Symmetries near the horizon

The Hilbert space of a quantum system with internal global symmetry G decomposes into sectors labelled by irreducible representations of G. If the system is chaotic, the energies in each sector should separately resemble ordinary random matrix theory. We show that such "sector-wise" random matrix ensembles arise as the boundary dual of two-dimensional gravity with a G gauge field in the bulk. Within each sector, the eigenvalue density is enhanced by a nontrivial factor of the dimension of the representation, and the ground state energy is determined by the quadratic Casimir. We study the consequences of 't Hooft anomalies in the matrix ensembles, which are incorporated by adding specific topological terms to the gauge theory action. The effect is to introduce projective representations into the decomposition of the Hilbert space. Finally, we consider ensembles with G symmetry and time reversal symmetry, and analyze a simple case of a mixed anomaly between time reversal and an internal Z 2 symmetry.

Section: Summary and Discussionmentioning

confidence: 99%

“…This is reminiscent of the construction in[45] of gauge-invariant SL2 operators that act on the Hilbert space of JT gravity coupled to matter, but do not commute with the Hamiltonian.…”

mentioning

confidence: 99%

Matrix ensembles with global symmetries and ’t Hooft anomalies from 2d gauge theory

Kapec

Mahajan

Stanford

2020

“…Note that we could have guessed an expression of this form by naively ignoring the P, B charges and using the effective action given by 3.10. It might seem rather peculiar that the oscillations are at a frequency ω which is determined by the breathing mode and not the AdS frequency, especially since there is a close connection between length and momentum [8]. However the momentum is given by…”

Section: (B30)mentioning

confidence: 99%

“…So there is no contradiction as long as we remember the relative signs. Note that in the usual coupled wormhole, the breathing mode and the AdS frequency are of the same order of magnitude, but in a slightly more complicated model, they can be different [8].…”

Section: (B30)mentioning

confidence: 99%

Complexity geometry and Schwarzian dynamics

Lin

Susskind

2020

Self Cite

A celebrated feature of SYK-like models is that at low energies, their dynamics reduces to that of a single variable. In many setups, this "Schwarzian" variable can be interpreted as the extremal volume of the dual black hole, and the resulting dynamics is simply that of a 1D Newtonian particle in an exponential potential. On the complexity side, geodesics on a simplified version of Nielsen's complexity geometry also behave like a 1D particle in a potential given by the angular momentum barrier. The agreement between the effective actions of volume and complexity succinctly summarizes various strands of evidence that complexity is closely related to the dynamics of black holes.

“…where O R,L are scalar operators of dimension ∆ ∈ (0, 1/2), dual to χ. On the other hand, by takingβ as the source term, this deformation could be realized as the non-local interaction with the SL(2, R) gauge constraint (see [5,21,24]). In this note, we take the L/R boundary proper time as the same oneũ.…”

Section: )mentioning

confidence: 99%

Experimental probes of traversable wormholes

Bak

Kim

2019

We propose possible probes which could be used to demonstrate experimentally the existence of the bulk and the formation of a traversable wormhole purely in terms of boundary operations only. In the two-dimensional Einstein-dilaton gravity, the traversable wormhole is realized by turning on a double trace interaction which couples the two boundaries of the AdS 2 black hole. Signals can propagate in the traversable wormhole through two different channels. The boundary channel is direct and instantaneous, while the bulk channel respects the bulk causality and takes a certain amount of time to complete signaling. In the latter case, we show that the signal frequency detected on the other side is highly modulated in general. The time delay as well as the frequency-modulation pattern could then be clear indications that the signal comes out through the bulk channel. We discuss the characteristics of the observed signal more explicitly for simple transitional configurations of the black hole from/to the eternal traversable wormhole.