One-loop Partition Functions of 3D Gravity

By S. Giombi, A. Maloney, Xi Yin. 2008

304 citations recorded by the source corpus.

We consider the one-loop partition function of free quantum field theory in locally Anti-de Sitter space-times. In three dimensions, the one loop determinants for scalar, gauge and graviton excitations are computed explicitly using heat kernel techniques. We obtain precisely the result anticipated by Brown and Henneaux: the partition function includes a sum over ``boundary excitations'' of AdS3, which are the Virasoro descendants of empty Anti-de Sitter space. This result also allows us to compute the one-loop corrections to the Euclidean action of the BTZ black hole as well its higher genus generalizations.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/d0671c03e7360f979c3c296be2067c4684b96324

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Citations in the corpus

An AdS_3 Dual for Minimal Model CFTs (2010, background): “The 1-loop contribution from each complex scalar field is [51] (see also [50])”
Logarithmic corrections to extremal black hole entropy from quantum entropy function (2010, background): “Similar calculations in AdS3 background, with a somewhat different application in mind, can be found in [75, 76].”
Instability in cosmological topologically massive gravity at the chiral point (2008, methodology): “The considerations in the previous paragraphs might be of interest for the Euclidean approach/CFT approach pursued in [42–50].”
Holographic entanglement beyond classical gravity (2013, methodology): “Fortunately, an elegant expression for functional determinants on quotients of AdS3 by a Schottky group Γ has been obtained in [8], following a conjecture in [19].”
Higher spin AdS3 supergravity and its dual CFT (2011, methodology): “B The heat kernel method Applying the heat kernel method as in [26, 27], we compute (3.”
A theory of reparameterizations for AdS3 gravity (2018, methodology): “ean BTZ geometry for any such ˝0. Its contribution to the bulk partition function (including the saddle and uctuations around it) is the Virasoro character of the vacuum module at complex structure ˝0[1,2], Z vac(˝0;˝0) = q0 k Y1 n=2 1 1 q0n 2 ; q0= e2ˇi˝0; k= c 24 : (1.1) The states counted are the”
Loops in AdS from conformal field theory (2016, unknown): “[28–33]).”
Black hole determinants and quasinormal modes (2009, methodology): “The UV finite local term does not depend on the regularization scheme and agrees with the finite local term found in [25].”
Partition functions of holographic minimal models (2011, methodology): “The one loop partition function on thermal AdS3 was evaluated in [18] using heat kernel techniques [29, 30].”
Virasoro conformal blocks and thermality from classical background fields (2015, unknown): “For instance, the addition of light states in the gravity theory produces quantum corrections to the Ryu-Takayanagi formula [65{67], and in terms of the (cid:12)eld theory these should involve conformal blocks for states with corresponding conformal weights; it would be interesting to investigate…”
Low-dimensional de Sitter quantum gravity (2019, background): “ explained in Section4above, should yield corresponding higher genus dS 3 wave functions of the universe. However, almost all of the work on Euclidean AdS 3 higher genus partition functions (see e.g. [67,75,122{125]) examines higher genus asymptotic 2-surfaces, but not higher genus interpolating 3-m”
Chiral gravity, log gravity, and extremal CFT (2009, background): “It would be interesting to derive this result directly by computing an appropriate one loop determinant, as in [57].”
Minimal model holography (2012, background): “This generalizes the expression for the case of pure gravity (s = 2) [96], as explicitly checked in [66].”