Journal
JOURNAL OF HIGH ENERGY PHYSICS
Volume -, Issue 12, Pages -Publisher
SPRINGER
DOI: 10.1007/JHEP12(2013)020
Keywords
Field Theories in Lower Dimensions; AdS-CFT Correspondence; Conformal and W Symmetry; Field Theories in Higher Dimensions
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Funding
- DoE [DE-SC0007859, DE-SC0007984]
- University of Virginia
- NSF CAREER award [DMR-0956053]
- Direct For Mathematical & Physical Scien
- Division Of Materials Research [0956053] Funding Source: National Science Foundation
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We derive a general relation between the ground state entanglement Hamiltonian and the physical stress tensor within the path integral formalism. For spherical entangling surfaces in a CFT, we reproduce the l o c a l ground state entanglement Hamiltonian derived by Casini, Huerta and Myers. The resulting reduced density matrix can be characterized by a spatially varying entanglement temperature. Using the entanglement Hamiltonian, we calculate the first order change in the entanglement entropy due to changes in conserved charges of the ground state, and find a local first law-like relation for the entanglement entropy. Our approach provides a field theory derivation and generalization of recent results obtained by holographic techniques. However, we note a discrepancy between our field theoretically derived results for the entanglement entropy of excited states with a non-uniform energy density and current holographic results in the literature. Finally, we give a CFT derivation of a set of constraint equations obeyed by the entanglement entropy of excited states in any dimension. Previously, these equations were derived in the context of holography.
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