Quantum chaos in 2D gravity

Abstract

We present a quantitative and fully non-perturbative description of the ergodic phase of quantum chaos in the setting of two-dimensional gravity. To this end we describe the doubly non-perturbative completion of semiclassical 2D gravity in terms of its associated universe field theory. The guiding principle of our analysis is a flavor-matrix theory (fMT) description of the ergodic phase of holographic gravity, which exhibits U(n|n) causal symmetry breaking and restoration. JT gravity and its 2D-gravity cousins alone do not realize an action principle with causal symmetry, however we demonstrate that their universe field theory, the Kodaira-Spencer (KS) theory of gravity, does. After directly deriving the fMT from brane-antibrane correlators in KS theory, we show that causal symmetry breaking and restoration can be understood geometrically in terms of different (topological) D-brane vacua. We interpret our results in terms of an open-closed string duality between holomorphic Chern-Simons theory and its closed-string equivalent, the KS theory of gravity. Emphasis will be put on relating these geometric principles to the characteristic spectral correlations of the quantum ergodic phase.

A Tale of Two Hungarians: Tridiagonalizing Random Matrices

“…It would also be interesting to connect our ideas and framework to the recently considered effective field theory of quantum chaos, see [53][54][55] and references therein, which also seeks to describe aspects of the long time dynamics of quantum chaotic systems, and the associated spectral structure. On a different note, as mentioned in [9], our approach may be a promising avenue for understanding the late time dynamics of black hole interiors, potentially connecting with [56,57].…”

“…Here, we assumed that the density of states is supported over a finite interval [E min , E max ]; if not, we can cut off the tail of the density of states as an approximation. The numerical algorithm works by discretizing x into M small intervals of size 1/M , and assuming that E left , E right are constant over those intervals, so that the integrals in (55,56) become discrete sums. Evaluating the resulting equations at the points m/M + gives us (57,58), which can be used to solve for the values of E left , E right at m/M from the values at i/M for i < m.…”

The power of Lorentzian wormholes

“…In section 2.2, 2.3 and 2.4 we discuss a few basic examples of Lorentzian AdS geometries with such delta function sources. 9 In particular in section 2.4 we describe the AdS version of crotches, which are the key actors in our work. Then, in section 2.5, we discuss the mechanism by which these singular geometries are picked up in the gravitational path integral.…”

“…Away from the singular point this metric satisfies R `2 " 0, which results (as anticipated above) in an imaginary contribution to the Euler character 10 ˆΣ{x sing d 2 x ? g R " ´2b i , (2.5) 9 For other interesting recent examples of such (almost) Lorentzian singular geometries in JT gravity, see [18], who focused on spacetimes without asymptotic boundaries. Our focus is on spacetimes with asymptotic boundaries.…”

“…Topology change is expected to be important in answering these questions, 1 The analogue of this in QFT is to understand tunneling from a purely Lorentzian point of view. 2 See recently [8,9] for the universe field theory of JT gravity, which is a string field theory.…”