Entanglement entropy and $T\bar T$ deformations beyond antipodal points from holography
Sebastian Grieninger
备注：
added discussion about Wald entropy associated with the counterterms in order to fit the EE in higher dimensions on both sides; matches version accepted in JHEP; 17+5 pages, 2 figures
We consider the entanglement entropies in dS$_d$ sliced (A)dS$_{d+1}$ in the presence of a hard radial cutoff for $2\le d\le 6$. By considering a one parameter family of analytical solutions, parametrized by their turning point in the bulk $r^\star$, we are able to compute the entanglement entropy for generic intervals on the cutoff slice. It has been proposed that the field theory dual of this scenario is a strongly coupled CFT, deformed by a certain irrelevant deformation -- the so-called $T\bar T$ deformation. Surprisingly, we find that we may write the entanglement entropies formally in the same way as the entanglement entropy for antipodal points on the sphere by introducing an effective radius $R_\text{eff}=R\,\cos(β_ε)$, where $R$ is the radius of the sphere and $β_ε$ related to the length of the interval. Geometrically, this is equivalent to following the $T\bar T$ trajectory until the generic interval corresponds to antipodal points on the sphere. Finally, we check our results by comparing the asymptotic behavior (no Dirichlet wall present) with the results of Casini, Huerta and Myers. We then switch on counterterms on the cutoff slice which are important with regards to the field theory calculation. We explicitly compute the contributions of the counterterms to the entanglement entropy by considering the Wald entropy. In the second part of this work, we extend the field theory calculation of the entanglement entropy for antipodal points for a $d$-dimensional field theory in context of DS/dS holography. We find excellent agreement with the results from holography and show, in particular, that the effects of the counterterms in the field theory calculation match the Wald entropy associated with the counterterms on the gravity side.
We outline a program for interpreting the higher-spin dS/CFT model in terms of physics in the causal patch of a dS observer. The proposal is formulated in "elliptic" de Sitter space dS_4/Z_2, obtained by identifying antipodal points in dS_4. We discuss recent evidence that the higher-spin model is especially well-suited for this, since the antipodal symmetry of bulk solutions has a simple encoding on the boundary. For context, we test some other (free and interacting) theories for the same property. Next, we analyze the notion of quantum field states in the non-time-orientable dS_4/Z_2. We com…
We calculate quantum corrections to holographic entanglement entropy in the proposed duality between $T\bar{T}$-deformed holographic 2D CFTs and gravity in AdS$_{3}$ with a finite cutoff. We first establish the dictionary between the two theories by mapping the flow equation of the deformed CFT to the bulk Wheeler-DeWitt equation. The latter reduces to an ordinary differential equation for the sphere partition function, which we solve to find the entanglement entropy for an entangling surface consisting of two antipodal points on a sphere. The entanglement entropy in the inverse central charge…
In this article we study large central charge partition function and entanglement entropy of $T\bar{T}$ deformed two dimensional conformal field theory, following the approach to $T\bar{T}$ deformation as integrated infinitesimal double trace deformation used by Guica et al.. For sphere partition function and entanglement entropy of half great circle with antipodal points being the entangling surface, we obtain different results compared to previous works, with more reasonable CFT limits and qualitatively different behaviour as the deformation parameter $μ$ goes to infinity, which contradicts …
We perform the first study of baryons in holographic QCD with $D4/D8/\bar{D8}$ multi-$D$ brane system in type IIA superstring theory. The baryon is described as a chiral soliton solution in the four-dimensional meson effective action derived from holographic QCD. We also present a brief review of the holographic model from the viewpoints of recent hadron physics and QCD phenomenologies.
In recent years, there have been two independent but related developments in the study of irrelevant deformations in two dimensional quantum field theories (QFTs). The first development is the deformation of a two dimensional QFT by the determinant of the energy momentum stress tensor, commonly referred to as $T{\bar T}$ deformation. The second development is in two dimensional holographic field theories which are dual to string theory in asymptotically Anti-de Sitter (AdS) spacetimes. In this latter development, the deformation is commonly referred to as single-trace $T{\bar T}$ deformation. …
We study thermodynamic aspects of a tractable toy model of holography for extremal Kerr black holes proposed in [arXiv:1806.10127]. On the gravity side, the theory can be described by the worldsheet action of string theory on a warped AdS$_3$ background supported by NS-NS flux. Once we turn on temperature, the deformed background is described by a black string solution of type IIB supergravity that features a locally warped AdS$_3$ factor. The dual field theory is conjectured to be a single-trace version of a $J\bar{T}$-deformed CFT at finite temperature. As evidence for the correspondence we …
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We present the exact solution for the scattering problem in the flat space Jackiw-Teitelboim (JT) gravity coupled to an arbitrary quantum field theory. JT gravity results in a gravitational dressing of field theoretical scattering amplitudes. The exact expression for the dressed $S$-matrix was previously known as a solvable example of a novel UV asymptotic behavior, dubbed asymptotic fragility. This dressing is equivalent to the $T\bar{T}$ deformation of the initial quantum field theory. JT gravity coupled to a single massless boson provides a promising action formulation for an integrable app…
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We study baryons as Skyrmions in holographic QCD with D4/D8/D8-bar multi-D brane system in type IIA superstring theory, and also in the non-linear sigma model with hidden local symmetry (HLS). Comparing these two models, we find that the extra-dimension and its nontrivial curvature can largely change the role of (axial) vector mesons for baryons in four-dimensional space-time. In the HLS approach, the rho-meson field as a massive Yang-Mills field has a singular configuration in Skyrmion, which gives a strong repulsion for the baryon as a stabilizer. When a_1 meson is added in this approach, th…
A new approach to black hole thermodynamics is proposed in Loop Quantum Gravity (LQG), by defining a new black hole partition function, followed by analytic continuations of Barbero-Immirzi parameter to $γ\in i\mathbb{R}$ and Chern-Simons level to $k\in i\mathbb{R}$. The analytic continued partition function has remarkable features: The black hole entropy $S=A/4\ell_P^2$ is reproduced correctly for infinitely many $γ= iη$, at least for $η\in\mathbb{Z}\setminus\{0\}$. The near-horizon Unruh temperature emerges as the pole of partition function. Interestingly, by analytic continuation the partit…
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It was recently shown that the theory obtained by deforming a general two dimensional conformal theory by the irrelevant operator $T\bar T$ 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 $T\bar T$ 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 …
We develop a two-dimensional gravity path integral formulation of the $T \bar T + Λ_2$ deformation of quantum field theory. This provides an exactly solvable generalization of the pure $T \bar T$ deformation that is relevant for de Sitter and flat space holography. The path integral sheds light on quantum aspects of these flows in curved space, most notably the Weyl anomaly, the operator relation for the trace of the energy-momentum tensor, and the renormalization of the composite $T \bar T$ operator. It also applies to both the Hagedorn and the holographic signs of such flows. We present expl…
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An exact time-dependent solution of a black hole is found in conformally invariant gravity on a warped Randall-Sundrum spacetime, by writing the metric $g_{μν}=ω^{\frac{4}{n-2}}\tilde g_{μν}$. Here $\tilde g_{μν}$ represents the "un-physical" spacetime and $ω$ the dilaton field, which will be treated on equal footing as any renormalizable scalar field. In the case of a five-dimensional warped spacetime, we write $ ^{(4)}{\tilde g_{μν}}=\barω^2{ ^{(4)}\bar g_{μν}}$ Both $ω$ and $\barω$ can be used to describe the different notion the in-going and outside observers have of the Hawking radiation …
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Neural Ordinary Differential Equations for Mapping the Magnetic QCD Phase Diagram via Holography
Jilin University（吉林大学）；Ningbo University（宁波大学）；Chinese Academy of Sciences（中国科学院）；Hangzhou Institute for Advanced Study, UCAS（杭州高等研究院，中国科学院大学）；Max Planck Institute for Gravitational Physics (Albert Einstein Institute)（马克斯·普朗克引力物理研究所（爱因斯坦研究所））；University of Chinese Academy of Sciences（中国科学院大学）
