Gravity without averaging

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 \(\textsf{H}_0\). Tightening the Gaussian rend...

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Bibliographic Details
Published in:arXiv.org 2021-07
Main Authors: Blommaert, Andreas, Kruthoff, Jorrit
Format: Article
Language:English
Subjects:
Dilatons
Gravitation theory
Integrals
Phase transitions
Saddle points
Online Access:Get full text
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Summary: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 \(\textsf{H}_0\). Tightening the Gaussian renders the matrix integral less random, and ultimately it collapses the ensemble to one Hamiltonian \(\textsf{H}_0\). 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.
ISSN:2331-8422
DOI:10.48550/arxiv.2107.02178