Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userComposite operators in $Tbar T$-deformed free QFTs
100
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We study perturbative renormalization of the composite operators in the $Tbar T$-deformed two-dimensional free field theories. The pattern of renormalization for the stress-energy tensor is different in the massive and massless cases. While in the latter case the canonical stress tensor is not renormalized up to high order in the perturbative expansion, in the massive theory there are induced counterterms at linear order. For a massless theory our results match the general formula derived recently in [1].
rate research
Read More
In this work, we try to construct the Lax connections of $Tbar{T}$-deformed integrable field theories in two different ways. With reasonable assumptions, we make ansatz and find the Lax pairs in the $Tbar{T}$-deformed affine Toda theories and the principal chiral model by solving the Lax equations directly. This way is straightforward but maybe hard to apply for general models. We then make use of the dynamical coordinate transformation to read the Lax connection in the deformed theory from the undeformed one. We find that once the inverse of the transformation is available, the Lax connection can be read easily. We show the construction explicitly for a few classes of scalar models, and find consistency with the ones in the first way.
We propose a symmetry of $Tbar T$ deformed 2D CFT, which preserves the trace relation. The deformed conformal killing equation is obtained. Once we consider the background metric runs with the deformation parameter $mu$, the deformation contributes an additional term in conformal killing equation, which plays the role of renormalization group flow of metric. The conformal symmetry coincides with the fixed point. On the gravity side, this deformed conformal killing equation can be described by a new boundary condition of AdS$_3$. In addition, based on the deformed conformal killing equation, we derive that the stress tensor of the deformed CFT equals to Brown-Yorks quasilocal stress tensor on a finite boundary with a counterterm. For a specific example, BTZ black hole, we get $Tbar T$ deformed conformal killing vectors and the associated conserved charges are also studied.
We study $Tbar T$ deformations of 2d CFTs with periodic boundary conditions. We relate these systems to string models on $mathbb{R}times {S}^1times{cal M}$, where $cal M$ is the target space of a 2d CFT. The string model in the light cone gauge is identified with the corresponding 2d CFT and in the static gauge it reproduces its $Tbar T$ deformed system. This relates the deformed system and the initial one by a worldsheet coordinate transformation, which becomes a time dependent canonical map in the Hamiltonian treatment. The deformed Hamiltonian defines the string energy and we express it in terms of the chiral Hamiltonians of the initial 2d CFT. This allows exact quantization of the deformed system, if the spectrum of the initial 2d CFT is known. The generalization to non-conformal 2d field theories is also discussed.
In this work we consider AdS$_3$ gravitational theory with certain mixed boundary conditions at spatial infinity. Using the Chern-Simons formalism of AdS$_3$ gravity, we find that these boundary conditions lead to non-trivial boundary terms, which, in turn, produce exactly the spectrum of the $Tbar{T}/Jbar{T}$-deformed CFTs. We then follow the procedure for constructing asymptotic boundary dynamics of AdS$_3$ to derive the constrained $Tbar{T}$-deformed WZW model from Chern-Simons gravity. The resulting theory turns out to be the $Tbar{T}$-deformed Alekseev-Shatashvili action after disentangling the constraints. Furthermore, by adding a $U(1)$ gauge field associated to the current $J$, we obtain one type of the $Jbar T$-deformed WZW model, and show that its action can be constructed from the gravity side. These results provide a check on the correspondence between the $Tbar{T}/Jbar{T}$-deformed CFTs and the deformations of boundary conditions of AdS$_3$, the latter of which may be regarded as coordinate transformations.
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.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
