$T\bar{T}$ deformation of the Ising model and its ultraviolet completion

Abstract

Pure $T\bar{T}$ deformations of conformal field theories are generally asymptotically incomplete in the ultra-violet (UV) due to square-root singularities in the ground state energy on a cylinder of circumference $R$, such that the theory is ill-defined for distances shorter than some critical $R_{\ast }$. In this article we show how a theory can be completed if one includes an infinite number of additional irrelevant perturbations. This is fully demonstrated in the case of the Ising model at $c_{IR}=1/2$ in the infra-red (IR), where we find two completions with central charges $c_{UV}=3/2$ and $c_{UV}=7/10$, the latter being the tri-critical Ising model. Both of these UV completions have $\mathcal{N}=1$ supersymmetry which is broken in the renormalization group flow to low energies. We also consider multiple $T\bar{T}$ deformations of a free massless boson, where we cannot find a UV completion that is consistent with the c-theorem. For negative coupling $g$, which violates the c-theorem, in both cases we find $c_{UV}=-c_{IR}$ as $g\to -\infty$. Finally we also study pure $T\bar{T}$ deformations of the off-critical Ising model.

14 pages, 2 figures

References in corpus (3)

• On space of integrable quantum field theories
• $T\bar{T}$-deformed 2D Quantum Field Theories
• $T\bar{T}$-deformation and Liouville gravity

Cited by in corpus (6)

• On the classification of UV completions of integrable $T\bar{T}$ deformations of CFT
• Thermodynamics of $T\bar{T}$ perturbations of some single particle field theories
• Mingling of the infrared and ultraviolet and the "cosmological constant" for interacting QFT in 2d
• Nonperturbative aspects of two-dimensional $T\bar{T}$-deformed scalar theory from functional renormalization group
• Ising model in a boundary magnetic field with random discontinuities
• Complete Minimal Form Factors for Irrelevant Deformations of Integrable Quantum Field Theory