P. Mitra
Counting of microscopic states of black holes is discussed within the framework of loop quantum gravity. There are two different ways, one allowing for all spin states and the other involving only pure horizon states. The number of states with a definite value of the total spin is also found.
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We argue that counting black hole states in loop quantum gravity one should take into account only states with the minimal spin at the horizon.
There are two ways of counting microscopic states of black holes in loop quantum gravity, one counting all allowed spin network labels $j,m$ and the other involving only the labels $m$. Counting states with $|m|=j$, as done in a recent Letter, does not follow either.
Counting of microscopic states of black holes is performed within the framework of loop quantum gravity. This is the first calculation of the pure horizon states using statistical methods, which reveals the possibility of additional states missed in the earlier calculations, leading to an increase of entropy. Also for the first time a microcanonical temperature is introduced within the framework.
The two ways of counting microscopic states of black holes in the U(1) formulation of loop quantum gravity, one counting all allowed spin network labels j,m and the other only m labels, are discussed in some detail. The constraints on m are clarified and the map between the flux quantum numbers and m discussed. Configurations with |m|=j, which are sometimes sought after, are shown to be important only when large areas are involved. The discussion is extended to the SU(2) formulation.
It has been argued that Horava gravity needs to be extended to include terms that mix spatial and time derivatives in order avoid unacceptable violations of Lorentz invariance in the matter sector. In an earlier paper we have shown that including such mixed derivative terms generically leads to 4th instead of 6th order dispersion relations and this could be (naively) interpreted as a threat to renormalizability. We have also argued that power-counting renormalizability is not actually compromised, but instead the simplest power-counting renormalizable model is not unitary. In this paper we con…
We consider the version of Hořava gravity where "detailed balance" is consistently implemented, so as to limit the huge proliferation of couplings in the full theory and obtain healthy dynamics at low energy. Since a superpotential which is third-order in spatial derivatives is not sufficient to guarantee the power-counting renormalizability of the spin-0 graviton, one needs to go an order beyond in derivatives, building a superpotential up to fourth-order spatial derivatives. Here we perturb the action to quadratic order around flat space and show that the power-counting renormalizability of …
It is well known that General Relativity cannot be considered under the standard of a perturbatively renormalizable quantum field theory, but asymptotic safety is taken into account as a possibility for the formulation of gravity as a non-perturbative renormalizable theory. Recently, the entropy argument has however stepped into the discussion claiming for a "no-go" to the asymptotic safety argument. In this paper, we present simple counter-examples, considering alternative theories of gravity, to the entropy argument as further indications, among others, on the possible flows in the assumptio…
State counting in gravity and maximal entropy principle
本文通过引力路径积分视角证明黑孔熵的状态计数与霍金辐射纠缠熵的Page曲线等价，从而解决信息丢失悖论。
We continue the study of covariant power-counting renormalizable gravity constrained by scalar Lagrange multiplier. Lorentz symmetry breaking is investigated in such a theory in comparison with the one in ghost condensation model. Covariant power-counting renormalizable vector gravity which is invariant under $U(1)$ gauge symmetry is proposed. Several forms of vector Lagrange multiplier in this theory are discussed. It is shown that covariant scalar/vector gravity under consideration may have power-law or de Sitter accelerating cosmological solution corresponding to inflationary era. Simplest …
A state of a black hole in loop quantum gravity is given by a distribution of spins on punctures on the horizon. The distribution is of the Boltzmann type, with the area playing the role of the energy. In investigations where the total area was kept approximately constant, there was a kind of thermal equilibrium between the spins which have the same analogue temperature and the entropy was proportional to the area. If the area is precisely fixed, however, multiple constraints appear, different spins have different analogue temperatures and the entropy is not strictly linear in the area, but is…
We suggest a new scenario of gravitation in which gravity at the fundamental level is described by a Riemannian (i.e. locally Euclidean) theory without the notion of time. The Lorentzian metric structure and the notion of time emerge as effective properties at long distances. On the other hand, at short distances, higher derivative terms compatible with the Riemannian diffeomorphism become important and the system is described by a power-counting renormalizable Riemannian theory.
In an earlier article [arXiv:0902.0590 [hep-th], Phys. Rev D80 (2009) 025011], I discussed the potential benefits of allowing Lorentz symmetry breaking in quantum field theories. In particular I discussed the perturbative power-counting finiteness of the normal-ordered :P(phi)^{z>=d}_{d+1}: scalar quantum field theories, and sketched the implications for Horava's model of quantum gravity. In the current rather brief addendum, I will tidy up some dangling issues and fill out some of the technical details of the argument indicating the power-counting renormalizability of a z>=d variant of Horava…
We investigated the distinction between two kinds of "Complexity equals Action"(CA) conjecture counting methods which are separately provided by Brown $ et\, al. $ and Lehner $et\, al.$ separately. For the late-time CA complexity growth rate, we show that the difference between two counting methods only comes from the boundary term of the segments on the horizon. However, both counting methods give the identical late-time result. Our proof is general, independent of the underlying theories of higher curvature gravity as well as the explicit stationary spacetime background. To be specific, we c…
Counting Black Hole Microstates at Future Null Infinity
提出基于二维伸缩子-引力系统在未来零无穷远处渐近对称性正则量子化的黑洞微观态计数方法，通过Cardy型公式导出贝肯斯坦-霍金熵，体自由度作为软引力子源。
On the power counting of loop diagrams in general relativity
广义相对论中的一类回路图似乎有一种行为，它会破坏能量膨胀对量子效应的效用。我们表明，通过研究特定的图表，取消发生恢复预期的行为的能量膨胀。通过考虑物理规范中的功率计数，我们证明了明显的不良行为是规范伪像，并且量子环以良好的能量膨胀进入。
Loop Gravity provides a microscopic derivation of Black Hole entropy. In this paper, I show that the microstates counted admit a semiclassical description in terms of shapes of a tessellated horizon. The counting of microstates and the computation of the entropy can be done via a mapping to an equivalent statistical mechanical problem: the counting of conformations of a closed polymer chain. This correspondence suggests a number of intriguing relations between the thermodynamics of Black Holes and the physics of polymers.
We analyse the power counting renormalizability of the quantum field theory of Einstein or Einstein-Gauss-Bonnet gravity in D+2 dimensional Lifshitz spacetime. We show the spectral dimension becomes 2+(D/z) at the UV region where z is the critical exponent. Since it is larger than two, the quantum theory of Einstein gravity is not power counting renormalizable. For the pure Einstein-Gauss-Bonnet gravity, where Lifshitz spacetime is allowed only when the parameters are fine tuned, it happens that the graviton modes do not propagate and the quantum field theory is accidentally renormalizable whe…
We apply a recent argument of Verlinde to loop quantum gravity, to conclude that Newton's law of gravity emerges in an appropriate limit and setting. This is possible because the relationship between area and entropy is realized in loop quantum gravity when boundaries are imposed on a quantum spacetime.
We investigate the Lagrange multiplier formulation of teleparallel theories, including f(T) gravity, in which the connection is not set to zero a priori and compare it with the pure frame theory. We show explicitly that the two formulations are equivalent, in the sense that the dynamical equations have the same content. One consequence is that the manifestly local Lorentz invariant f(T) theory cannot be expected to be free of pathologies, which were previously found to plague f(T) gravity formulated in the usual pure frame approach.
In this paper, we provide an approach for the calculation of one-loop effective actions, vacuum energies, and spectral counting functions and discuss the application of this approach in some physical problems. Concretely, we construct the equations for these three quantities; this allows us to achieve them by directly solving equations. In order to construct the equations, we introduce shifted local one-loop effective actions, shifted local vacuum energies, and local spectral counting functions. We solve the equations of one-loop effective actions, vacuum energies, and spectral counting functi…
In the recently proposed non-local theory of quantum gravity one can avoid massive tensor ghosts at the tree level by a special choice of the non-local form factor between the two Ricci tensors. We show that at the quantum level this theory has an infinite amount of massive unphysical states, mostly corresponding to complex poles.
It is shown that a relation between entropy and minimal area holds in loop quantum gravity, reminiscent of the Ryu-Takayanagi relation.
We give a complete and detailed description of the computation of black hole entropy in loop quantum gravity by employing the most recently introduced number-theoretic and combinatorial methods. The use of these techniques allows us to perform a detailed analysis of the precise structure of the entropy spectrum for small black holes, showing some relevant features that were not discernible in previous computations. The ability to manipulate and understand the spectrum up to the level of detail that we describe in the paper is a crucial step towards obtaining the behavior of entropy in the asym…
Loop Quantum gravity predicts that black holes evolve into white holes.
We introduce squeezed vacua in loop quantum gravity, a new overcomplete basis of states that contain prescribable correlations between geometric operators. We study the behavior of long-range correlations and discuss the relevance of these states for the reconstruction of a semiclassical spacetime from loop quantum gravity.
Horava gravity has been constructed so as to exhibit anisotropic scaling in the ultraviolet, as this renders the theory power-counting renormalizable. However, when coupled to matter, the theory has been shown to suffer from quadratic divergences. A way to cure these divergences is to add terms with both time and space derivatives. We consider this extended version of the theory in detail. We perform a perturbative analysis that includes all modes, determine the propagators and discuss how including mixed-derivative terms affects them. We also consider the Lifshitz scalar with mixed-derivative…
An outstanding challenge for models of non-perturbative quantum gravity is the consistent formulation and quantitative evaluation of physical phenomena in a regime where geometry and matter are strongly coupled. After developing appropriate technical tools, one is interested in measuring and classifying how the quantum fluctuations of geometry alter the behaviour of matter, compared with that on a fixed background geometry. In the simplified context of two dimensions, we show how a method invented to analyze the critical behaviour of spin systems on flat lattices can be adapted to the fluctuat…
Counting Degrees of Freedom: A Method Applicable from Scalars to f(Q) Gravity and Beyond
本文提出一种直接作用于场方程、非拉格朗日也非哈密顿的逐步方法，用于计算一般场论自由度并识别约束，并成功应用于传统 Dirac-Bergmann 算法失效的 f(Q) 引力，得到七个传播自由度。
We introduce a new loop expansion that provides a resolution of the identity in the Hilbert space of loop quantum gravity on a fixed graph. We work in the bosonic representation obtained by the canonical quantization of the spinorial formalism. The resolution of the identity gives a tool for implementing the projection of states in the full bosonic representation onto the space of solutions to the Gauss and area matching constraints of loop quantum gravity. This procedure is particularly efficient in the semiclassical regime, leading to explicit expressions for the loop expansions of coherent,…
We compute the grand partition function of $\mathcal{N}=4$ SYM at one-loop in the $SU(2)$ sector with general chemical potentials, extending the results of Pólya's theorem. We make use of finite group theory, applicable to all orders of $1/N_c$ expansion. We show that only the planar terms contribute to the grand partition function, which is therefore equal to the grand partition function of an ensemble of XXX$_\frac12$ spin chains. We discuss how Hagedorn temperature changes on the complex plane of chemical potentials.
Ambiguity of the one-loop calculations in a nonrenormalizable quantum gravity.
本文讨论了不可重正化引力理论中背景场法计算单圈反项时的不确定性。给出了这种模糊计算的一些例子。证明了量子引力中一阶和二阶形式的不等价性。
A simple argument indicates that covariant loop gravity (spinfoam theory) predicts a maximal acceleration, and hence forbids the development of curvature singularities. This supports the results obtained for cosmology and black holes using canonical methods.
In this paper we summarize "loop quantum gravity" (LQG) and we show how ideas developed in LQG can solve the black hole singularity problem when applied to a minisuperspace model.
By making use of the background field method, the one-loop quantization for Euclidean Einstein-Weyl quadratic gravity model on the de Sitter universe is investigated. Using generalized zeta function regularization, the on-shell and off-shell one-loop effective actions are explicitly obtained and one-loop renormalizability, as well as the corresponding one-loop renormalization group equations, are discussed. The so called critical gravity is also considered.
We numerically study the topologically twisted index of several three-dimensional supersymmetric field theories on a genus $g$ Riemann surface times a circle, $Σ_g\times S^1$. We show that for a large class of theories with leading term of the order $N^{3/2}$, where $N$ is generically the rank of the gauge group, there is a universal logarithmic correction of the form $\frac{g-1}{2} \log N$. We explain how this logarithmic subleading correction can be obtained as a one-loop effect on the dual supergravity theory for magnetically charged, asymptotically AdS$_4\times M^7$ black holes for a large…
Unlike the one-loop QG divergences in D=4, which can all be transformed away, those in arbitrary higher (even) dimension cannot.
In this article we further investigate the construction of graph coherent states, first introduced in [1], in the context of loop quantum gravity. We specifically investigate the possibility of defining a family of graph coherent states adapted to the canonical loop quantum gravity Hamiltonian. After discussing various aspects of the general framework and the choice of operators, we use the Euclidean part of the Hamiltonian operator to propose a generator of the generalized canonical structure, necessary to define the coherent states. We then apply the construction procedure, leading to a new …
We present the complete set of universal one-loop beta functions of cubic gravity in six dimensions. The system admits over 8000 distinct fixed points, of which more than 200 are real. Some of them might be relevant for the quantisation of gravity in the physical case of four dimensions.
I review the definition of n-point functions in loop quantum gravity, discussing what has been done and what are the main open issues. Particular attention is dedicated to gauge aspects and renormalization.
The space of states of quantum gravity in terms of loops and extended loops: some remarks
本文综述了量子引力所有约束的几种解决方案的现状，这些解决方案是根据回路和扩展回路提出的。我们讨论了几个结果的陷阱，特别是讨论的问题的协方差和正则化的约束条件的扩展循环。我们还提出了一个形式主义的“加厚了循环”，它不面临扩展循环的协方差问题，并可能允许正则表达式在一个一致的方式。
The entropy of a black hole can be obtained by counting states in loop quantum gravity. The dominant term depends on the Immirzi parameter involved in the quantization and is proportional to the area of the horizon, while there is a logarithmic correction with coefficient -1/2.
We discuss the meaning of geometrical constructions associated to loop quantum gravity states on a graph. In particular, we discuss the "twisted geometries" and derive a simple relation between these and Regge geometries.
Loop quantum gravity, a non-perturbative and manifestly background free, quantum theory of gravity implies that at the kinematical level the spatial geometry is discrete in a specific sense. The spirit of background independence also requires a non-standard quantum representation of matter. While loop quantization of standard model fields has been proposed, detail study of its implications is not yet available. This review aims to survey the various efforts and results.
Calculation of amplitudes in perturbative quantum field theory involve large loop integrals. The complexity of those integrals, in combination with the large number of Feynman diagrams, make the calculations very difficult. Reduction methods proved to be very helpful, lowering the number of integrals that need to be actually calculated. Especially, the reduction at the integrand level technique, improves the speed and set-up of these calculations. In this article we demonstrate, by counting the numbers of tensor structures and independent coefficients, how to write such relations at the integr…
In this note we reply to the criticism by Corichi concerning our proposal for an equidistant area spectrum in loop quantum gravity. We further comment on the emission properties of black holes and on the statistics of links.
Motivated by the analogy proposed by Witten between Chern-Simons and Conformal Field Theories, we explore an alternative way of computing the entropy of a black hole starting from the isolated horizon framework in Loop Quantum Gravity. The consistency of the result opens a window for the interplay between Conformal Field Theory and the description of black holes in Loop Quantum Gravity.
Gauge and parametrization dependencies of the one-loop counterterms in the Einstein gravity.
研究了爱因斯坦引力中质量壳上单圈反项的参数化和规范依赖性。讨论了质量壳上的环计算结果的物理意义和不可重整化理论中重整化群函数的参数化依赖性。
In this note we point out that the one-loop partition function of three-dimensional flat gravity, computed along the lines originally developed for the anti-de Sitter case, reproduces characters of the BMS3 group.
Models of loop quantum gravity based on real connections have a deformed notion of general covariance, which leads to the phenomenon of signature change. This result is confirmed here in a general analysis of all midisuperspace models without local degrees of freedom. As a subclass of models, 2-dimensional theories of dilaton gravity appear, but a larger set of examples is possible based only on the condition of anomaly freedom. While the classical dilaton gravity models are the only such systems without deformed covariance, they do give rise to signature change when holonomy modifications are…
I give a brief introduction to the relation between loop quantum gravity and twistor theory, and comment on some perspectives on the problem of time.
Projective Invariance and One-Loop Effective Action in Affine-Metric Gravity Interacting with Scalar Field
我们研究了射影不变性对理论重整化性质的影响。在引力与标量场相互作用的最一般情况下，计算了单圈反项。
We evaluate the 1-loop partition function of conformal gravity in four dimensions around an $AdS_4$ background, using the heat kernel techniques. We give expressions for the relevant thermodynamical quantities and compare our results with the ones from the literature.
This is a historical note. In 1974 I was an undergraduate student of L.D. Faddeev. I was working on quantum gravity [without matter] in one loop approximation. I discovered [simultaneously with G. t'Hooft M. Veltman] that on mass shell ultra-violet divergences cancel. The submission is a translation of the Diploma.
We explicitly construct and characterize all possible independent loop states in 3+1 dimensional loop quantum gravity by regulating it on a 3-d regular lattice in the Hamiltonian formalism. These loop states, characterized by the (dual) angular momentum quantum numbers, describe SU(2) rigid rotators on the links of the lattice. The loop states are constructed using the Schwinger bosons which are harmonic oscillators in the fundamental (spin half) representation of SU(2). Using generalized Wigner Eckart theorem, we compute the matrix elements of the volume operator in the loop basis. Some simpl…
Motivated by the dark energy issue, the one-loop quantization approach for a class of relativistic higher order theories is discussed in some detail. A specific F(R,P,Q) gravity model at the one-loop level in a de Sitter universe is investigated, extending the similar program developed for the case of $F(R)$ gravity. The stability conditions under arbitrary perturbations are derived.
We construct the operator that projects on the physical states in loop quantum gravity. To this aim, we consider a diffeomorphism invariant functional integral over scalar functions. The construction defines a covariant, Feynman-like, spacetime formalism for quantum gravity and relates this theory to the spin foam models. We also discuss how expectation values of physical quantity can be computed.
In non-supersymmetric covariant quantum gravity theory, for each system of gravity coupled with single field is one-loop divergent. Since adding other fields or other interactions to each system generates more possible counter-Lagrangian terms, there is room for improvement to restore renormalizability. In this paper, we consider Einstein-Maxwell fields coupled with electrically charged scalar which is the simplest model among the systems of gravity coupled with multiple fields having their own interaction. First, we introduce how to calculate the possible one-loop diagrams in Einstein-SQED sy…
We introduce the group field theory formalism for quantum gravity, mainly from the point of view of loop quantum gravity, stressing its promising aspects. We outline the foundations of the formalism, survey recent results and offer a perspective on future developments.
We outline how the Wald entropy formula naturally arises in loop quantum gravity based on recently introduced dimension-independent connection variables. The key observation is that in a loop quantization of a generalized gravity theory, the analog of the area operator turns out to measure, morally speaking, the Wald entropy rather than the area. We discuss the explicit example of (higher-dimensional) Lanczos-Lovelock gravity and comment on recent work on finding the correct numerical prefactor of the entropy by comparing it to a semiclassical effective action.
All Loop Scattering As A Counting Problem
本文通过运动学空间中的组合计数问题重新表述带色标量粒子三次相互作用理论的全阶圈积分振幅，摆脱传统费曼图求和，为从更深数学结构涌现时空与量子力学规则提供了新路径。
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