Universal corner entanglement from twist operators

DOI10.1007/JHEP09(2015)091zbMATH Open1388.83194arXiv1507.06997OpenAlexW3125830317WikidataQ60667875 ScholiaQ60667875MaRDI QIDQ2635833

Author name not available (Why is that?)

Publication date: 31 May 2018

Published in: (Search for Journal in Brave)

Abstract: The entanglement entropy in three-dimensional conformal field theories (CFTs) receives a logarithmic contribution characterized by a regulator-independent function

a (h e t a)

when the entangling surface contains a sharp corner with opening angle

h e t a

. In the limit of a smooth surface (

h e t a i g h t a r r o w p i

), this corner contribution vanishes as

a (h e t a) = s i g m a, (h e t a - p i)^{2}

. In arXiv:1505.04804, we provided evidence for the conjecture that for any

d = 3

CFT, this corner coefficient

s i g m a

is determined by

C_{T}

, the coefficient appearing in the two-point function of the stress tensor. Here, we argue that this is a particular instance of a much more general relation connecting the analogous corner coefficient

s i g m a_{n}

appearing in the

n

th R'enyi entropy and the scaling dimension

h_{n}

of the corresponding twist operator. In particular, we find the simple relation

h_{n} / s i g m a_{n} = (n - 1) p i

. We show how it reduces to our previous result as

n i g h t a r r o w 1

, and explicitly check its validity for free scalars and fermions. With this new relation, we show that as

n i g h t a r r o w 0

,

s i g m a_{n}

yields the coefficient of the thermal entropy,

c_{S}

. We also reveal a surprising duality relating the corner coefficients of the scalar and the fermion. Further, we use our result to predict

s i g m a_{n}

for holographic CFTs dual to four-dimensional Einstein gravity. Our findings generalize to other dimensions, and we emphasize the connection to the interval R'enyi entropies of

d = 2

CFTs.

Full work available at URL: https://arxiv.org/abs/1507.06997

zbMATH Keywords

No records found.

Mathematics Subject Classification ID

No records found.

This page was built for publication: Universal corner entanglement from twist operators

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q2635833)