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Register a new userThermodynamics of $T bar T$, $J bar T$, $T bar J$ deformed conformal field theories
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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.
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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.
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.
We discuss lepton charge asymmetries in $t bar t$ and $t bar t gamma$ production at the LHC, which can be measured in the semileptonic decay channel $t bar t to W^+ b , W^- bar b to ell^+ u b , q bar q bar b$ (or the charge conjugate). Considering several variants of a new physics scenario with a light colour octet, it is seen that for $t bar t$ these asymmetries may have a sensitivity competitive with the dilepton asymmetry already measured. For $t bar t gamma$ the new leptonic asymmetries, as well as the $t bar t$ charge asymmetry, will reach their full potential with the high luminosity LHC upgrade. These asymmetries can pinpoint deviations at the $3sigma-4sigma$ level for new physics scenarios where the charge asymmetries already measured in $t bar t$ production agree within $1sigma$.
It has been recently discovered that the $text{T}bar{text{T}}$ deformation is closely-related to Jackiw-Teitelboim gravity. At classical level, the introduction of this perturbation induces an interaction between the stress-energy tensor and space-time and the deformed EoMs can be mapped, through a field-dependent change of coordinates, onto the corresponding undeformed ones. The effect of this perturbation on the quantum spectrum is non-perturbatively described by an inhomogeneous Burgers equation. In this paper, we point out that there exist infinite families of models where the geometry couples instead to generic combinations of local conserved currents labelled by the Lorentz spin. In spirit, these generalisations are similar to the $text{J}bar{text{T}}$ model as the resulting theories and the corresponding scattering phase factors are not Lorentz invariant. The link with the $text{J}bar{text{T}}$ model is discussed in detail. While the classical setup described here is very general, we shall use the sine-Gordon model and its CFT limit as explanatory quantum examples. Most of the final equations and considerations are, however, of broader validity or easily generalisable to more complicated systems.
The dilepton azimuthal correlation, namely the difference $phi$ between the azimuthal angles of the positive and negative charged lepton in the laboratory frame, provides a stringent test of the spin correlation in $t bar t$ production at the Large Hadron Collider. We introduce a parameterisation of the differential cross section $dsigma / dphi$ in terms of a Fourier series and show that the third-order expansion provides a sufficiently accurate approximation. This expansion can be considered as a `bridge between theory and data, making it very simple to cast predictions in the Standard Model (SM) and beyond, and to report measurements, without the need to provide the numbers for the whole binned distribution. We show its application by giving predictions for the coefficients in the presence of (i) an anomalous top chromomagnetic dipole moment; (ii) an anomalous $tbW$ interaction. The methods presented greatly facilitate the study of this angular distribution, which is of special interest given the $3.2(3.7)sigma$ deviation from the SM next-to-leading order prediction found by the ATLAS Collaboration in Run 2 data.
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