Partition Function Of Quantum Gravity Research Articles

3D Quantum Gravity Partition Function at Three Loops

3D Quantum Gravity Partition Function at Three Loops

Logarithmic corrections, entanglement entropy, and UV cutoffs in de Sitter spacetime

It has been argued that the entropy of de Sitter space corresponds to the entanglement between disconnected regions computable by switching on a replica parameter q modeled by the quotient dS/ℤq. Within this framework, we show that the centrally-extended asymptotic symmetry algebra near the cosmic horizon is a single copy of the Virasoro algebra. The resulting density of states matches the semi-classical result of Gibbons and Hawking up to an undetermined constant that is chosen to reproduce the entanglement entropy previously found in the literature. It follows that the logarithmic quantum corrections to the Cardy entropy reproduces the known one-loop result computed in the bulk in the presence of a cutoff. The resulting entanglement entropy follows the divergent area law, where the UV cutoff is now a function of the replica parameter. Thus, as the near-horizon CFT fixes the cutoff in units of the Planck scale, the model can be viewed as a probe into whether the defect Hilbert space has a finite dimension; indeed, the limit q → 0, reproduces Banks’ formula. We also study the quantum corrections of the effective description of the horizon entropy by means of Liouville field theory, where the large q limit corresponds to a realization of dS3/CFT2 correspondence matching the logarithmic corrections to three-dimensional de Sitter space obtained by computing the one-loop contribution to the quantum gravity partition function in the round three-sphere.

Supersymmetric localization on dS: sum over topologies

We find the exact quantum gravity partition function on the static patch of 3d de Sitter spacetime. We have worked in the Chern Simons formulation of 3d gravity. To obtain a non-perturbative result, we supersymmetrized the Chern Simons action and used the technique of supersymmetric localization. We have obtained an exact non-perturbative result for the spin-2 gravity case. We comment on the divergences present in the theory. We also comment on higher spin gravity theories and analyse the nature of divergences present in such theories.

Dimensionally restricted causal set quantum gravity: examples in two and three dimensions

We study dimensionally restricted non-perturbative causal set quantum dynamics in 2 and 3 spacetime dimensions with non-trivial global spatial topology. The causal set sample space is generated from causal embeddings into spacetime lattices with global spatial topology S1 and T2 in 2 and 3 dimensions, respectively. The quantum gravity partition function over these sample spaces is studied using Markov chain Monte Carlo (MCMC) simulations after analytic continuation. In both 2 and 3 dimensions we find a phase transition that separates the dominance of the action from that of the entropy. The action dominated phase is characterised by ‘layered’ posets with a high degree of connectivity, while the causal sets in the entropy dominated phase are manifold-like. This phase transition is similar in character to that seen for the sample space of 2-orders, which are topologically trivial, hence suggesting that this is a generic feature of dimensionally restricted sample spaces. The simulations use a newly developed framework for causal set MCMC calculations. Ours is the first implementation of a causal set dynamics restricted to 3 dimensions.

Exact path integral for 3D quantum gravity. II.

Continuing the work [Phys. Rev. Lett. 115, 161304 (2015)], we discuss various aspects of three-dimensional quantum gravity partition function in anti--de Sitter spacetime in the semiclassical limit. The partition function is holomorphic and is the one which we obtained by using the localization technique of Chern-Simons theory in Phys. Rev. Lett. 115, 161304 (2015). We obtain a good expression for it in the summation form over Virasoro characters for the vacuum and primaries. A key ingredient for that is an interpretation of boundary-localized fermion. We also check that the coefficients in the summation form over Virasoro characters of the partition function are positive integers and satisfy the Cardy formula. These give a physical interpretation that these coefficients represent the number of primary fields in the dual conformal field theory in the large $k$ limit.

AdS2 holography is (non-)trivial for (non-)constant dilaton

We study generic two-dimensional dilaton gravity with a Maxwell field and prove its triviality for constant dilaton boundary conditions, despite of the appearance of a Virasoro algebra with non-zero central charge. We do this by calculating the canonical boundary charges, which turn out to be trivial, and by calculating the quantum gravity partition function, which turns out to be unity. We show that none of the following modifications changes our conclusions: looser boundary conditions, non-linear interactions of the Maxwell field with the dilaton, inclusion of higher spin fields, inclusion of generic gauge fields. Finally, we consider specifically the charged Jackiw--Teitelboim model, whose holographic study was pioneered by Hartman and Strominger, and show that it is non-trivial for certain linear dilaton boundary conditions. We calculate the entropy from the Euclidean path integral, using Wald's method and exploiting the chiral Cardy formula. The macroscopic and microscopic results for entropy agree with each other.

Exact Path Integral for 3D Quantum Gravity.

Three-dimensional Euclidean pure gravity with a negative cosmological constant can be formulated in terms of the Chern-Simons theory, classically. This theory can be written in a supersymmetric way by introducing auxiliary gauginos and scalars. We calculate the exact partition function of this Chern-Simons theory by using the localization technique. Thus, we obtain the quantum gravity partition function, assuming that it can be obtained nonperturbatively by summing over partition functions of the Chern-Simons theory on topologically different manifolds. The resultant partition function is modular invariant, and, in the case in which the central charge is expected to be 24, it is the J function, predicted by Witten.

Localization in supergravity and quantum AdS 4 /CFT3 holography

We compute the quantum gravity partition function of M-theory on $AdS_4 \times X_7 $ by using localization techniques in four-dimensional gauged supergravity obtained by a consistent truncation on the Sasaki-Einstein manifold $X_{7}$. The supergravity path integral reduces to a finite dimensional integral over two collective coordinates that parametrize the localizing instanton solutions. The renormalized action of the off-shell instanton solutions depends linearly and holomorphically on the "square root" prepotential evaluated at the center of $AdS_{4}$. The partition function resembles the Laplace transform of the wave function of a topological string and with an assumption about the measure for the localization integral yields an Airy function in precise agreement with the computation from the boundary ABJM theory on a 3-sphere. Our bulk quantum gravity computation is nonperturbatively exact in four-dimensional Planck length but ignores corrections due to brane-instantons.

On spectral triples in quantum gravity: I

This paper establishes a link between noncommutative geometry and canonical quantum gravity. A semi-finite spectral triple over a space of connections is presented. The triple involves an algebra of holonomy loops and a Dirac-type operator, which resembles a global functional derivation operator. The commutation relation between the Dirac operator and the algebra has a structure related to the Poisson bracket of general relativity. Moreover, the associated Hilbert space corresponds, up to a certain symmetry group, to the Hilbert space of diffeomorphism-invariant states known from loop quantum gravity. Correspondingly, the square of the Dirac operator has, in terms of loop quantum gravity, the form of a global area-squared operator. Furthermore, the spectral action functional resembles a partition function of quantum gravity. The construction is background independent and is based on an inductive system of triangulations. This paper is the first of two papers on the subject.

Quantum gravity on dS3

We study quantum gravity on dS3 using the Chern–Simons formulation of three-dimensional gravity. We derive an exact expression for the partition function for quantum gravity on dS3 in a Euclidean path integral approach. We show that the topology of the space relevant for studying de Sitter entropy is a solid torus. The quantum fluctuations of de Sitter space are sectors of configurations of point masses taking a discrete set of values. The partition function gives the correct semiclassical entropy. The sub-leading correction to the entropy is logarithmic in horizon area, with a coefficient −1. We discuss this correction in detail, and show that the sub-leading correction to the entropy from the dS/CFT correspondence agrees with our result. A comparison with the corresponding results for the AdS3 BTZ black hole is also presented.

(2+1)-DIMENSIONAL QUANTUM GRAVITY AND THE 3D-ISING MODEL

We show that (2+1)-dimensional Euclidean quantum gravity is equivalent, under mild topological assumptions, to a Gaussian fermionic system. Furthermore we argue that the corresponding (2+1)-dimensional Euclidean quantum gravity partition function may be related to the partition function of the reduced 3D-lattice Ising model for finite lattices.