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:
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Publisher Copyright:
© 2020, The Author(s).
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 -