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Register a new userThe 2D Volkov-Akulov model as a $T bar{T}$ deformation
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We show that the two-dimensional $N=(2,2)$ Volkov-Akulov action that describes the spontaneous breaking of supersymmetry is a $Tbar{T}$ deformation of a free fermionic theory. Our findings point toward a possible relation between nonlinear supersymmetry and $T bar T$ flows.
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We construct a supergravity model whose scalar degrees of freedom arise from a chiral superfield and are solely a scalaron and an axion that is very heavy during the inflationary phase. The model includes a second chiral superfield $X$, which is subject however to the constraint $X^2=0$ so that it describes only a Volkov - Akulov goldstino and an auxiliary field. We also construct the dual higher - derivative model, which rests on a chiral scalar curvature superfield ${cal R}$ subject to the constraint ${cal R}^2=0$, where the goldstino dual arises from the gauge - invariant gravitino field strength as $gamma^{mn} {cal D}_m psi_n$. The final bosonic action is an $R+R^2$ theory involving an axial vector $A_m$ that only propagates a physical pseudoscalar mode.
A scale invariant Goldstino theory coupled to Supergravity is obtained as a standard supergravity dual of a rigidly scale invariant higher--curvature Supergravity with a nilpotent chiral scalar curvature. The bosonic part of this theory describes a massless scalaron and a massive axion in a de Sitter Universe.
We derive the geodesic equation for determining the Ryu-Takayanagi surface in $AdS_3$ deformed by single trace $mu T bar T + varepsilon_+ J bar T + varepsilon_- T bar J$ deformation for generic values of $(mu, varepsilon_+, varepsilon_-)$ for which the background is free of singularities. For generic values of $varepsilon_pm$, Lorentz invariance is broken, and the Ryu-Takayanagi surface embeds non-trivially in time as well as spatial coordinates. We solve the geodesic equation and characterize the UV and IR behavior of the entanglement entropy and the Casini-Huerta $c$-function. We comment on various features of these observables in the $(mu, varepsilon_+, varepsilon_-)$ parameter space. We discuss the matching at leading order in small $(mu, varepsilon_+, varepsilon_-)$ expansion of the entanglement entropy between the single trace deformed holographic system and a class of double trace deformed theories where a strictly field theoretic analysis is possible. We also comment on expectation value of a large rectangular Wilson loop-like observable.
We compute the Hagedorn temperature of $mu T bar T + varepsilon_+ J bar T + varepsilon_-T bar J$ deformed CFT using the universal kernel formula for the thermal partition function. We find a closed analytic expression for the free energy and the Hagedorn temperature as a function of $mu$, $varepsilon_+$, and $varepsilon_-$ for the case of a compact scalar boson by taking the large volume limit. We also compute the Hagedorn temperature for the single trace deformed $AdS_3 times S^1 times T^3 times S^3$ using holographic methods. We identify black hole configurations whose thermodynamics matches the functional dependence on $(mu, varepsilon_+, varepsilon_-)$ of the double trace deformed compact scalars.
Smirnov and Zamolodchikov recently introduced a new class of two-dimensional quantum field theories, defined through a differential change of any existing theory by the determinant of the energy-momentum tensor. From this $Tbar T$ flow equation one can find a simple expression for both the energy spectrum and the $S$-matrix of the $Tbar T$ deformed theories. Our goal is to find the renormalized Lagrangian of the $Tbar T$ deformed theories. In the context of the $Tbar T$ deformation of an integrable theory, the deformed theory is also integrable and, correspondingly, the $S$-matrix factorizes into two-to-two $S$-matrices. One may thus hope to be able to extract the renormalized Lagrangian from the $S$-matrix. We do this explicitly for the $Tbar T$ deformation of a free massive scalar, to second order in the deformation parameter. Once one has the renormalized Lagrangian one can, in principle, compute all other observables, such as correlation functions. We briefly discuss this, as well as the relation between the renormalized Lagrangian, the $Tbar T$ flow equation, and the $S$-matrix. We also mention a more general class of integrability-preserving deformations of a free scalar field theory.
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