In this paper, we study mathematical functions of relevance to pure gravity in AdS3. Modular covariance places stringent constraints on the space of such functions; modular invariance places even stronger constraints on how they may be combined into physically viable candidate partition functions. We explicitly detail the list of holomorphic and anti-holomorphic functions that serve as candidates for chiral and anti-chiral partition functions and note that modular covariance is only consistent with such functions when the left (resp. right) central charge is an integer multiple of 8, $c\in 8\mathbb{N}$. We then find related constraints on the symmetry group of the corresponding topological, Chern-Simons, theory in the bulk of AdS. The symmetry group of the theory can be one of two choices: either $SO(2; 1) \times SO(2; 1)$ or its three-fold diagonal cover. We introduce the generalized Hecke operators which map the modular covariant functions to the modular covariant functions. With these mathematical results, we obtain conjectural partition functions for extremal CFT2s, and the corresponding microcanonical entropies, when the chiral central charges are multiples of eight. Finally, we compute subleading corrections to the Beckenstein-Hawking entropy in the bulk gravitational theory with these conjectural partition functions
We define a theory of gravity by constructing a gravitational holonomy operator in twistor space. The theory is a gauge theory whose Chan-Paton factor is given by a trace over elements of Poincaré algebra and Iwahori-Hecke algebra. This corresponds to a fact that, in a spinor-momenta formalism, gravitational theories are invariant under spacetime translations and diffeomorphism. The former symmetry is embedded in tangent spaces of frame fields while the latter is realized by a braid trace. We make a detailed analysis on the gravitational Chan-Paton factor and show that an S-matrix functional f…
We show that there is a dual description of conformal blocks of $d=2$ rational CFT in terms of Hecke eigenfields and eigensheaves. In particular, partition functions, conformal characters and lattice theta functions may be reconstructed from the action of Hecke operators. This method can be applied to: 1) rings of integers of Galois number fields equipped with the trace (or anti-trace) form; 2) root lattices of affine Kac-Moody algebras and WZW-models; 3) minimal models of Belavin-Polyakov-Zamolodchikov and related $d=2$ spin-chain/lattice models; 4) vertex algebras of Leech and Niemeier latti…
We introduce a complex pure connection action with constraints which is diffeomorphism and gauge invariant. Taking as an internal group $SU(2)$, we obtain, from the equations of motion, anti-self-dual Einstein spaces together with the zero torsion condition thanks to Bianchi identity. By applying the same procedure, we take as internal symmetry the super group $OSp(1|2)$ and by means of the Bianchi identity and integrability conditions, the equations of motion are those that come from anti-self-dual supergravity $N=1$ with cosmological constant sector.
The product spacetimes of constant curvature describe in Einstein gravity, which is linear in Riemann curvature, Nariai metric which is a solution of $Λ$-vacuum when curvatures are equal, $k_1=k_2$, while it is Bertotti-Robinson metric describing uniform electric field when curvatures are equal and opposite, $k_1=-k_2$. We probe pure Lovelock gravity by these simple product spacetimes and prove that the same characterization of these solutions is indeed true in general for pure Lovelock gravitational equation of order $N$ in $d=2N+2$ dimension. We also consider these solutions for the conventi…
We study an $SO(1,3)$ pure connection formulation in four dimensions for real-valued fields, inspired by the Capovilla, Dell and Jacobson complex self-dual approach. By considering the CMPR BF action, also, taking into account a more general class of the Cartan-Killing form for the Lie algebra $\mathfrak{so(1,3)}$ and by refining the structure of the Lagrange multipliers, we integrate out the metric variables in order to obtain the pure connection action. Once we have obtained this action, we impose certain restrictions on the Lagrange multipliers, in such a way that the equations of motion le…
We present a generalization of the n-dimensional (pure) Lovelock Gravity theory based on an enlarged Lorentz symmetry. In particular, we propose an alternative way to introduce a cosmological term. Interestingly, we show that the usual pure Lovelock gravity is recovered in a matter-free configuration. The five and six-dimensional cases are explicitly studied.
General expressions for the anomalies appearing in pure W_3 gravity are found by requiring that they satisfy a modified version of the Wess-Zumino consistency conditions in which the Ward identities are treated as nonvanishing quantities.
We explore the possibility of finding Pure Lovelock gravity as a particular limit of a Chern-Simons action for a specific expansion of the AdS algebra in odd dimensions. We derive this relation at the level of the action in five and seven dimensions. Additionally we provide the general result for higher dimensions and discuss some issues arising from the obtained dynamics.
The three-dimensional pure quantum gravity with negative cosmological constant is supposed to be dual to the extremal conformal field theory of central charge $c=24k$ in two dimensions. We employ the conformal bootstrap method to analyze the extremal CFTs, and find numerical evidence for the non-existence of the extremal CFTs for sufficiently large central charge ($k \ge 20$). We also explore near-extremal CFTs, a small modification of extremal ones, and find similar evidence for their non-existence for large central charge. This indicates, under the assumption of holomorphic factorization, th…
We study the classical dynamics of a completion of pure AdS gravity in 3D, whose only degrees of freedom are boundary gravitons and long strings. We argue that the best regime for describing pure gravity is that of "heavy" strings, for which back-reaction effects on the metric must be taken into account. We show that once back-reaction is properly accounted for, regular finite-energy states are produced by heavy strings even in the infinite-tension limit. Such a process is similar to, but different from, nucleation of space out of a "bubble of nothing."
The three-dimensional pure quantum gravity with a negative cosmological constant has been conjectured to be dual to an extremal conformal field theory (ECFT), of central charge c=24k for some positive integer k. We compute the partition function of the dual ECFT by summing over gravitational instanton contributions. In particular, we conjecture an exact expression for the contribution from handlebodies to the partition function for all genera and all values of k, and provide nontrivial evidences for the conjecture at genus two.
In this paper, we introduce higher dimensional thin-shell wormholes in pure Gauss-Bonnet gravity. The focus is on thin-shell wormholes constructed by $N\geq5$-dimensional spherically symmetric vacuum solutions. The results suggest that, under certain conditions, it is possible to have thin-shell wormholes that both satisfy the weak energy condition and be stable against radial perturbations.
We study collapse of inhomogeneous dust and null dust (Vaidya radiation) in pure Lovelock gravity in higher dimensions. Since pure Lovelock gravity is kinematic in odd d=2N+1 dimension, hence pertinent dimension for the study is even d=2N+2, where N is degree of Lovelock polynomial. It turns out that pure Lovelock collapse favors naked singularity as against black hole for the Einstein case in the same dimension while strength of singularity as measured by divergence of Kretshmann scalar is interestingly the same in the two cases; i.e. the corresponding scalars have the same fall off behavior.
We find a dual gravity theory to pure confining N=1 supersymmetric SU(N) gauge theory in four dimensions which has the correct gauge coupling running in addition to reproducing the appropriate pattern of chiral symmetry breaking. It is constructed in type IIB string theory on R^{1,3} X R^1 X S^2 X S^3 background with N number of electric D5 and 2N number of magnetic D7-branes filling four dimensional spacetime and wrapping respectively two and four cycles.
We probe the pure Einstein's gravity contributions to the second-order density power spectrum. In the small-scale, we discover that the Einstein's gravity contribution is negligibly small. This guarantees that Newton's gravity is sufficient to handle the baryon acoustic oscillation scale. In the large scale, however, we discover that the Einstein's gravity contribution to the second-order power spectrum dominates the linear-order power spectrum. Thus, pure Einstein gravity contribution appearing in the third-order perturbation leads to an infrared divergence in the power spectrum.
We calculate the expectation value of the Wilson line in the pure AdS$_3$ Einstein gravity theory and also the entanglement entropy in the boundary theory. Our one-loop calculation of entanglement entropy shows a shift of the central charge 26. Finally, we show that the Wilson line provides the equivalent description to the boundary entanglement entropy. This equivalence leads to a concrete example of the building of "minimum surface=entanglement entropy".
A proposal for the path-integral of pure-spin-connection formulation of gravity is described, based on the two-form formulation of Capovilla et. al. It is shown that the resulting effective-action for the spin-connection, upon functional integration of the two-form field $Σ$ and the auxiliary matrix field $ψ$ is {\it non-polynomial}, even for the case of vanishing cosmological constant and absence of any matter couplings. Further, a diagramatic evaluation is proposed for the contribution of the matrix-field to the pure spin connection action.
W_4 gravity is treated algebraically, represented by a set of transformations on classical fields. The Ward identities of the theory are determined by requiring the algebra to close. The general forms for the anomalies are found by looking for solutions to the Wess-Zumino consistency conditions, and some specific cases are considered.
Pure $R^2$ gravity has been shown to be equivalent to Einstein gravity with non-zero cosmological constant and a massless scalar field. We show that the Palatini formulation of pure $R^2$ gravity is equivalent to Einstein gravity with non-zero cosmological constant as before but with no massless scalar field. This is an important new development because the massless scalar field is not readily identifiable with any known particle in nature or unknown particles like cold dark matter which are expected to be massive. We then include a non-minimally coupled Higgs field as well as fermions to disc…
The first truly non-MHV interaction vertices in the light-cone formulation of pure gravity appear at order 6. From a closed form expression, for gravitation in the light-cone gauge, we extract and present all 6-point interaction vertices. We invoke symmetry arguments to explain the structure of these vertices. Symmetry considerations also allow us to place constraints on the structure of all even- and odd-point vertices in the theory. The origin of MHV vertices within this formalism is also discussed.
In first order formulation of pure gravity, we find a new class of solutions to the equations of motion represented by degenerate four-geometries. These configurations are described by non- invertible tetrads with two zero eigenvalues and admit non-vanishing torsion. The homogeneous ones among these infinitely many degenerate solutions admit a geometric classification provided by the three fundamental geometries that a closed two-surface can accomodate, namely, E^2 , S^2 and H^2.
We study how the standard definitions of ADM mass and Brown-York quasi-local energy generalize to pure Lovelock gravity. The quasi-local energy is renormalized using the background subtraction prescription and we consider its limit for large surfaces. We find that the large surface limit vanishes for asymptotically flat fall-off conditions except in Einstein gravity. This problem is avoided by focusing on the variation of the quasi-local energy which correctly approaches the variation of the ADM mass for large surfaces. As a result, we obtain a new simple formula for the ADM mass in pure Lovel…
The general structure of the renormalization group equations for the low energy effective field theory formulation of pure gravity is presented. The solution of these equations takes a particular simple form if the mass scale of the effective theory is much smaller than the Planck mass (a possibility compatible with the renormalization of the effective theory). A theory with just one free renormalized parameter is obtained when contributions suppressed by inverse powers of the Planck mass are neglected.
We show that without introducing additional fields or extra degrees of freedom, a specific higher derivative extension of Einstein's gravity that has only a massless spin-2 excitation in its perturbative spectrum, has an inflationary period, a quasi-de Sitter phase with enough number of e-foldings required to solve the horizon and related problems. The crucial ingredient in the construction is the curvature dependence of the effective Newton's constant.
The Barbero-Immirzi (BI) parameter is promoted to a field and a canonical analysis is performed when it is coupled with a Nieh-Yan topological invariant. It is shown that, in the effective theory, the BI field is a canonical pseudoscalar minimally coupled with gravity. This framework is argued to be more natural than the one of the usual Holst action. Potential consequences in relation with inflation and the quantum theory are briefly discussed.
We study two exactly solvable five-dimensional thick brane world models in pure metric $f(R)$ gravity. Working in the Einstein frame, we show that these solutions are stable against small linear perturbations, including the tensor, vector, and scalar modes. For both models, the corresponding gravitational zero mode is localized on the brane, which leads to the four-dimensional Newton's law; while the massive modes are nonlocalized and only contribute a small correction to the Newton's law at a large distance.
We study dynamical structure of Pure Lovelock gravity in spacetime dimensions higher than four using the Hamiltonian formalism. The action consists of cosmological constant and a single higher-order polynomial in the Riemann tensor. Similarly to Einstein-Hilbert action, it possesses a unique constant curvature vacuum and charged black hole solutions. We analyze physical degrees of freedom and local symmetries in this theory. In contrast to the Einstein-Hilbert case, a number of degrees of freedom depends on the background and can vary from zero to the maximal value carried by the Lovelock theo…
We propose a spin foam model for pure gauge fields coupled to Riemannian quantum gravity in four dimensions. The model is formulated for the triangulation of a four-manifold which is given merely combinatorially. The Riemannian Barrett--Crane model provides the gravity sector of our model and dynamically assigns geometric data to the given combinatorial triangulation. The gauge theory sector is a lattice gauge theory living on the same triangulation and obtains from the gravity sector the geometric information which is required to calculate the Yang--Mills action. The model is designed so that…
The microscopic theories of quantum gravity related to integrable lattice models can be constructed as special deformations of pure gravity. Each such deformation is defined by a second order differential operator acting on the coupling constants. As a consequence, the theories with matter fields satisfy a set of constraints inherited from the integrable structure of pure gravity. In particular, a set of bilinear functional equations for each theory with matter fields follows from the Hirota equations defining the KP (KdV) structure of pure gravity.
Strings propagating in three-dimensional anti-de Sitter space with a background antisymmetric tensor field are well understood, even at the quantum level. Pure three-dimensional gravity with a negative cosmological constant is potentially important because of the existence of black hole solutions and an asymptotic conformal symmetry, but it is mysterious and surprisingly resistant to analysis. In this letter, the two theories are related by a map on the classical level. The map is obtained by gauge fixing the string completely, like in a light cone gauge, and comparing the resulting constraine…
How to deal with conformal and pure scale-invariant theories of gravity in d dimensions?
Kavli IPMU (WPI), UTIAS, The University of Tokyo（东京大学 Kavli宇宙物理数学研究所（WPI）、UTIAS）；Center for Data-Driven Discovery（数据驱动发现中心）；Arnold Sommerfeld Center for Theoretical Physics, Ludwig–Maximilians–Universität München（慕尼黑大学阿诺德·索末菲理论物理中心）
It is well known that a rotating black hole in four dimension could be overspun by linear order test particle accretion which however always gets overturned when non-linear perturbations are included. It turns out that in the Einstein gravity, repulsion due to rotation dominates over attraction due to mass in dimensions, $D>5$, and consequently black hole cannot be overspun even for linear order accretion. For the pure Lovelock rotating black hole, this dimensional threshold is $D>4N+1$ where $N$ is degree of single $N$th order term in the Lovelock polynomial in the action. Thus the pure Lovel…
The assumptions of the Hawking-Penrose singularity theorem are not covariant under field redefinitions. Thus we propose to study singularities in field space, where the spacetime metric is treated as a coordinate along with any other fields. We show that the field-space Kretschmann scalar for a certain choice of the DeWitt field-space metric is everywhere finite. This fact could be interpreted as an indication that no singularities actually exist in pure gravity for any gravitational action. In particular, all vacuum singularities of General Relativity result from an unhappy choice of field va…
We obtain rotating black hole metric for higher dimensional Einstein and pure Lovelock gravity by employing two independent and well motivated methods. One is based on the principle of incorporation of Newtonian acceleration for timelike motion while no acceleration for null motion. The other is the well known Newman-Janis alogrithm that converts a static black hole into a rotating one through a complex transformation. It turns out that both the methods give the same metric which for Einst of the eour pure Lovelock metricein black hole is an exact vacuum solution while for pure Lovelock black …
The pure gravity Lagrangian can be written as the "square" of the pure Yang-Mills Lagrangian to second order in coupling constants. This paper uses this form of the gravity Lagrangian as a starting point to arrive at a compact light-cone superspace Lagrangian for N=8 Supergravity to order $κ$^2.
In this paper the Seiberg-Witten map is first analyzed for non-commutative Yang-Mills theories with the related methods, developed in the literature, for its explicit construction, that hold for any gauge group. These are exploited to write down the second-order Seiberg-Witten map for pure gravity with a constant non-commutativity tensor. In the analysis of pure gravity when the classical space-time solves the vacuum Einstein equations, we find for three distinct vacuum solutions that the corresponding non-commutative field equations do not have solution to first order in non-commutativity, wh…
The Lovelock gravity is a fascinating extension of general relativity, whose action consists of the dimensionally extended Euler densities. Compared to other higher order derivative gravity theories, the Lovelock gravity is attractive since it has a lot of remarkable features such as that there are no more than second order derivatives with respect to metric in its equations of motion, and that the theory is free of ghost. Recently in the study of black string and black brane in the Lovelock gravity, a special class of Lovelock gravity is considered, which is named pure Lovelock gravity, where…
We perform a canonical quantization of pure gravity on AdS3 using as a technical tool its equivalence at the classical level with a Chern-Simons theory with gauge group SL(2,R)xSL(2,R). We first quantize the theory canonically on an asymptotically AdS space --which is topologically the real line times a Riemann surface with one connected boundary. Using the "constrain first" approach we reduce canonical quantization to quantization of orbits of the Virasoro group and Kaehler quantization of Teichmuller space. After explicitly computing the Kaehler form for the torus with one boundary component…
We consider the BRST and superconformal properties of the ghost action of 2-D supergravity. Using the background spin structure on the worldsheet, we show that this action can be transformed by canonical field transformations to reach other conformal models such as the 2-D topological gravity or the chiral models for which the gauge variation of the action reproduces the left or right conformal anomaly. Our method consists in using the gravitino and its ghost as fundamental blocks to build fields with different conformal weights and statistics. This indicates in particular that the twisting of…
In the first order formalism of gravitational theories, the spacetime connection is considered as an independent variable to vary together with the metric. However, the metric still generates its Levi-Civita connection that turns out to determine the geodesics of matter. Recently, "hybrid" gravity theories have been introduced by constructing actions involving both the independent Palatini connection and the metric Levi-Civita connection. In this study a method is developed to analyse the field content of such theories, in particular to determine whether the propagating degrees of freedom are …
The pure $R^2$ gravity is equivalent to Einstein gravity with cosmological constant and a massless scalar field and it further possesses the so-called restricted Weyl symmetry which is a symmetry larger than scale symmetry. To incorporate matter, we consider a restricted Weyl invariant action composed of pure $R^2$ gravity, SU(2) Yang-Mills fields and a non-minimally coupled massless Higgs field (a triplet of scalars). When the restricted Weyl symmetry is spontaneously broken, it is equivalent to an Einstein-Yang-Mills-Higgs (EYMH) action with a cosmological constant and a massive Higgs non-mi…
We explore the large spin spectrum in two-dimensional conformal field theories with a finite twist gap, using the modular bootstrap in the lightcone limit. By recursively solving the modular crossing equations associated to different $PSL(2,\mathbb{Z})$ elements, we identify the universal contribution to the density of large spin states from the vacuum in the dual channel. Our result takes the form of a sum over $PSL(2,\mathbb{Z})$ elements, whose leading term generalizes the usual Cardy formula to a wider regime. Rather curiously, the contribution to the density of states from the vacuum beco…
The quantization scheme based on reduction of the physical states \cite{Park:2014tia} is extended to two gravity-matter systems and pure dS gravity. For the gravity-matter systems we focus on quantization in a flat background for simplicity, and renormalizability is established through gauge-fixing of matter degrees of freedom. Quantization of pure dS gravity has several new novel features. It is noted that the infrared divergence does not arise in the present scheme of quantization. The lapse function constraint plays a crucial role.
We provide evidence in favor of the conjectured duality between color and kinematics for the case of nonsupersymmetric pure Yang-Mills amplitudes by constructing a form of the one-loop four-point amplitude of this theory that makes the duality manifest. Our construction is valid in any dimension. We also describe a duality-satisfying representation for the two-loop four-point amplitude with identical four-dimensional external helicities. We use these results to obtain corresponding gravity integrands for a theory containing a graviton, dilaton, and antisymmetric tensor, simply by replacing col…
In this letter I study the universality of the nonperturbative effects and the vacua structure of the stochastic stabilization of the matrix models which defines Pure 2D Quantum Gravity. I show also that there is not tunneling, in the continuum limit, between the one-arc and three-arc solutions of the simplest matrix model which defines the flow between Pure Gravity and the Lee-Yang model.
A field theory is constructed in the context of parameterized absolute parallelism geometry. The theory is shown to be a pure gravity one. It is capable of describing the gravitational field and a material distribution in terms of the geometric structure of the geometry used (the parallelization vector fields). Three tools are used to attribute physical properties to the geometric objects admitted by the theory. Poisson and Laplace equations are obtained in the linearized version of the theory. The spherically symmetric solution of the theory, in free space, is found to coincide with the Schwa…
We consider pure states in the SYK model. These are given by a simple local condition on the Majorana fermions, evolved over an interval in Euclidean time to project on to low energy states. We find that "diagonal" correlators are exactly the same as thermal correlators at leading orders in the large $N$ expansion. We also describe "off diagonal" correlators that decay in time, and are given simply in terms of thermal correlators. We also solved the model numerically for low values of $N$ and noticed that subsystems become typically entangled after an interaction time. In addition, we identifi…
We discuss the quantization of pure string--inspired dilaton--gravity in $(1+1)$--dimensions, and of the same theory coupled to scalar matter. We perform the quantization using the functional Schroedinger and BRST formalisms. We find, both for pure gravity and the matter--coupled theory, that the two quantization procedures give inequivalent ``physical'' results.
