Title: Holographic entanglement entropy and the internal space

Abstract

We elaborate on the role of extremal surfaces probing the internal space in AdS/CFT. Extremal surfaces in AdS quantify the "geometric" entanglement between different regions in physical space for the dual CFT. This, however, is just one of many ways to split a given system into subsectors, and extremal surfaces in the internal space should similarly quantify entanglement between subsectors of the theory. For the case of AdS₅×S⁵, their area was interpreted as entanglement entropy between U(_n) and U(_m) subsectors of U(_n+m) $N=4$ SYM. Making this proposal precise is subtle for a number of reasons, the most obvious being that from the bulk one usually has access to gauge-invariant quantities only, while a split into subgroups is inherently gauge variant. We study $N=4$ SYM on the Coulomb branch, where some of the issues can be mitigated and the proposal can be sharpened. Continuing back to the original AdS₅×S⁵ geometry, we obtain a modified proposal, based on the relation of the internal space to the R-symmetry group.

Authors:

Karch, Andreas ^[1]; Uhlemann, Christoph F. ^[1]

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+ Show Author Affiliations

1. Univ. of Washington, Seattle, WA (United States)

Publication Date:

Mon Apr 06 00:00:00 EDT 2015

Research Org.:

Univ. of Washington, Seattle, WA (United States)

Sponsoring Org.:

USDOE Office of Science (SC), High Energy Physics (HEP)

OSTI Identifier:

1595205

Alternate Identifier(s):

OSTI ID: 1179321

Grant/Contract Number:  

SC0011637

Resource Type:

Accepted Manuscript

Journal Name:

Physical Review. D, Particles, Fields, Gravitation and Cosmology

Additional Journal Information:

Journal Volume: 91; Journal Issue: 8; Journal ID: ISSN 1550-7998

Publisher:

American Physical Society (APS)

Country of Publication:

United States

Language:

English

Subject:

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS