# $T \bar{T}$-Deformed Actions and (1,1) Supersymmetry

## TL;DR

This paper introduces a simplified algebraic method to compute $T\bar{T}$-deformed Lagrangians, demonstrated on (1,1) supersymmetry, showing off-shell invariance and SUSY algebra consistency up to second order in deformation.

## Contribution

The paper presents a new algebraic algorithm derived from topological gravity for calculating $T\bar{T}$ deformations, simplifying previous PDE-based approaches.

## Key findings

- Deformed Lagrangian for (1,1) supersymmetry constructed.
- Off-shell invariance verified up to order $\lambda^2$.
- SUSY algebra confirmed through order $\lambda$.

## Abstract

We describe an algorithmic method to calculate the $T\bar{T}$ deformed Lagrangian of a given seed theory by solving an algebraic system of equations. This method is derived from the topological gravity formulation of the deformation. This algorithm is far simpler than the direct partial differential equations needed in most earlier proposals. We present several examples, including the deformed Lagrangian of (1,1) supersymmetry. We show that this Lagrangian is off-shell invariant through order $\lambda^2$ in the deformation parameter and verify its SUSY algebra through order $\lambda$.