and Practical Implications

The implications of this research are significant in both the practical understanding of dualities in string theory and theoretical advancements in integrable systems. By structurally connecting exact CFTs with non-Abelian T-duals, the work suggests mechanisms that can bridge essential symmetries and facilitate further exploration within the field of high energy physics and string theory.

Moreover, the paper's methodologies may find applications in analyzing renormalization group flows and exploring underlying algebraic structures such as Yangian algebras within integrable models. The authors hint at the potential to discover novel solutions and general conditions for integrability, influencing future research directions in theoretical physics.

Future Directions

This work opens several avenues for future exploration—specifically, the investigation into the renormalization group behavior offers intriguing questions, such as whether the interpolations inherently flow from UV CFTs to IR non-Abelian T-duals. The analysis encourages the search for integrable models with non-zero parameter ρ and anisotropic extensions, which could further generalize the findings presented.

Additionally, there's potential to apply these developments in broader contexts, including supergravity and the AdS/CFT correspondence, where integrable deformations could play crucial roles. Exploring these extensions could yield new insights into the gauge/gravity duality, possibly offering interpretations of physical phenomena in string-inspired models.

In summary, this paper significantly advances the understanding of integrable models. By establishing connections between disparate theoretical constructs, the authors not only expand the scope of known integrable theories but also provide a robust framework for further explorations within duality symmetries and integrable systems in field theory.