We study quantum JT gravity at finite cutoff using a mapping to the statistical mechanics of a self-avoiding loop in hyperbolic space, with positive pressure and fixed length. The semiclassical limit (small $G_N$) corresponds to large pressure, and we solve the problem in that limit in three overlapping regimes that apply for different loop sizes. For intermediate loop sizes, a semiclassical effective description is valid, but for very large or very small loops, fluctuations dominate. For large loops, this quantum regime is controlled by the Schwarzian theory. For small loops, the effective description fails altogether, but the problem is controlled using a conjecture from the theory of self-avoiding walks.
The possibility of asymptotic safety scenario (asymptotic freedom) for quantum gravity has been pointed out in many contexts recently. From this point of view, we discuss some applications of cutoff identification to the black hole. If we consider the condition that the Newton coupling becomes weaker as approaching the origin, the curvature singularity still remains.
We analyze the unbinding transition for a two dimensional lattice polymer in which the constituent strands are mutually avoiding random walks. At low temperatures the strands are bound and form a single self-avoiding walk. We show that unbinding in this model is a strong first order transition. The entropic exponents associated to denaturated loops and end-segments distributions show sharp differences at the transition point and in the high temperature phase. Their values can be deduced from some exact arguments relying on a conformal mapping of copolymer networks into a fluctuating geometry, …
We study the black hole entropy as entanglement entropy and propose a resolution to the species puzzle. This resolution comes out naturally due to the fact that in the presence of $N$ species the universal gravitational cutoff is $Λ=M_{\rm Planck}/\sqrt{N}$, as opposed to $M_{\rm Planck}$. We demonstrate consistency of our solution by showing the equality of the two entropies in explicit examples in which the relation between $M_{\rm Planck}$ and $Λ$ is known from the fundamental theory.
We study ultraviolet cutoffs associated with the Weak Gravity Conjecture (WGC) and Sublattice Weak Gravity Conjecture (sLWGC). There is a magnetic WGC cutoff at the energy scale $e G_N^{-1/2}$ with an associated sLWGC tower of charged particles. A more fundamental cutoff is the scale at which gravity becomes strong and field theory breaks down entirely. By clarifying the nature of the sLWGC for nonabelian gauge groups we derive a parametric upper bound on this strong gravity scale for arbitrary gauge theories. Intriguingly, we show that in theories approximately saturating the sLWGC, the scale…
Within asymptotically safe Quantum Einstein Gravity (QEG), the quantum 4-sphere is discussed as a specific example of a fractal spacetime manifold. The relation between the infrared cutoff built into the effective average action and the corresponding coarse graining scale is investigated. Analyzing the properties of the pertinent cutoff modes, the possibility that QEG generates a minimal length scale dynamically is explored. While there exists no minimal proper length, the QEG sphere appears to be "fuzzy" in the sense that there is a minimal angular separation below which two points cannot be …
Using the non-relativistic hydrodynamic expansion, we solve equations of motion for Einstein gravity and Gauss-Bonnet gravity with a negative cosmological constant within the region between a finite cutoff surface and a black brane horizon, up to the second order of the expansion parameter. Through the Brown-York tensor, we calculate the stress energy tensor of dual fluids living on the cutoff surface. With the black brane solutions, we show that for both Einstein gravity and Gauss-Bonnet gravity, the ratio of shear viscosity to entropy ensity of dual fluid does not run with the cutoff surface…
Recently there has been interest in extending ghost-free massive gravity, bi-gravity, and multi-gravity by including non-standard kinetic terms and matter couplings. We first review recent proposals for this class of extensions, emphasizing how modifications of the kinetic and potential structure of the graviton and modifications of the coupling to matter are related. We then generalize existing no-go arguments in the metric language to the vielbein language in second-order form. We give an ADM argument to show that the most promising extensions to the kinetic term and matter coupling contain …
A new perspective on dilaton gravity at finite cutoff
Università di Parma（帕尔马大学）；Ghent University（根特大学）；Università di Firenze（佛罗伦萨大学）；INFN Gruppo Collegato di Parma（意大利国家核物理研究所帕尔马协作组）；INFN Sezione di Firenze（意大利国家核物理研究所佛罗伦萨分部）
Based on the previous paper arXiv:1207.5309, we investigate the possibility to find out the bulk viscosity of dual fluid at the finite cutoff surface via gravity/fluid correspondence in Einstein-Maxwell gravity. We find that if we adopt new conditions to fix the undetermined parameters contained in the stress tensor and charged current of the dual fluid, two new terms appear in the stress tensor of the dual fluid. One new term is related to the bulk viscosity term, while the other can be related to the perturbation of energy density. In addition, since the parameters contained in the charged c…
We set an upper bound on the gravitational cutoff in theories with exact quantum numbers of large N periodicity, such as Z_N discrete symmetries. The bound stems from black hole physics. It is similar to the bound appearing in theories with N particle species, though a priori, a large discrete symmetry does not imply a large number of species. Thus, there emerges a potentially wide class of new theories, that address the hierarchy problem by lowering the gravitational cutoff due to existence of large Z_{10^32}-type symmetries.
We show that lowering of the gravitational cutoff relative to the Planck mass, imposed by black hole physics in theories with N species, has an independent justification from quantum information theory. First, this scale marks the limiting capacity of any information processor. Secondly, by taking into the account the limitations of the quantum information storage in any system with species, the bound on the gravity cutoff becomes equivalent to the holographic bound, and this equivalence automatically implies the equality of entanglement and Bekenstein-Hawking entropies. Next, the same bound f…
Previously it has been shown that imposing a Petrov-like boundary condition on a hypersurface may reduce the Einstein equation to the incompressible Navier-Stokes equation, but all these correspondences are established in the near horizon limit. In this note, we remark that this strategy can be extended to an arbitrary finite cutoff surface which is spatially flat, and the Navier-Stokes equation is obtained by employing a non-relativistic long-wavelength limit.
We investigate the nonperturbative structure of Jackiw-Teitelboim gravity at finite cutoff, as given by its proposed formulation in terms of a $T\bar{T}$-deformed Schwarzian quantum mechanics. Our starting point is a careful computation of the disk partition function to all orders in the perturbative expansion in the cutoff parameter. We show that the perturbative series is asymptotic and that it admits a precise completion exploiting the analytical properties of its Borel transform, as prescribed by resurgence theory. The final result is then naturally interpreted in terms of the nonperturbat…
In the context of phenomenological models of quantum gravity, it is claimed that the ultraviolet and infrared natural cutoffs can be realized from local deformations of the Hamiltonian systems. In this paper, we scrutinize this hypothesis and formulate a cutoff-regularized Hamiltonian system. The results show that while local deformations are necessary to have cutoffs, they are not sufficient. In fact, the cutoffs can be realized from globally-deformed Hamiltonian systems that are defined on compact symplectic manifolds. By taking the universality of quantum gravity effects into account, we th…
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 th…
The holographic charged fluid with anomalous current in Einstein-Maxwell gravity has been generalized from the infinite boundary to the finite cutoff surface by using the gravity/fluid correspondence. After perturbing the boosted Reissner-Nordstrom (RN)-AdS black brane solution of the Einstein-Maxwell gravity with the Chern-Simons term, we obtain the first order perturbative gravitational and Maxwell solutions, and calculate the stress tensor and charged current of the dual fluid at finite cutoff surfaces which contains undetermined parameters after demanding regularity condition at the future…
Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院）；University of Catania（卡塔尼亚大学）；INFN-Catania（意大利国家核物理研究所卡塔尼亚分部）；Scuola Superiore Meridionale（南方高等学院）；INFN-Napoli（意大利国家核物理研究所那不勒斯分部）
In this article we probe the proposed holographic duality between $T\bar{T}$ deformed two dimensional conformal field theory and the gravity theory of $\rm AdS_3$ with a Dirichlet cutoff by computing correlators of energy-momentum tensor. We focus on the large central charge sector of the $T\bar{T}$ CFT in a Euclidean plane and in a sphere, and compute the correlators of energy-momentum tensor using an operator identity promoted from the classical trace relation. The result agrees with a computation of classical pure gravity in $\rm AdS_3$ with the corresponding cutoff surface, given a hologra…
We compute the partition function of $2D$ Jackiw-Teitelboim (JT) gravity at finite cutoff in two ways: (i) via an exact evaluation of the Wheeler-DeWitt wave-functional in radial quantization and (ii) through a direct computation of the Euclidean path integral. Both methods deal with Dirichlet boundary conditions for the metric and the dilaton. In the first approach, the radial wavefunctionals are found by reducing the constraint equations to two first order functional derivative equations that can be solved exactly, including factor ordering. In the second approach we perform the path integra…
The problem of gravitational fluctuations confined inside a finite cutoff at radius $r=r_c$ outside the horizon in a general class of black hole geometries is considered. Consistent boundary conditions at both the cutoff surface and the horizon are found and the resulting modes analyzed. For general cutoff $r_c$ the dispersion relation is shown at long wavelengths to be that of a linearized Navier-Stokes fluid living on the cutoff surface. A cutoff-dependent line-integral formula for the diffusion constant $D(r_c)$ is derived. The dependence on $r_c$ is interpreted as renormalization group (RG…
In quantum models of gravity, it is surmized that configurations with degenerate coframes could occur during topology change of the underlying spacetime structure. However, the coframe is not the true Yang--Mills type gauge field of the translations, since it lacks the inhomogeneous gradient term in the gauge transformations. By explicitly restoring this ``hidden" piece within the framework of the affine gauge approach to gravity, one can avoid the metric or coframe degeneracy which would otherwise interfere with the integrations within the path integral. This is an important advantage for qua…
We conjecture an intrinsic UV cutoff for the validity of the effective field theory with a large number of species coupled to gravity. In four dimensions such a UV cutoff takes the form $Λ=\sqrt{λ/ N}M_p$ for $N$ scalar fields with the same potential $λϕ_i^4$, $i=1,...,N$. This conjecture implies that the assisted chaotic inflation or N-flation might be in the swampland, not in the landscape. Similarly a UV cutoff $Λ=gM_p/\sqrt{N}$ is conjectured for the U(1) gauge theory with $N$ species.
Any theory can be made Weyl invariant by introducing a dilaton. It is shown how to construct renormalization group equations for gravity that maintain this property. Explicit calculations are given only in the simplest approximation, namely for the one loop beta functions of a dilaton conformally coupled to a dynamical metric, but the results have wider validity. This formalism could be used to define the meaning of a theory with a position-dependent cutoff: it is equivalent to a theory with a constant cutoff, but a conformally related metric.
We show that with suitable choices of parametrization, gauge fixing and cutoff, the anomalous variation of the effective action under global rescalings of the background metric is identical to the derivative with respect to the cutoff, i.e. to the beta functional, as defined by the exact RG equation. The Ward identity and the RG equation can be combined, resulting in a modified flow equation that is manifestly invariant under global background rescalings.
The exact renormalization group equation for pure quantum gravity is used to derive the non-perturbative $\Fbeta$-functions for the dimensionless Newton constant and cosmological constant on the theory space spanned by the Einstein-Hilbert truncation. The resulting coupled differential equations are evaluated for a sharp cutoff function. The features of these flow equations are compared to those found when using a smooth cutoff. The system of equations with sharp cutoff is then solved numerically, deriving the complete renormalization group flow of the Einstein-Hilbert truncation in $d=4$. The…
Pure gravity in AdS$_3$ is a theory of boundary excitations, most simply expressed as a constrained free scalar with an improved stress tensor that is needed to match the Brown--Henneaux central charge. Excising a finite part of AdS gives rise to a static gauge Nambu--Goto action for the boundary graviton. We show that this is the $T\bar{T}$ deformation of the infinite volume theory, as the effect of the improvement term on the deformed action can be absorbed into a field redefinition. The classical gravitational stress tensor is reproduced order by order by the $T\bar{T}$ trace equation. We c…
We propose an effective model of strongly coupled gauge theory at finite temperature on $R^3$ in the presence of an infrared cutoff. It is constructed by considering the theory on $S^3$ with an infrared cutoff and then taking the size of the $S^3$ to infinity while keeping the cutoff fixed. This model reproduces various qualitative features expected from its gravity dual.
We show that the most general scalar-tensor theory of gravity up to four derivatives in $3+1$ dimensions is well-posed in a modified version of the CCZ4 formulation of the Einstein equations in singularity-avoiding coordinates. We demonstrate the robustness of our new formulation in practise by studying equal mass black hole binary mergers for different values of the coupling constants. Although our analysis of well-posedness is restricted to cases in which the couplings are small, we find that in simulations we are able to push the couplings to larger values, so that a certain weak coupling c…
Many examples of gravitational duals exist of theories that are highly supersymmetric and conformal in the UV yet have the same massless states as {\cal N}=2,1,0 QCD. We discuss such theories with an explicit UV cutoff and propose that, by tuning higher dimension operators at the cutoff by hand, the effects of the extra matter states in the UV may be removed from the IR physics. We explicitly work in the AdS-Schwartzschild description of QCD_4 and tune the operator TrF^4 by relaxing the near horizon limit to reproduce the lattice 0^{++} glueball mass results. We find that to reproduce the latt…
The future finite-time singularities emerging in alternative gravity dark energy models are classified and studied in Jordan and Einstein frames. It is shown that such singularity may occur even in flat spacetime for the specific choice of the effective potential. The conditions for the avoidance of finite-time singularities are presented and discussed. The problem is reduced to the study of a scalar field evolving on an effective potential by using the conformal transformations. Some viable modified gravity models are analyzed in detail and the way to cure singularity is considered by introdu…
In (2+1)-dimensional hydrodynamic systems with broken parity, the shear and bulk viscosity is joined by the Hall viscosity and curl viscosity. The dual holographic model has been constructed by coupling a pseudo scalar to the gravitational Chern-Simons term in (3+1)-dimensional bulk gravity. In this paper, we investigate the non-relativistic fluid with Hall viscosity and curl viscosity living on a finite radial cutoff surface in the bulk. Employing the non-relativistic hydrodynamic expansion method, we obtain the incompressible Navier-Stokes equations with Hall viscosity and curl viscosity. Un…
Quantum gravity is analyzed from the viewpoint of the renormalization group. The analysis is based on methods introduced by J. Polchinski concerning the perturbative renormalization with flow equations. In the first part of this work, the program of renormalization with flow equations is reviewed and then extended to effective field theories that have a finite UV cutoff. This is done for a scalar field theory by imposing additional renormalization conditions for some of the nonrenormalizable couplings. It turns out that one so obtains a statement on the predictivity of the effective theory at …
It has been shown that the primary, old-fashioned idea of Sakharov's induced gravity and gauge interactions, in the "one-loop dominance" version, works astonishingly well yielding phenomenologically reasonable results. As a byproduct, the issue of the role of the UV cutoff in the context of the induced gravity has been reexamined (an idea of self-cutoff induced gravity). As an additional check, the black hole entropy has been used in the place of the action. Finally, it has been explicitly shown that the induced coupling constants of gauge interactions of the standard model assume qualitativel…
We study the dual fluid on a finite cutoff surface outside the black brane horizon in the third order Lovelock gravity. Using nonrelativistic long-wavelength expansion, we obtain the incompressible Navier-Stokes equations of dual fluid with external force density on the finite cutoff surface. The viscosity to entropy density ratio $η/s$ is independent of cutoff surface and does not get modification from the third order Lovelock gravity influence. The obtained ratio agrees with the results obtained by using other methods, such as the Kubo formula at the AdS boundary and the membrane paradigm at…
We generalize the $T\overline{T}$ deformation of CFT$_2$ to higher-dimensional large-$N$ CFTs, and show that in holographic theories, the resulting effective field theory matches semiclassical gravity in AdS with a finite radial cutoff. We also derive the deformation dual to arbitrary bulk matter theories. Generally, the deformations involve background fields as well as CFT operators. By keeping track of these background fields along the flow, we demonstrate how to match correlation functions on the two sides in some simple examples, as well as other observables.
We proposed the generalized holographic dark energy model where infrared cutoff is identified with the combination of the FRW universe parameters: the Hubble rate, particle and future horizons, cosmological constant, the universe life-time (if finite) and their derivatives. It is demonstrated that with the corresponding choice of the cutoff one can map such holographic dark energy to modified gravity or gravity with general fluid. Explicitly, F(R) gravity and general perfect fluid are worked out in detail and corresponding infrared cutoff is found. Using this correspondence, we get realistic i…
We study numerically the first order radiative corrections to the self-energy, in covariant loop quantum gravity. We employ the recently developed 'sl2cfoam-next' spinfoam amplitudes library, and some original numerical methods. We analyze the scaling of the divergence with the infrared cutoff, for which previous analytical estimates provided widely different lower and upper bounds. Our findings suggest that the divergence is approximately linear in the cutoff. We also investigate the role of the Barbero-Immirzi parameter in the asymptotic behavior, the dependence of the scaling on some bounda…
We argue that quantum gravity is nonlocal, first by recalling well-known arguments that support this idea and then by focusing on a point not usually emphasized: that making a conventional effective field theory (EFT) for quantum gravity is particularly difficult, and perhaps impossible in principle. This inability to realize an EFT comes down to the fact that gravity itself sets length scales for a problem: when integrating out degrees of freedom above some cutoff, the effective metric one uses will be different, which will itself re-define the cutoff. We also point out that even if the previ…
A recently conjectured relashionship between UV and IR cutoffs in an effective field theory without quantum gravity is generalized in the presence of large extra dimensions. Estimates for the corrections to the usual calculation of observables within quantum field theory are used to put very stringent limits, in some cases, on the characteristic scale of the additional compactified dimensions. Implications for the cosmological constant problem are also discussed.
We develop the Schwinger-DeWitt technique for the covariant curvature expansion of the quantum effective action for brane induced gravity models in curved spacetime. This expansion has a part nonanalytic in DGP type scale parameter, leading to the cutoff scale which is given by the geometric average of the mass of the quantum field in the bulk and DGP scale. This cutoff is much higher than the analogous strong coupling scale of the DGP model treated by weak field expansion in the tree-level approximation. The lowest orders of this curvature expansion are calculated for the case of the scalar f…
We study tunneling of massless particles through quantum horizon of a Schwarzschild black hole where quantum gravity effects are taken into account. These effects are encoded in the existence of natural cutoffs as a minimal length, a minimal momentum and a maximal momentum through a generalized uncertainty principle. We study possible correlations between emitted particles to address the information loss problem. We focus also on the role played by these natural cutoffs on the tunneling rate through quantum horizon.
We propose the holographic principle as a dynamical cutoff for any quantum theory of gravity with a geometric description at low energies, incorporating ideas of effective field theory. We illustrate the proposal by revisiting the problem of defining a measure for homogeneous and isotropic spacetimes coupled to a scalar field and conclude by discussing the implications to the inflationary model.
We consider effective theories with massive fields that have spins larger than or equal to two. We conjecture a universal cutoff scale on any such theory that depends on the lightest mass of such fields. This cutoff corresponds to the mass scale of an infinite tower of states, signalling the breakdown of the effective theory. The cutoff can be understood as the Weak Gravity Conjecture applied to the Stückelberg gauge field in the mass term of the high spin fields. A strong version of our conjecture applies even if the graviton itself is massive, so to massive gravity. We provide further eviden…
Investigations of Quantum Einstein Gravity (QEG) based upon the effective average action employ a flow equation which does not contain any ultraviolet (UV) regulator. Its renormalization group trajectories emanating from a non-Gaussian fixed point define asymptotically safe quantum field theories. A priori these theories are, somewhat unusually, given in terms of their effective rather than bare action. In this paper we construct a functional integral representation of these theories. We fix a regularized measure and show that every trajectory of effective average actions, depending on an IR c…
The gravitational $\mathcal{S}$-matrix defined with an infrared (IR) cutoff factorizes into hard and soft factors. The soft factor is universal and contains all the IR and collinear divergences. Here we show, in a momentum space basis, that the intricate expression for the soft factor is fully reproduced by two boundary currents, which live on the celestial sphere. The first of these is the supertranslation current, which generates spacetime supertranslations. The second is its symplectic partner, the Goldstone current for spontaneously broken supertranslations. The current algebra has an off-…
On Integrable Structures on Non-compact Boundaries in Three-Dimensional Gravity
Fudan University（复旦大学）；Shanghai Institute for Mathematics and Interdisciplinary Sciences (SIMIS)（上海数学与交叉学科研究院）；Centro de Estudios Científicos (CECs)（科学研究中心）；Facultad de Ingeniería, Universidad San Sebastián（圣塞巴斯蒂安大学工程学院）；Qom University of Technology（库姆理工大学）；Julius-Maximilians-Universität Würzburg（维尔茨堡大学）
We propose a scenario of gravity mediated supersymmetry breaking (gravity mediation) in a supersymmetric Randall-Sundrum model. In our setup, both of the visible sector and the hidden sector co-exist on the infrared (IR) brane. We introduce the Polonyi model as a simple hidden sector. Due to the warped metric, the effective cutoff scale on the IR brane is ``warped down'', so that the gravity mediation occurs at a low scale. As a result, the gravitino is naturally the lightest superpartner (LSP) and contact interactions between the hidden and the visible sector fields become stronger. We addres…
This work is a continuation of studies presented in the papers arXiv:0911.5597, arXiv:1003.4523. In the work it is demonstrated that with the use of one and the same parameter deformation may be described for several cases of the General Relativity within the scope of both the Generalized Uncertainty Principle (UV-cutoff) and the Extended Uncertainty Principle (IR-cutoff). All these cases have a common thermodynamic interpretation of the corresponding gravitational equations. Consideration is given to the possibility for extension of the obtained results to more general cases. Possible general…
Weak Gravity Conjecture in the sky: gravitational waves from preheating in Einstein-Maxwell-Scalar EFT
School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, UCAS（基础物理与数学科学学院，杭州高等研究院，中国科学院大学）；Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；University of Chinese Academy of Sciences（中国科学院大学）；Department of Physics, Blackett Laboratory, Imperial College London（帝国理工学院布莱克特物理学系）；International Centre for Theoretical Physics Asia-Pacific（亚太理论物理中心）
