Integrable deformed $T^{1,1}$ sigma models from 4D Chern-Simons theory

Abstract

Recently, a variety of deformed $T^{1,1}$ manifolds, with which 2D non-linear sigma models (NLSMs) are classically integrable, have been presented by Arutyunov, Bassi and Lacroix (ABL) [arXiv:2010.05573]. We refer to the NLSMs with the integrable deformed $T^{1,1}$ as the ABL model for brevity. Motivated by this progress, we consider deriving the ABL model from a 4D Chern-Simons (CS) theory with a meromorphic one-form with four double poles and six simple zeros. We specify boundary conditions in the CS theory that give rise to the ABL model and derive the sigma-model background with target-space metric and anti-symmetric two-form. Finally, we present two simple examples 1) an anisotropic $T^{1,1}$ model and 2) a $G/H$ $\lambda$-model. The latter one can be seen as a one-parameter deformation of the Guadagnini-Martellini-Mintchev model.

arXiv comment23 pages: minor modifications, references added

References in corpus (43)

• Gauge Theory Correlators from Non-Critical String Theory
• The Large N Limit of Superconformal Field Theories and Supergravity
• Review of AdS/CFT Integrability: An Overview
• Superconformal Field Theory on Threebranes at a Calabi-Yau Singularity
• Deforming field theories with $U(1)\times U(1)$ global symmetry and their gravity duals
• On integrability of the Yang-Baxter $\si$-model
• Large N Limit of Non-Commutative Gauge Theories
• An integrable deformation of the AdS_5 x S^5 superstring action
• Lax Pair for Strings in Lunin-Maldacena Background
• Yang-Baxter $\sigma$-models and dS/AdS T-duality
• Comments on string theory backgrounds with non-relativistic conformal symmetry
• Integrable interpolations: From exact CFTs to non-Abelian T-duals
• Non-Commutative Yang-Mills and the AdS/CFT Correspondence
• Heating up Galilean holography
• Hot Spacetimes for Cold Atoms
• Derivation of the action and symmetries of the q-deformed AdS_5 x S^5 superstring
• Jordanian deformations of the AdS_5xS^5 superstring
• An Integrable Deformation of the AdS5 x S5 Superstring
• Integrability of the bi-Yang-Baxter sigma-model
• Integrable Deformations of Strings on Symmetric Spaces
• Chaos Rules out Integrability of Strings in AdS_5 x T^{1,1}
• Chaos in the Gauge/Gravity Correspondence
• Analytic Non-integrability in String Theory
• Chaos around Holographic Regge Trajectories
• Integrability Lost
• A unifying 2d action for integrable $\sigma$-models from 4d Chern-Simons theory
• Chaotic strings in a near Penrose limit of AdS${}_5\times T^{1,1}$
• Assembling integrable sigma-models as affine Gaudin models
• The Chern-Simons Origin of Superstring Integrability
• The non-integrability of $L^{a,b,c}$ quiver gauge theories
• Integrable sigma models and 2-loop RG flow
• Conformal Sigma Models for a Class of $T^{p,q}$ Spaces
• The fate of chaotic strings in a confining geometry
• Comments on $\eta$-deformed principal chiral model from 4D Chern-Simons theory
• Integrable $\mathcal{E}$-Models, 4d Chern-Simons Theory and Affine Gaudin Models. I. Lagrangian Aspects
• On the Zakharov-Mikhailov action: $4$d Chern-Simons origin and covariant Poisson algebra of the Lax connection
• New integrable coset sigma models
• An exact symmetry in $\lambda$-deformed CFTs
• Yang-Baxter deformations of the AdS${}_5\times$S${}^5$ supercoset sigma model from 4D Chern-Simons theory
• The Faddeev-Reshetikhin model from a 4D Chern-Simons theory
• Holomorphic Chern-Simons theory and lambda models: PCM case
• Integrability vs. RG flow in $G\times G$ and $G\times G/H$ sigma models
• Yang-Baxter Deformations of the $Ad{S}_5\times T^{1,1}$ Superstring and their Backgrounds

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