$T \Tbar$ deformation of the Ising model and its ultraviolet completion

Abstract: Pure $T\Tbar$ 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 $R_*$. 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 $\CN=1$ supersymmetry which is broken in the renormalization group flow to low energies. We also consider multiple $T\Tbar$ 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 $T\Tbar$ deformations of the off-critical Ising model.

HEP - theory

Audience: researchers in the topic

Exact Results on Irrelevant Deformations of QFTs

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