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We re-examine holographic versions of the c-theorem and entanglement entropy
in the context of higher curvature gravity and the AdS/CFT correspondence. We
select the gravity theories by tuning the gravitational couplings to eliminate
non-unitary operators in the boundary theory and demonstrate that all of these
theories obey a holographic c-theorem...
Context in source publication
Context 1
... of a heat bath in R H . While this discussion can be made more precise [40], we would like to frame the same identification within a more conventional calculation of entanglement entropy in this section. Generally entanglement entropy arises as follows [41, 39]: One divides a given system into two parts, say, A and B, and integrates out the degrees of freedom in one subsystem, B. The remaining degrees of freedom in A are described by a density matrix ρ A . The entanglement entropy is then simply the von Neumann entropy of this density matrix, i.e., S = − T r [ ρ A log ρ A ]. In field theories, the system is typically subdivided by introducing a boundary Σ which separates the space ( i.e., a constant time slice) into two regions, as shown in figure 2. A standard approach to calculating the entanglement entropy is to apply the replica trick [41]. Since the operator log ρ A often lacks a clear definition, this construction begins by considering (integer) powers of the density matrix, which may be defined ...
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Citations
... II, we argue for the irreversibility of the flow from the UVof a generic round black hole to its IR, as well as the irreversibility of this flow's trans-IR analytic continuation toward the classical singularity. As in earlier AdS=CFT literature [46][47][48][49], we assume the null energy condition to construct a monotone that counts the degrees of freedom along the flow. Our statements in this section are analogous to those of the planar case [23]. ...
... The a theorem in 4D has been proven for nonholographic flows [52]. However, holographic flows are nice in part because the a theorem can be extended to and proven in any number of dimensions [47][48][49] assuming reasonable energy constraints on the bulk matter, although the field-theoretic interpretation of the odd-dimensional holographic a function is not connected to an anomaly but rather entanglement entropy. ...
... where l is the curvature radius. The trace anomaly coefficient a à goes as l d−1 , and in keeping with the normalization conventions of [48,49], it is Holographic a functions in Einstein gravity 3 can be constructed by using a à as a starting point [47]. Basically, we take gravity sourced by matter such that there is a relevant deformation at the boundary triggering an RG flow. ...
Under the AdS / CFT correspondence, asymptotically anti–de Sitter geometries with backreaction can be viewed as conformal field theory states subject to a renormalization group (RG) flow from an ultraviolet (UV) description toward an infrared (IR) sector. For black holes, however, the IR point is the horizon, so one way to interpret the interior is as an analytic continuation to a “trans-IR” imaginary-energy regime. In this paper, we demonstrate that this analytic continuation preserves some imprints of the UV physics, particularly near its “end point” at the classical singularity. We focus on holographic phase transitions of geometric objects in round black holes. We first assert the consistency of interpreting such black holes, including their interiors, as RG flows by constructing a monotonic a function. We then explore how UV phase transitions of entanglement entropy and scalar two-point functions, each of which are encoded by bulk geometry under the holographic mapping, are related to the structure of the near-singularity geometry, which is quantified by Kasner exponents. Using 2D holographic flows triggered by relevant scalar deformations as test beds, we find that the 3D bulk’s near-singularity Kasner exponents can be viewed as functions of the UV physics precisely when the deformation is nonzero.
Published by the American Physical Society 2024
... For RG relevant flows, the c−function is found to diminish from the free fermion central charge c = 1/3, reaching the value of zero at the fixed point (where only the central n = 0 mode remains and the rest have been removed because of the large mass gap). The nonnegative, non-increasing nature of the c−function, and its flow towards its minimum at the fixed point, leads to speculate that equation (48) can be thought of as a holographic counterpart of Zamalodchikov's c−theorem [53,[146][147][148]. For RG irrelevant flows, the behaviour is reversed. ...
We demonstrate the emergence of a holographic dimension in a system of 2D non-interacting Dirac fermions placed on a torus, by studying the scaling of multipartite entanglement measures under a sequence of renormalisation group (RG) transformations applied in momentum space. Geometric measures defined in this emergent space can be related to the RG beta function of the spectral gap, hence establishing a holographic connection between the spatial geometry of the emergent spatial dimension and the entanglement properties of the boundary quantum theory. We prove, analytically, that changing the boundedness of the holographic space involves a topological transition accompanied by a critical Fermi surface in the boundary theory. We go on to show that this results in the formation of a quantum wormhole geometry that connects the UV and the IR of the emergent dimension. The additional conformal symmetry at the transition also supports a relation between the emergent metric and the stress-energy tensor. In the presence of an Aharonov–Bohm flux, the entanglement gains a geometry-independent piece which is shown to be topological, sensitive to changes in boundary conditions, and related to the Luttinger volume of the system. Upon the insertion of a strong transverse magnetic field, we show that the Luttinger volume is linked to the Chern number of the occupied single-particle Landau levels.
... Second, since an analogous requirement in the context of spherically symmetric solutions has turned out to be greatly successful [14,18,[67][68][69][70][71][72][73]. And third, because theories with second-order equations of motion on cosmological backgrounds automatically provide instances of holographic theories satisfying a holographic c-theorem [74][75][76][77][78]. ...
We examine higher-curvature gravities whose Friedmann–Lemaître–Robertson–Walker configurations are specified by equations of motion which are of second order in derivatives, just like in Einstein gravity. We name these theories Cosmological Gravities and initiate a systematic exploration in dimensions D⩾3 . First, we derive an instance of Cosmological Gravity to all curvature orders and dimensions D⩾3 . Second, we study Cosmological Gravities admitting non-hairy generalizations of the Schwarzschild solution characterized by a single function whose equation of motion is, at most, of second order in derivatives. We present explicit instances of such theories for all curvature orders and dimensions D⩾4 . Finally, we investigate the equations of motion for cosmological perturbations in the context of generic Cosmological Gravities. Remarkably, we find that the linearized equations of motion for scalar cosmological perturbations in any Cosmological Gravity in D⩾3 contain no more than two time derivatives. We explicitly corroborate this aspect by presenting the equations for the scalar perturbations in some four-dimensional Cosmological Gravities up to fifth order in the curvature.
... Entanglement is a key feature of quantum systems [1][2][3][4] and has a very broad range of implications, ranging from those in condensed-matter physics [5][6][7] to those relevant for high-energy theory, black-hole physics, and holography [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]. Finally, entanglement is also an important quantum resource in quantum information theory [27,28]: for example, entanglement distillation can be used in quantum error-correction [29,30]. ...
A bstract
The study of entanglement in gauge theories is expected to provide insights into many fundamental phenomena, including confinement. However, calculations of quantities related to entanglement in gauge theories are limited by ambiguities that stem from the non-factorizability of the Hilbert space. In this work we study lattice gauge theories that admit a dual description in terms of spin models, for which the replica trick and Rényi entropies are well defined. In the first part of this work, we explicitly perform the duality transformation in a replica geometry, deriving the structure of a replica space for a gauge theory. Then, in the second part, we calculate, by means of Monte Carlo simulations, the entropic c-function of the ℤ 2 gauge theory in three spacetime dimensions, exploiting its dual description in terms of the three-dimensional Ising model.
... [163,164]. This has been exploited to study many physical properties, and to discover various universal relations valid for completely general theories [120,[165][166][167][168][169][170]. GQTs are particularly useful for this, as many of the holographic quantities which can be accessed using black holes and other solutions are much easier to obtain and can be extracted fully analytically. ...
In this note we revisit the analysis performed in De Felice and Tsujikawa (2023 Phys. Lett. B 843 138047) of odd-parity perturbations around static and spherically symmetric black holes in Einsteinian cubic gravity (ECG). We show that the additional propagating modes always have masses much above the cutoff of the theory. Therefore, contrary to what is claimed in that paper, the ECG black holes remain stable within the effective field theory regime. We consider the same analysis for a general cubic theory, showing that the ECG results are not special in this regard. We use the occasion to make some clarifications on the role, uses and limitations of ECG and its generalizations.
... In arbitrary even-dimensional CFTs, there is generally a tower of B-type anomalies each of which is exactly Weyl invariant and built out of non-topological, rank-d 2 monomials in curvatures. The Weyl anomaly coefficients of a 4d CFT control correlation functions of the stress-energy tensor [33], and have strong upper and lower bounds on their ratio [34]; a 4d also appears in the EE [35], and obeys an 'a'-theorem under renormalization group (RG) flows [36,37]. For 4d SCFTs with an R-symmetry, a 4d and c are both related to the cubic and mixed R-anomalies through non-perturbative formulae [38]. ...
A bstract
In this note, we study 1/4- and 1/2-BPS co-dimension two superconformal defects in the 6d $$ \mathcal{N} $$ N = (2, 0) A N− 1 SCFT at large N using their holographic descriptions as solutions of 11 d supergravity. In this regime, we are able to compute the defect contribution to the sphere entanglement entropy and the change in the stress-energy tensor one-point function due to the presence of the defect using holography. From these quantities, we are then able to unambiguously compute the values for two of the twenty-nine total Weyl anomaly coefficients that characterize 4 d conformal defects in six and higher dimensions. We are able to demonstrate the consistency of the supergravity description of the defect theories with the average null energy condition on the field theory side. For each class of defects that we consider, we also show that the A-type Weyl anomaly coefficient is non-negative. Lastly, we uncover and resolve a discrepancy between the on-shell action of the 7 d 1/4-BPS domain wall solutions and that of their 11 d uplift.
... This section proves the holographic c-theorem by using NEC in bulk C. We follow the approach of [65,66]. ...
... Inspired by [65,66], we assume the solution to Einstein gravity coupled with bulk matter fields takes the form ...
... Following the standard approach [65,66], we impose NEC for matter fields in bulk C ...
A bstract
Cone holography is a codimension- n doubly holographic model, which can be interpreted as the holographic dual of edge modes on defects. The initial model of cone holography is based on mixed boundary conditions. This paper formulates cone holography with Neumann boundary conditions, where the brane-localized gauge fields play an essential role. Firstly, we illustrate the main ideas in an AdS 4 /CFT 1 toy model. We show that the U(1) gauge field on the end-of-the-world brane can make the typical solution consistent with Neumann boundary conditions. Then, we generalize the discussions to general codimension- n cone holography by employing brane-localized p -form gauge fields. We also investigate perturbative solutions and prove the mass spectrum of Kaluza-Klein gravitons is non-negative. Furthermore, we prove that cone holography obeys holographic c -theorem. Finally, inspired by the recently proposed chiral model in AdS/BCFT, we construct another type of cone holography with Neumann boundary conditions by applying massive vector (Proca) fields on the end-of-the-world brane.
... (3.2) springs an intriguing observation: if the square root in the integrand were removed, the result would simply be the tension T DW of the domain wall, since |∂|Z|| 2 is proportional to d|Z| dr [52] (we take |Z| to be monotonically increasing for definiteness). On the other hand, as we will discuss in section 5, a natural holographic JHEP02(2024)227 counterpart of the domain wall distance is the length of its dual RG flow 3 [57][58][59][60][61]. The analog of the quantum information distance [39,41,43] (see also [62] for a related notion) with the square root removed was investigated in [63], where it was shown that the corresponding "length" yields the difference in a-central charges of the conformal field theories (CFTs) at the endpoints of the flow. ...
A bstract
We explore a notion of distance between vacua of a discrete landscape that takes into account scalar potentials and fluxes via transitions mediated by domain walls. Such settings commonly arise in supergravity and string compactifications with stabilized moduli. We derive general bounds and simple estimates in supergravity which constrain deviations from the ordinary swampland distance conjecture based on moduli space geodesics, and we connect this picture to renormalization group flows via holography.
... Luckily, using the ideas of Refs. [43,44] one can still generalize a à d to d odd. According to these results for even dimensions a à d is the usual coefficient of the d-dimensional Euler density in the conformal anomaly, and in odd dimensions a à d ≃ log Z S d with Z S d being the partition function of the CFT on the sphere. ...
... where V d ¼ Volð♢ × B d−2 L Þ is the volume of our string world sheet segment ♢ times a (d − 2)-dimensional ball with radius equals the AdS length. Moreover, relating the relevant a à d generalization [43,44] valid also for d odd to similar terms we expect a similar relation to hold for general d. Now the volume V d is a codimension one object in AdS dþ1 . ...
In this paper we establish a connection between segmented strings propagating in AdSd+1 and CFTd subsystems in Minkowski spacetime characterized by quantum information theoretic quantities calculated for the vacuum state. We show that the area of the world sheet of a string segment on the AdS side can be connected to fidelity susceptibility (the real part of the quantum geometric tensor) on the CFT side. This quantity has another interpretation as the computational complexity for infinitesimally separated states corresponding to causal diamonds that are displaced in a spacelike manner according to the metric of kinematic space. These displaced causal diamonds encode information for a unique reconstruction of the string world sheet segments in a holographic manner. Dually the bulk segments are representing causally ordered sets of consecutive boundary events in boosted inertial frames or in noninertial ones proceeding with constant acceleration. For the special case of AdS3 one can also see the segmented stringy area in units of 4GL (G is Newton’s constant and L is the AdS length) as the conditional mutual information I(A,C|B) calculated for a trapezoid configuration arising from boosted spacelike intervals A, B and C. In this special case the variation of the discretized Nambu-Goto action leads to an equation for entanglement entropies in the boundary theory of the form of a Toda equation. For arbitrary d the string world sheet patches are living in the modular slices of the entanglement wedge. They seem to provide some sort of tomography of the entanglement wedge where the patches are linked together by the interpolation ansatz, i.e., the discretized version of the equations of motion for the Nambu-Goto action.
... In the context of fully relativistic holographic RG flows, a parallel program has been developed [14][15][16]. In this case, the holographic charges are the effective AdS radius at the UV and IR geometries. ...
A bstract
We use the radial null energy condition to construct a monotonic a -function for a certain type of non-relativistic holographic RG flows. We test our a -function in three different geometries that feature a Boomerang RG flow, characterized by a domain wall between two AdS spaces with the same AdS radius, but with different (and sometimes direction-dependent) speeds of light. We find that the a -function monotonically decreases and goes to a constant in the asymptotic regimes of the geometry. Using the holographic dictionary in this asymptotic AdS spaces, we find that the a -function not only reads the fixed point central charge but also the speed of light, suggesting what the correct RG charge might be for non-relativistic RG flows.
