TY - JOUR

T1 - Liouville description of conical defects in dS4, Gibbons-Hawking entropy as modular entropy, and dS3 holography

AU - Arias, Cesar

AU - Diaz, Felipe

AU - Olea, Rodrigo

AU - Sundell, Per

N1 - Funding Information:
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited

PY - 2020/4/1

Y1 - 2020/4/1

N2 - We model the back-reaction of a static observer in four-dimensional de Sitter spacetime by means of a singular ℤq quotient. The set of fixed points of the ℤq action consists of a pair of codimension two minimal surfaces given by 2-spheres in the Euclidean geometry. The introduction of an orbifold parameter q > 1 permits the construction of an effective action for the bulk gravity theory with support on each of these minimal surfaces. The effective action corresponds to that of Liouville field theory on a 2-sphere with a finite vacuum expectation value of the Liouville field. The intrinsic Liouville theory description yields a thermal Cardy entropy that we reintrepret as a modular free energy at temperature T = q−1, whereupon the Gibbons-Hawking entropy arises as the corresponding modular entropy. We further observe that in the limit q → ∞ the four-dimensional geometry reduces to that of global dS3 spacetime, where the two original minimal surfaces can be mapped to the future and past infinities of dS3 by means of a double Wick rotation. In this limit, the Liouville theories on the minimal surfaces become boundary theories at zero temperature whose total central charge equals that computed using the dS3/CFT2 correspondence.

AB - We model the back-reaction of a static observer in four-dimensional de Sitter spacetime by means of a singular ℤq quotient. The set of fixed points of the ℤq action consists of a pair of codimension two minimal surfaces given by 2-spheres in the Euclidean geometry. The introduction of an orbifold parameter q > 1 permits the construction of an effective action for the bulk gravity theory with support on each of these minimal surfaces. The effective action corresponds to that of Liouville field theory on a 2-sphere with a finite vacuum expectation value of the Liouville field. The intrinsic Liouville theory description yields a thermal Cardy entropy that we reintrepret as a modular free energy at temperature T = q−1, whereupon the Gibbons-Hawking entropy arises as the corresponding modular entropy. We further observe that in the limit q → ∞ the four-dimensional geometry reduces to that of global dS3 spacetime, where the two original minimal surfaces can be mapped to the future and past infinities of dS3 by means of a double Wick rotation. In this limit, the Liouville theories on the minimal surfaces become boundary theories at zero temperature whose total central charge equals that computed using the dS3/CFT2 correspondence.

KW - Conformal and W Symmetry

KW - Conformal Field Theory

KW - Gauge-gravity correspondence

KW - Models of Quantum Gravity

UR - http://www.scopus.com/inward/record.url?scp=85083674771&partnerID=8YFLogxK

U2 - 10.1007/JHEP04(2020)124

DO - 10.1007/JHEP04(2020)124

M3 - Article

AN - SCOPUS:85083674771

VL - 2020

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 4

M1 - 124

ER -