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It was recently shown that the theory obtained by deforming a general two dimensional conformal theory by the irrelevant operator $Tbar T$ is solvable. In the context of holography, a large class of such theories can be obtained by studying string theory on $AdS_3$. We show that a certain $Tbar T$ deformation of the boundary $CFT_2$ gives rise in the bulk to string theory in a background that interpolates between $AdS_3$ in the IR and a linear dilaton spacetime in the UV, i.e. to a two dimensional vacuum of Little String Theory. This construction provides holographic duals for a large class of vacua of string theory in asymptotically linear dilaton spacetimes, and sheds light on the UV behavior of $Tbar T$ deformed $CFT_2$. It may provide a step towards holography in flat spacetime.
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In this work, we continue our study of string theory in the background that interpolates between $AdS_3$ in the IR to flat spacetime with a linear dilaton in the UV. The boundary dual theory interpolates between a CFT$_2$ in the IR to a certain two-dimensional Little String Theory (LST) in the UV. In particular, we study emph{computational complexity} of such a theory through the lens of holography and investigate the signature of non-locality in the short distance behavior of complexity. When the cutoff UV scale is much smaller than the non-locality (Hagedorn) scale, we find exotic quadratic and logarithmic divergences (for both volume and action complexity) which are not expected in a local quantum field theory. We also generalize our computation to include the effects of finite temperature. Up to second order in finite temperature correction, we do not any find newer exotic UV-divergences compared to the zero temperature case.
The $Tbar T$ deformation of a conformal field theory has a dual description as a cutoff $AdS_3$ spacetime, at least at the level of pure 3d gravity. We generalize this deformation in such a way that it builds up a patch of bulk $dS_3$ spacetime instead. At each step along the trajectory in the space of $2d$ theories, the theory is deformed by a specific combination of $Tbar T$ and the two-dimensional cosmological constant. This provides a concrete holographic dual for the warped throat on the gravity side of the dS/dS duality, at leading order in large central charge. We also analyze a sequence of excitations of this throat on both sides of the duality, as well as the entanglement entropy. Our results point toward a mechanism for obtaining de Sitter solutions starting from seed conformal field theories with AdS duals.
We construct a solvable deformation of two-dimensional theories with $(2,2)$ supersymmetry using an irrelevant operator which is a bilinear in the supercurrents. This supercurrent-squared operator is manifestly supersymmetric, and equivalent to $Tbar{T}$ after using conservation laws. As illustrative examples, we deform theories involving a single $(2,2)$ chiral superfield. We show that the deformed free theory is on-shell equivalent to the $(2,2)$ Nambu-Goto action. At the classical level, models with a superpotential exhibit more surprising behavior: the deformed theory exhibits poles in the physical potential which modify the vacuum structure. This suggests that irrelevant deformations of $Toverline{T}$ type might also affect infrared physics.
We consider a gravitational perturbation of the Jackiw-Teitelboim (JT) gravity with an arbitrary dilaton potential and study the condition under which the quadratic action can be seen as a $Tbar{T}$-deformation of the matter action. As a special case, the flat-space JT gravity discussed by Dubovsky et al[arXiv:1706.06604 ] is included. Another interesting example is a hyperbolic dilaton potential. This case is equivalent to a classical Liouville gravity with a negative cosmological constant and then a finite $Tbar{T}$-deformation of the matter action is realized as a gravitational perturbation on AdS$_2$.
We investigate the $Tbar{T}$ deformations of two-dimensional supersymmetric quantum field theories. More precisely, we show that, by using the conservation equations for the supercurrent multiplet, the $Tbar{T}$ deforming operator can be constructed as a supersymmetric descendant. Here we focus on $mathcal{N}=(1,0)$ and $mathcal{N}=(1,1)$ supersymmetry. As an example, we analyse in detail the $Tbar{T}$ deformation of a free $mathcal{N}=(1,0)$ supersymmetric action. We also argue that the link between $Tbar{T}$ and string theory can be extended to superstrings: by analysing the light-cone gauge fixing for superstrings in flat space, we show the correspondence of the string action to the $Tbar{T}$ deformation of a free theory of eight $mathcal{N}=(1,1)$ scalar multiplets on the nose. We comment on how these constructions relate to the geometrical interpretations of $Tbar{T}$ deformations that have recently been discussed in the literature.
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