{"arxiv_id":"hep-th/0005183","incoming":{"papers":110,"sentences":333,"groups":[{"kind":"contests","label":"Contests it","papers":4,"sentences":4,"quotes":[{"arxiv_id":"2312.14253","title":"Quantum Entanglement on Black Hole Horizons in String Theory and Holography","url":"/paper/2312.14253","section":"Horizon Orbifolds","sentence":"Z^AdS, B_nm; k ℓ (τ) = β√(κ)/2π√(τ_2) exp( - (κ+ 2) β^2/4πL^2 τ_2 |m - n τ|^2 + 2π/τ_2 ( U_nm; kℓ)^2 )/|ϑ_1 ( U_nm;kℓ | τ) |^2 , where[Note that it is $τ$ and not $τ̅$ that appears inside the $ϑ$-function in [ref] correcting a typo in [ref] .","intent_p":0.31,"contests_p":0.88},{"arxiv_id":"0706.0663","title":"Winding tachyons in BTZ","url":"/paper/0706.0663","section":"Comments on the 3 partition function","sentence":"The contribution to the torus partition function from the thermal AdS factor is, for a fixed world-sheet modular parameter [ref] [In writing this expression we have corrected a typo in [ref] 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of a feature that slightly modifies the description of the discrete spectrum.","intent_p":0.93,"contests_p":null},{"arxiv_id":"2207.05361","title":"Long Strings and Quasinormal Winding Modes","url":"/paper/2207.05361","section":"Introduction","sentence":"In particular, extending the intuition developed in finite temperature $AdS_3$ [ref] , we identify pole regions in the Euclidean BTZ partition sum that correspond to the contribution of long string winding modes that surround the black hole.","intent_p":0.95,"contests_p":null},{"arxiv_id":"2505.14380","title":"Strings and near-extremal black holes in theories with large $\\mathcal{N}=4$ superconformal symmetry","url":"/paper/2505.14380","section":"Introduction","sentence":"Recently, in [ref] we reanalyzed the one-loop partition function for strings on 3 backgrounds (building on the original results of [ref] ), specifically for $T^4$ in the case of the superstring.","intent_p":0.95,"contests_p":null},{"arxiv_id":"2408.14567","title":"Strings in AdS$_3$: one-loop partition function and near-extremal BTZ thermodynamics","url":"/paper/2408.14567","section":"Construction of the partition function","sentence":"The contribution of the $_k+2$ is the result from [ref] given earlier in [ref] with the replacement $k→k+2$:","intent_p":0.88,"contests_p":null},{"arxiv_id":"2403.03979","title":"Thermal partition function of $J_3 \\bar{J}_3$ deformed $AdS_3$","url":"/paper/2403.03979","section":"Review of $SL(2,R)$ sigma model","sentence":"The analysis of [ref] can be understood as the generalization of [ref] where the compact Euclidean time coordinate $x$ is warped non-trivially along the radial direction as can be seen in ([ref]).","intent_p":0.81,"contests_p":null}]},{"kind":"method_or_tool","label":"Uses its method or tool","papers":15,"sentences":36,"quotes":[{"arxiv_id":"2403.03979","title":"Thermal partition function of $J_3 \\bar{J}_3$ deformed $AdS_3$","url":"/paper/2403.03979","section":"Statement of problem","sentence":"In the remainder of this section, we will provide a solution in the form of an integral expression which we will obtain using the fact that (1) the deformed action has a concrete gauged sigma model form, (2) the folding/unfolding trick of [ref] can be utilized, and the fact that the $l_1=0$ limit is already solved in [ref] .","intent_p":0.9,"contests_p":null},{"arxiv_id":"2012.08404","title":"Superstrings in Thermal Anti-de Sitter Space","url":"/paper/2012.08404","section":"The Single String Free Energy","sentence":"Our calculation follows the original computation done in [ref] and for some of the details we refer to the original treatment.","intent_p":0.98,"contests_p":null},{"arxiv_id":"0705.4514","title":"Hagedorn Strings and Correspondence Principle in AdS(3)","url":"/paper/0705.4514","section":"AdS$_3$ string and its thermal partition function","sentence":"As shown in [ref] by adopting the technique in dealing with path integral of $H_3$ WZW model [ref] , one can exactly evaluate the partition function of the AdS sector, and the result is _AdS(β, μ;τ) =β(1-2/k)^1/2/(4π^2τ_2)^1/2 ∑_(n,m)(0,0) e^-β^2|m-nτ|^2/4πτ_2+2π(U_n,m)^2/τ_2/|ϑ_1(τ,U_n,m)|^2, where U_n,m(τ) =iβ(n τ̅-m)/2π√() (1/√(k)-i μ√()) , and the theta function is defined as ϑ_1(τ,U)=2q^1/8 sin(πU) ∏_m=1^∞(1-q^m)(1-zq^m)(1-z^-1q^m) , where $q=e^2πi τ, z=e^2πiU$.","intent_p":0.88,"contests_p":null},{"arxiv_id":"2408.14567","title":"Strings in AdS$_3$: one-loop partition function and near-extremal BTZ thermodynamics","url":"/paper/2408.14567","section":"Spectral decomposition of worldsheet partition function","sentence":"The strategy to take this into account [ref] is to break up the domain $_2 ∈[0,∞]$ into a series of subdomains $β/2π [(w+1)^-1, w^-1]$ with $w∈ℤ_≥0$.","intent_p":1.0,"contests_p":null},{"arxiv_id":"2604.15566","title":"One-loop effect in the charged 2D black hole near 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Equation","sentence":"From the explicit expression for the partition function on thermal $AdS_3$ computed in [ref] , the exact $AdS_3$ Hagedorn inverse temperature is computed as[Nota Bene: In many places in the literature, there is an overall factor of $k$ in the $AdS_3$ metric that is not present in the Minkowski metric, so that the flat space coordinates are $√(k)$ times the $AdS_3$ coordinates in the $k→∞$ limit.","intent_p":0.96,"contests_p":null}]},{"kind":"comparison","label":"Compares with it","papers":10,"sentences":17,"quotes":[{"arxiv_id":"2012.08404","title":"Superstrings in Thermal Anti-de Sitter Space","url":"/paper/2012.08404","section":"The Single String Free Energy","sentence":"By comparing the equation [ref] with the string one loop vacuum amplitude [ref], we obtain an expression for (minus) the single string free energy $f$ [ref] :","intent_p":0.8,"contests_p":null},{"arxiv_id":"2403.03979","title":"Thermal partition function of $J_3 \\bar{J}_3$ deformed $AdS_3$","url":"/paper/2403.03979","section":"One-loop amplitude of the $J_3 J̅_3$ deformed $AdS_3 ×N$","sentence":"The density of state naturally interpolates between the known results for $AdS_3 ×N$ of [ref] and $R_t ×(SL(2,R) /U(1)) ×N$ of [ref] .","intent_p":0.86,"contests_p":null},{"arxiv_id":"2506.20028","title":"Localization of strings on group manifolds","url":"/paper/2506.20028","section":"Formulas","sentence":"(27) of [ref] , we set $α'=α”=0$ (since those parameters are not included in [ref] ).","intent_p":0.98,"contests_p":null},{"arxiv_id":"2604.15566","title":"One-loop effect in the charged 2D black hole near extremality","url":"/paper/2604.15566","section":"One-loop target space free energy","sentence":"The structure of the exponential in ([ref]) closely resembles the expression found in [ref] .","intent_p":1.0,"contests_p":null},{"arxiv_id":"2410.16904","title":"Deriving the long-string CFT in AdS$_3$","url":"/paper/2410.16904","section":"Thermal AdS3/Euclidean 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