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Register a new userA 2D Stress Tensor for 4D Gravity
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We use the subleading soft-graviton theorem to construct an operator $T_{zz}$ whose insertion in the four-dimensional tree-level quantum gravity $mathcal{S}$-matrix obeys the Virasoro-Ward identities of the energy momentum tensor of a two-dimensional conformal field theory (CFT$_2$). The celestial sphere at Minkowskian null infinity plays the role of the Euclidean sphere of the CFT$_2$, with the Lorentz group acting as the unbroken $SL(2,mathbb{C})$ subgroup.
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We consider the tree-level scattering of massless particles in $(d+2)$-dimensional asymptotically flat spacetimes. The $mathcal{S}$-matrix elements are recast as correlation functions of local operators living on a space-like cut $mathcal{M}_d$ of the null momentum cone. The Lorentz group $SO(d+1,1)$ is nonlinearly realized as the Euclidean conformal group on $mathcal{M}_d$. Operators of non-trivial spin arise from massless particles transforming in non-trivial representations of the little group $SO(d)$, and distinguished operators arise from the soft-insertions of gauge bosons and gravitons. The leading soft-photon operator is the shadow transform of a conserved spin-one primary operator $J_a$, and the subleading soft-graviton operator is the shadow transform of a conserved spin-two symmetric traceless primary operator $T_{ab}$. The universal form of the soft-limits ensures that $J_a$ and $T_{ab}$ obey the Ward identities expected of a conserved current and energy momentum tensor in a Euclidean CFT$_d$, respectively.
We investigate the stress tensor for holographic fluids at the finite cutoff surface through perturbing the Schwarzchild-AdS black brane background to the first order perturbations in the scenario of fluid/gravity correspondence. We investigate the most general perturbations of the metric without any gauge fixing. We consider various boundary conditions and demonstrate the properties of the corresponding holographic fluids. The critical fact is that the spatial components of the first order stress tensors of the holographic fluids can be rewritten in a concordant form, which implicates that there is an underlying universality in the first order stress tensor. We find this universality in the first order stress tensor for holographic fluids at the finite cutoff surface by an exhaustive investigation of perturbations of the full bulk metric.
We extend previous work on the numerical diagonalization of quantum stress tensor operators in the Minkowski vacuum state, which considered operators averaged in a finite time interval, to operators averaged in a finite spacetime region. Since real experiments occur over finite volumes and durations, physically meaningful fluctuations may be obtained from stress tensor operators averaged by compactly supported sampling functions in space and time. The direct diagonalization, via a Bogoliubov transformation, gives the eigenvalues and the probabilities of measuring those eigenvalues in the vacuum state, from which the underlying probability distribution can be constructed. For the normal-ordered square of the time derivative of a massless scalar field in a spherical cavity with finite degrees of freedom, analysis of the tails of these distributions confirms previous results based on the analytical treatment of the high moments. We find that the probability of large vacuum fluctuations is reduced when spatial averaging is included, but the tail still decreases more slowly than exponentially as the magnitude of the measured eigenvalues increases, suggesting vacuum fluctuations may not always be subdominant to thermal fluctuations and opening up the possibility of experimental observation under the right conditions.
We investigate the neutral AdS black-hole solution in the consistent $Drightarrow4$ Einstein-Gauss-Bonnet gravity proposed in [K. Aoki, M.A. Gorji, and S. Mukohyama, Phys. Lett. B {bf 810}, 135843 (2020)] and construct the gravity duals of ($2+1$)-dimensional superconductors with Gauss-Bonnet corrections in the probe limit. We find that the curvature correction has a more subtle effect on the scalar condensates in the s-wave superconductor in ($2+1$)-dimensions, which is different from the finding in the higher-dimensional superconductors that the higher curvature correction makes the scalar hair more difficult to be developed in the full parameter space. However, in the p-wave case, we observe that the higher curvature correction always makes it harder for the vector condensates to form in various dimensions. Moreover, we note that the higher curvature correction results in the larger deviation from the expected relation in the gap frequency $omega_g/T_capprox 8$ in both ($2+1$)-dimensional s-wave and p-wave models.
Recently a boundary energy-momentum tensor $T_{zz}$ has been constructed from the soft graviton operator for any 4D quantum theory of gravity in asymptotically flat space. Up to an anomaly which is one-loop exact, $T_{zz}$ generates a Virasoro action on the 2D celestial sphere at null infinity. Here we show by explicit construction that the effects of the IR divergent part of the anomaly can be eliminated by a one-loop renormalization that shifts $T_{zz}$.
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