Related papers: Universality of Rényi Entropy in Conformal Field Theory

Universality of Rényi Entropy in Conformal Field Theory

URL: http://arxiv.org/abs/2503.24353v2
Date: Mon, 07 Apr 2025 18:11:16 GMT
Title: Universality of Rényi Entropy in Conformal Field Theory
Authors: Yuya Kusuki, Hirosi Ooguri, Sridip Pal,
Abstract summary: We prove that for the vacuum state in any conformal field theory in $d$ dimensions, the $n$-th R'enyi entropy $S_A(n)$ behaves as $S_A(n) = fracf (2pi n)d-1 frac rm Area(partial A)(d-2)epsilond-2left (1+O(n)right)$ in the $n rightarrow 0$ limit when the boundary of the entanglement domain $A$ is
Score: 0.0
License: http://creativecommons.org/licenses/by/4.0/
Abstract: We use the thermal effective theory to prove that, for the vacuum state in any conformal field theory in $d$ dimensions, the $n$-th R\'enyi entropy $S_A^{(n)}$ behaves as $S_A^{(n)} = \frac{f}{(2\pi n)^{d-1}} \frac{ {\rm Area}(\partial A)}{(d-2)\epsilon^{d-2}}\left(1+O(n)\right)$ in the $n \rightarrow 0$ limit when the boundary of the entanglement domain $A$ is spherical with the UV cutoff $\epsilon$.The theory dependence is encapsulated in the cosmological constant $f$ in the thermal effective action. Using this result, we estimate the density of states for large eigenvalues of the modular Hamiltonian for the domain $A$. In two dimensions, we can use the hot spot idea to derive more powerful formulas valid for arbitrary positive $n$. We discuss the difference between two and higher dimensions and clarify the applicability of the hot spot idea. We also use the thermal effective theory to derive an analog of the Cardy formula for boundary operators in higher dimensions.

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