$T\overline{T}$ deformation in SCFTs and integrable supersymmetric theories

Abstract

We calculate the $\mathcal{S}$-multiplets for two-dimensional Euclidean $\mathcal{N}=(0,2)$ and $\mathcal{N}=(2,2)$ superconformal field theories under the $T\overline{T}$ deformation at leading order of perturbation theory in the deformation coupling. Then, from these $\mathcal{N}=(0,2)$ deformed multiplets, we calculate two- and three-point correlators. We show the $\mathcal{N}=(0,2)$ chiral ring's elements do not flow under the $T\overline{T}$ deformation. Specializing to integrable supersymmetric seed theories, such as $\mathcal{N}=(2,2)$ Landau-Ginzburg models, we use the thermodynamic Bethe ansatz to study the S-matrices and ground state energies. From both an S-matrix perspective and Melzer's folding prescription, we show that the deformed ground state energy obeys the inviscid Burgers' equation. Finally, we show that several indices independent of $D$-term perturbations including the Witten index, Cecotti-Fendley-Intriligator-Vafa index and elliptic genus do not flow under the $T\overline{T}$ deformation.

arXiv comment46 pages; v2 published version; v3 typos fixed

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• $T\bar{T}$ in JT Gravity and BF Gauge Theory
• Field Theory of Interacting Boundary Gravitons
• Correlation Functions in $\text{T}\bar{\text{T}}$-deformed Conformal Field Theories
• Stress Tensor Flows, Birefringence in Non-Linear Electrodynamics, and Supersymmetry
• $T\bar{T}$ flow as characteristic flows
• $T\overline{T}$ Deformations of Supersymmetric Quantum Mechanics
• ModMax Oscillators and Root-$T\overline{T}$-Like Flows in Supersymmetric Quantum Mechanics
• $T\overline{T}$-Like Flows and $3d$ Nonlinear Supersymmetry
• Flows in the Space of Interacting Chiral Boson Theories
• Deforming the ODE/IM correspondence with $\mathrm{T}\bar{\mathrm{T}}$
• Renormalisation in $\text{T}\bar{\text{T}}$-Deformed (Non-)Integrable Theories
• Supersymmetric black holes and $T\bar{T}$ deformation
• Aspects of $T\bar{T}+J\bar{T}$ deformed Schwarzian: From gravity partition function to late-time spectral form factor
• $T\overline{T}$-deformed free energy of the Airy model
• Correlation Functions in $\text{T}\bar{\text{T}}$-deformed Theories on the Torus
• Systematic approach to correlators in $T\bar{T}$ deformed CFTs