Gravity without averaging

Abstract

We present a gravitational theory that interpolates between JT gravity, and a gravity theory with a fixed boundary Hamiltonian. For this, we consider a matrix integral with the insertion of a Gaussian with variance ${\sigma }^2$, centered around a matrix ${\text{H}}_0$. Tightening the Gaussian renders the matrix integral less random, and ultimately it collapses the ensemble to one Hamiltonian ${\text{H}}_0$. This model provides a concrete setup to study factorization, and what the gravity dual of a single member of the ensemble is. We find that as ${\sigma }^2$ is decreased, the JT gravity dilaton potential gets modified, and ultimately the gravity theory goes through a series of phase transitions, corresponding to a proliferation of extra macroscopic holes in the spacetime. Furthermore, we observe that in the Efetov model approach to random matrices, the non-averaged factorizing theory is described by one simple saddle point.

47 pages, 15 figures and many delta functions

References in corpus (19)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• JT gravity as a matrix integral
• Weil-Petersson volume of moduli spaces, Mirzakhani's recursion and matrix models
• Late Time Correlation Functions, Baby Universes, and ETH in JT Gravity
• AdS Euclidean wormholes
• Summing over Geometries in String Theory
• JT gravity, KdV equations and macroscopic loop operators
• More quantum noise from wormholes
• An effective matrix model for dynamical end of the world branes in Jackiw-Teitelboim gravity
• Wormholes and Spectral Statistics in the Narain Ensemble
• Wormholes without averaging
• FZZT branes in JT gravity and topological gravity
• Density matrices in quantum gravity
• Poincaré Series, 3d Gravity and Averages of Rational CFT
• Vertices from replica in a random matrix theory
• Deconstructing the Wormhole: Factorization, Entanglement and Decoherence
• Gaussian matrix model in an external field and non-intersecting Brownian motions
• The double cone geometry is stable to brane nucleation
• Towards a String Dual of SYK

Cited by in corpus (8)

• Half-wormholes in nearly AdS${}_2$ holography
• Microstructure in matrix elements
• Comments on wormholes and factorization
• Factorizing Wormholes in a Partially Disorder-Averaged SYK Model
• Les Houches lectures on two-dimensional gravity and holography
• Baby universes, ensemble averages and factorizations with matters
• Product of Random States and Spatial (Half-)Wormholes
• The Schur Expansion of Characteristic Polynomials and Random Matrices