$T\bar{T}$ Flows and (2,2) Supersymmetry

Abstract

We construct a solvable deformation of two-dimensional theories with $(2,2)$ supersymmetry using an irrelevant operator which is a bilinear in the supercurrents. This supercurrent-squared operator is manifestly supersymmetric, and equivalent to $T\bar{T}$ after using conservation laws. As illustrative examples, we deform theories involving a single $(2,2)$ chiral superfield. We show that the deformed free theory is on-shell equivalent to the $(2,2)$ Nambu-Goto action. At the classical level, models with a superpotential exhibit more surprising behavior: the deformed theory exhibits poles in the physical potential which modify the vacuum structure. This suggests that irrelevant deformations of $T\overline{T}$ type might also affect infrared physics.

arXiv comment39 pages

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• Root-$T\overline{T}$ Deformations in Two-Dimensional Quantum Field Theories
• Entanglement and Rényi Entropy of Multiple Intervals in $T\overline{T}$-Deformed CFT and Holography
• Correlation functions of the CFTs on torus with $T\bar{T}$ deformation
• $T\bar{T}$ deformations and integrable spin chains
• $T\overline{T}$, $\tilde{J}J$, $JT$ and $\tilde{J}T$ deformations
• Flow equations for generalised $T\bar{T}$ deformations
• The correlation function of (1,1) and (2,2) supersymmetric theories with $T\bar{T}$ deformation
• $T\bar{T}$-like Flows in Non-linear Electrodynamic Theories and S-duality
• Duality-Invariant Non-linear Electrodynamics and Stress Tensor Flows
• On the Classical Integrability of Root-$T\overline{T}$ Flows
• Non-Linear Supersymmetry and $T\bar{T}$-like Flows
• $T\bar{T}$ in JT Gravity and BF Gauge Theory
• A Non-Abelian Analogue of DBI from $T\overline{T}$
• Heating up holography for single-trace $J\bar{T}$ deformations
• Sequential Flows by Irrelevant Operators
• Stress Tensor Flows, Birefringence in Non-Linear Electrodynamics, and Supersymmetry
• Root-$T\overline{T}$ Deformed Boundary Conditions in Holography
• $T\bar{T}$-flow effects on torus partition functions
• $T\overline{T}$ Deformations of Supersymmetric Quantum Mechanics
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• $T\bar{T}$-deformation and Liouville gravity
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• ModMax Oscillators and Root-$T\overline{T}$-Like Flows in Supersymmetric Quantum Mechanics
• $T\bar{T}$ deformed YM${}_2$ on general backgrounds from an integral transformation
• Flows in the Space of Interacting Chiral Boson Theories
• $T\overline{T}$ Deformations of nonrelativistic models
• Exact $T\overline{T}$ deformation of two-dimensional Maxwell theory
• Irrelevant Deformations of Chiral Bosons
• Renormalisation in $\text{T}\bar{\text{T}}$-Deformed (Non-)Integrable Theories
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• Chiral Decoupling from Irrelevant Deformations
• Holographic Entanglement Entropy in $T\bar{T}$-deformed CFTs
• Note on higher-point correlation functions of the $T\bar{T}$ or $J\bar{T}$ deformed CFTs
• Properties of multiple D0-brane system: 11D origin, equations of motion and their solutions
• Nonlocal charges from marginal deformations of 2D CFTs: Holographic $T\bar{T}$, $T\bar{J}$ and Yang-Baxter deformations
• Metric approach to a $\mathrm{T}\bar{\mathrm{T}}-$like deformation in arbitrary dimensions
• On Current-Squared Flows and ModMax Theories