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Revisiting the Thermal AdS partition function
High Energy Physics - Theory · Submitted 27 Mar 2023
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Using this, we show that the spectrum of the Euclidean BTZ black hole and Lorentzian AdS3 can be extracted -- the latter as a zero temperature limit.
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The abstract, sentence by sentence
We rewrite the worldsheet torus partition function of the Thermal AdS CFT by isolating the boundary parameters. Using this, we show that the spectrum of the Euclidean BTZ black hole and Lorentzian AdS3 can be extracted -- the latter as a zero temperature limit. A similar procedure recovers the Lorentzian BTZ spectrum proposed in an earlier work. We then use our expression to construct a boundary modular invariant expression as a Poincar\'e series.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We rewrite the worldsheet torus partition function of the Thermal AdS CFT by isolating the boundary parameters. | contribution 0.56 | 0.95 | 0.15 | asserted 1.00 |
| s1 | Using this, we show that the spectrum of the Euclidean BTZ black hole and Lorentzian AdS3 can be extracted -- the latter as a zero temperature limit. | result 0.96 | 0.93 | 0.48 | asserted 1.00 |
| s2 | A similar procedure recovers the Lorentzian BTZ spectrum proposed in an earlier work. | result 0.87 | 0.82 | 0.12 | asserted 1.00 |
| s3 | We then use our expression to construct a boundary modular invariant expression as a Poincar\'e series. | contribution 0.87 | 0.94 | 0.20 | asserted 1.00 |
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The paper
Original abstract
We rewrite the worldsheet torus partition function of the Thermal AdS CFT by isolating the boundary parameters. Using this, we show that the spectrum of the Euclidean BTZ black hole and Lorentzian AdS3 can be extracted -- the latter as a zero temperature limit. A similar procedure recovers the Lorentzian BTZ spectrum proposed in an earlier work. We then use our expression to construct a boundary modular invariant expression as a Poincar\'e series.
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What this paper does with the arXiv papers it cites
What it cites · 31 sentences without a confident label
Uses the method or tool of 3 papers
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The above partition can be expanded (following [ref] ) into the same form as that in Eqn[ref] so that we can compare the spectrum.
Superstrings on NS5 backgrounds, deformed AdS3 and holography · Wick Rotation of the TADS partition function · 0.91
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We will now expand the above expression following the ideas of [ref] so that we can compare the conformal weights with expectations based on classical analysis of strings moving on the Thermal AdS geometry.
Strings in AdS_3 and the SL(2,R) WZW Model. Part 2: Euclidean Black Hole · q-Expansion · 0.99
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The grand potential is evaluated by the procedure of Holographic Renormalization [ref] which requires the addition of specific counterterms to the gravitational action.
Holographic Reconstruction of Spacetime and Renormalization in the AdS/CFT Correspondence · Thermodynamics and Phase transition · 1.00
Uses data or values from 1 paper
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This torus amplitude computed in [ref] is: Z_TAdS_3( , ; ) = k-22 _2 _n,m Z e^- k ^24 _2|m-n |^2 + 2 ( I(U_n,m))^2 _2| _1(U_n,m| )|^2, where Our $U_n,m$ is the complex conjugate of that used in~ [ref] because we work in conventions where the left factor of the solution of the WZW model is holomorphic (left-moving on Lorentzian worldsheet).
Strings in AdS_3 and the SL(2,R) WZW Model. Part 2: Euclidean Black Hole · Partition functions · 0.88
Compares with 7 papers
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These may be compared with the form of current eigenvalues for Lorentzian BTZ presented in [ref] , which is
The BTZ black hole spectrum and partition function · The other Wick rotation · 0.99
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In fact, the entire partition function matches the proposal presented in [ref] .
Superstrings on NS5 backgrounds, deformed AdS3 and holography · Introduction · 0.95
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In this section, we will study the conformal weights obtained from the above q-series and show that it agrees with the expected structure for the BTZ black hole [ref] once we take into account Wick rotation.
String theory on three dimensional black holes · Interpretation – Euclidean BTZ viewpoint · 0.89
Cites as background 5 papers
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While a modular invariant torus partition function for Thermal $AdS_3$ (TADS) was constructed in [ref] , that of Lorentzian $AdS_3$ (LADS) was proposed in [ref] .
Strings in AdS_3 and the SL(2,R) WZW Model. Part 2: Euclidean Black Hole · Introduction · 0.95
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While a modular invariant torus partition function for Thermal $AdS_3$ (TADS) was constructed in [ref] , that of Lorentzian $AdS_3$ (LADS) was proposed in [ref] .
Superstrings on NS5 backgrounds, deformed AdS3 and holography · Introduction · 0.95
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The spectrum of states for strings on the Lorentzian spacetimes of $AdS_3$ and BTZ black holes have been presented in [ref] and [ref] .
The BTZ black hole spectrum and partition function · The Lorentzian spacetimes · 0.90
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