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.
Highlights
1.1 BackgroundRecent attention has been drawn toward irrelevant deformations of two-dimensional quantum field theories (QFTs) and applications in holography
There are an abundance of applications of the T T deformation,3 but for the main scope of this paper, we focus on two-dimensional Euclidean N = (0, 2) and N = (2, 2) superconformal field theories (SCFTs) as well as some N = (2, 2) integrable theories
We find that naively the T T deformation breaks both U(1)A and U(1)V R-symmetries, so the S-multiplet becomes the generic one without superconformal symmetry
Summary
Recent attention has been drawn toward irrelevant deformations of two-dimensional quantum field theories (QFTs) and applications in holography. There are other examples one could see this non-locality property Another notable example is that when one T T deforms the seed action of a Yang-Mills gauge field coupled to a scalar, the deformed theory gives a non-abelian analogue of a two-dimensional DBI action [8]. There are recent studies of other irrelevant deformations, such as JT or JT [23,24,25,26,27,28,29] that break Lorentz invariance, in the context of supersymmetry [30] From these recent developments on the T T deformation in supersymmetric field theories, one can in principle calculate correlators associated to each N = (p, q) supersymmetric theory via superconformal Ward identities.
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