Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Green-Schwarz Strings in TsT-transformed backgrounds

L. F. Alday, G. Arutyunov, S. Frolov

TL;DR

The paper develops a general framework to study Green-Schwarz strings in backgrounds obtained by TsT transformations, proving a universal relation between angle variables and showing that twisted boundary conditions fully capture the deformed dynamics while preserving integrability. It applies the method to γ_i-deformed AdS5×S5, deriving the twisted boundary conditions for bosons and fermions and constructing the Lax pair and monodromy matrix for the deformed theory, implying the existence of finite-gap structures. By connecting the deformed string dynamics to twisted strings in the original background, the authors provide a robust approach to extract classical spectra and explore fermionic Neumann-Rosochatius generalizations for zero modes. This framework has implications for understanding holographic duals of β-deformed and nonsupersymmetric gauge theories, and sets the stage for quantization and 1/J corrections in deformed backgrounds.

Abstract

We consider classical strings propagating in a background generated by a sequence of TsT transformations. We describe a general procedure to derive the Green-Schwarz action for strings. We show that the U(1) isometry variables of the TsT-transformed background are related to the isometry variables of the initial background in a universal way independent of the details of the background. This allows us to prove that strings in the TsT-transformed background are described by the Green-Schwarz action for strings in the initial background subject to twisted boundary conditions. Our construction implies that a TsT transformation preserves integrability properties of the string sigma model. We discuss in detail type IIB strings propagating in the \g_i-deformed AdS_5 x S^5 space-time, find the twisted boundary conditions for bosons and fermions, and use them to write down an explicit expression for the monodromy matrix. We also discuss string zero modes whose dynamics is governed by a fermionicgeneralization of the integrable Neumann model.

Green-Schwarz Strings in TsT-transformed backgrounds

TL;DR

The paper develops a general framework to study Green-Schwarz strings in backgrounds obtained by TsT transformations, proving a universal relation between angle variables and showing that twisted boundary conditions fully capture the deformed dynamics while preserving integrability. It applies the method to γ_i-deformed AdS5×S5, deriving the twisted boundary conditions for bosons and fermions and constructing the Lax pair and monodromy matrix for the deformed theory, implying the existence of finite-gap structures. By connecting the deformed string dynamics to twisted strings in the original background, the authors provide a robust approach to extract classical spectra and explore fermionic Neumann-Rosochatius generalizations for zero modes. This framework has implications for understanding holographic duals of β-deformed and nonsupersymmetric gauge theories, and sets the stage for quantization and 1/J corrections in deformed backgrounds.

Abstract

We consider classical strings propagating in a background generated by a sequence of TsT transformations. We describe a general procedure to derive the Green-Schwarz action for strings. We show that the U(1) isometry variables of the TsT-transformed background are related to the isometry variables of the initial background in a universal way independent of the details of the background. This allows us to prove that strings in the TsT-transformed background are described by the Green-Schwarz action for strings in the initial background subject to twisted boundary conditions. Our construction implies that a TsT transformation preserves integrability properties of the string sigma model. We discuss in detail type IIB strings propagating in the \g_i-deformed AdS_5 x S^5 space-time, find the twisted boundary conditions for bosons and fermions, and use them to write down an explicit expression for the monodromy matrix. We also discuss string zero modes whose dynamics is governed by a fermionicgeneralization of the integrable Neumann model.

Paper Structure

This paper contains 11 sections, 88 equations.

Table of Contents

  1. Introduction
  2. The $\gamma$-deformed action
  3. Green-Schwarz strings in $\gamma_i$-deformed ${\rm AdS}_5\times {\rm S}^5$
  4. Superstring on ${\rm AdS}_5\times {\rm S}^5$ as the coset sigma-model
  5. Fermions twisting
  6. Lax Pair and Monodromy Matrix
  7. Spinning particle and Neumann model
  8. Conclusion
  9. T-duality Transformation and Rules
  10. The background after TsT transformation
  11. The matrices