\n In the first par
t of this talk we will present a path integral derivation of a general rel
ation between the ground state entanglement Hamiltonian and the physical s
tress tensor for a Conformal Field Theory (CFT). For spherical entangling
surfaces in a CFT\, this leads to first law-like relation between variatio
ns of entanglement entropy (EE) and energy as well as a set of constraint
equations for the EE variation.

\n Via AdS/CFT\, these equations can
be recast as Perturbative Einstein'\;s Equations in the bulk dual.

\n In the second part\, we will present results on the entanglement Ha miltonian (EH) of chiral fermions living on a spatial circle. In particula r we focus on the effects of periodic vs. anti periodic boundary condition s on the EH. We will relate the calculation of the fermion EH to the solut ion of a Riemann Hilbert Problem\, and propose a generalization of Riemann Hilbert Problem for spinor bundles in higher dimensions.

\n DTSTART:20150408T193000Z LOCATION:Physics Building\, Room 204 SUMMARY:Entanglement Hamiltonians and the First Law for Entanglement Entrop y END:VEVENT END:VCALENDAR