Emergent area laws from entangled matrices

Frenkel, Alexander; Hartnoll, Sean A.

doi:10.1007/jhep05(2023)084

Emergent area laws from entangled matrices

Journal Article · Wed May 10 00:00:00 EDT 2023 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/jhep05(2023)084· OSTI ID:2420712

Frenkel, Alexander ^[1]; Hartnoll, Sean A. ^[2]

Stanford Univ., CA (United States); Stanford Univ., CA (United States)
Univ. of Cambridge (United Kingdom)

We consider a wavefunction of large N matrices supported close to an emergent classical fuzzy sphere geometry. The SU(N) Gauss law of the theory enforces correlations between the matrix degrees of freedom associated to a geometric subregion and their complement. We call this ‘Gauss law entanglement’. We show that the subregion degrees of freedom transform under a single dominant, low rank representation of SU(N). The corresponding Gauss law entanglement entropy is given by the logarithm of the dimension of this dominant representation. It is found that, after coarse-graining in momentum space, the SU(N) Gauss law entanglement entropy is proportional to the geometric area bounding the subregion. The constant of proportionality goes like the inverse of an emergent Maxwell coupling constant, reminiscent of gravitational entropy.

View Accepted Manuscript (DOE)

Research Organization:: Stanford Univ., CA (United States)

Sponsoring Organization:: National Science Foundation (NSF); USDOE Office of Science (SC)

Grant/Contract Number:: SC0018134

OSTI ID:: 2420712

Journal Information:: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 5 Vol. 2023; ISSN 1029-8479

Publisher:: Springer NatureCopyright Statement

Country of Publication:: United States

Language:: English

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