Abstract
We consider the universal part of entanglement entropy across a plane in flat space for a QFT, giving a non-perturbative expression in terms of a spectral function. We study the change in entanglement entropy under a deformation by a relevant operator, providing a pertrubative expansion where the terms are correlation functions in the undeformed theory. The entanglement entropy for free massive fermions and scalars easily follows. Finally, we study entanglement entropy across a plane in a background geometry that is a deformation of flat space, finding new universal terms arising from mixing of geometry and couplings of the QFT.
Highlights
We study the change in entanglement entropy under a deformation by a relevant operator, providing a pertrubative expansion where the terms are correlation functions in the undeformed theory
We study entanglement entropy across a plane in a background geometry that is a deformation of flat space, finding new universal terms arising from mixing of geometry and couplings of the QFT
We achieve this by computing the first order change in the entanglement entropy of a plane in a background metric that is a small perturbation of flat space
Summary
Consider some subregion V of a manifold M. Since we could have evaluated the modular Hamiltonian on any constant Rindler time slice, and not necessarily the θ = 0 slice, we can use O(2) symmetry in the (x1, x2) space to alternatively write (2.13) in the form δS = −δλ Rd 0|O(x)Kλ0 |0 λ0. This result matches the expression found in [11, 19]. There, we considered an arbitrary entangling surface in an arbitrary background and made use of the path integral representation of the reduced density matrix to find the appropriate generalization of (2.14). In the more general case [11], we instead did a perturbative expansion within the path integral to obtain (2.14)
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