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http://hdl.handle.net/1903/13249

Title:  Vacuum entanglement and black hole entropy of gauge fields 
Authors:  Donnelly, William 
Advisors:  Jacobson, Theodore 
Department/Program:  Physics 
Type:  Dissertation 
Sponsors:  Digital Repository at the University of Maryland University of Maryland (College Park, Md.) 
Subjects:  Physics 
Issue Date:  2012 
Abstract:  Black holes in general relativity carry an entropy whose value is given by the BekensteinHawking formula, but whose statistical origin remains obscure. Such horizons also possess an entanglement entropy, which has a clear statistical meaning but no a priori relation to the dynamics of gravity. For free minimallycoupled scalar and spinor fields, these two quantities are intimately related: the entanglement entropy is the oneloop correction to the black hole entropy due to renormalization of Newton's constant. For gauge fields, the entanglement entropy and the oneloop correction to the black hole entropy differ. This dissertation addresses two issues concerning the entanglement entropy of gauge fields, and its relation black hole entropy.
First, for abelian gauge fields Kabat identified a negative divergent contribution to the black hole entropy that is not part of the entanglement entropy, known as a ``contact term''. We show that the contact term can be attributed to an ambiguous expression for the gauge field's contribution to the Wald entropy. Moreover, in twodimensional de Sitter space, the contact term arises from an incorrect treatment of zero modes and is therefore unphysical. In a manifestly gaugeinvariant reduced phase space quantization of twodimensional gauge theory, the gauge field contribution to the entropy is positive, finite, and equal to the entanglement entropy. This suggests that the contact term in more than two dimensions may also be unphysical.
Second, we consider lattice gauge theory and point out that the Hilbert space corresponding to a region of space includes edge states that transform nontrivially under gauge transformations. By decomposing these edge states in irreducible representations of the gauge group, the entanglement entropy of an arbitrary state is shown to be a sum of a bulk entropy and a boundary entropy associated to the edge states. This entropy formula agrees with the twodimensional results from the reduced phase space quantization. These results are applied to several examples, including the ground state in the strong coupling expansion of Kogut and Susskind, and the entropy of the edge states is found to be the dominant contribution to the entanglement entropy. 
URI:  http://hdl.handle.net/1903/13249 
Appears in Collections:  Physics Theses and Dissertations UMD Theses and Dissertations

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