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here we want to prove this for an arbitrary number of them.","intent_p":0.97,"contests_p":null},{"arxiv_id":"1704.08667","title":"Higher spins on AdS$_{3}$ from the worldsheet","url":"/paper/1704.08667","section":"Worldsheet string theory on AdS$_3$","sentence":"The bosonic version of this theory was discussed in some detail in the seminal papers [ref] ; in what follows we extend, following [ref] , some aspects of their analysis to the supersymmetric case.","intent_p":0.88,"contests_p":null}]},{"kind":"method_or_tool","label":"Uses its method or tool","papers":12,"sentences":23,"quotes":[{"arxiv_id":"1007.2720","title":"Worldsheet four-point functions in AdS(3)/CFT(2)","url":"/paper/1007.2720","section":"Moduli integration and integral over $h$","sentence":"Following [ref] , we therefore regularize the $u$-integral by introducing a cut-off parameter $ε$ and divide the range of $u$ into two regions: [equation] In region I there are only operators in the intermediate channel whose $SL(2)$ part is associated with short strings with winding number $w=0$ [ref] .","intent_p":0.99,"contests_p":null},{"arxiv_id":"1106.5876","title":"Worldsheet operator product expansions and p-point functions in AdS3/CFT2","url":"/paper/1106.5876","section":"Introduction","sentence":"Recently, in [ref] , (the one-particle contributions of) some extremal four-point correlators have been computed on the worldsheet using a general method for $SL(2)$ correlation functions developed in [ref] .","intent_p":0.83,"contests_p":null},{"arxiv_id":"0903.2001","title":"Three-point functions in superstring theory on AdS3xS3xT4","url":"/paper/0903.2001","section":"Three-point functions of chiral states","sentence":"We now compute the SL(2,$ℝ)$ correlators, applying the technique developed in [ref] .","intent_p":1.0,"contests_p":null},{"arxiv_id":"2211.02521","title":"Spectral flow and string correlators in AdS$_3\\times S^3 \\times T^4$","url":"/paper/2211.02521","section":"Introduction","sentence":"Next, in order to deduce the corresponding results for operators in the spacetime representation, we follow a path similar to that introduced in [ref] and further developed in [ref] .","intent_p":0.97,"contests_p":null},{"arxiv_id":"1511.07256","title":"Notes on the SL(2,R) CFT","url":"/paper/1511.07256","section":"Introduction","sentence":"The unit spectral flowed three-point function is then computed using a similar approach to that outlined in [ref] , but involving a distinct basis of flowed primary fields \\(Φ_j^w(x)\\).","intent_p":0.8,"contests_p":null}]},{"kind":"data_used","label":"Uses its data or values","papers":2,"sentences":2,"quotes":[{"arxiv_id":"0903.2001","title":"Three-point functions in superstring theory on AdS3xS3xT4","url":"/paper/0903.2001","section":"Three-point functions of chiral states","sentence":"Taking into account that in the SL(2,$ℝ)$ sector they are given by [ref] ⟨Φ_H,H^h,w(x_1, x_1) Φ_ H,H^h,w (x_2, x_2)⟩= g_s^-2 (2h-1+k w)B(h) x_12^-2Hx_12^-2H , the normalized chiral operators are defined as: [equation]","intent_p":0.93,"contests_p":null},{"arxiv_id":"2406.04247","title":"Spectral flow and the conformal block expansion for strings in AdS$_3$","url":"/paper/2406.04247","section":"The $= (0,0,2,0)$ case","sentence":"The numerical constants then combine to give the relevant product of flowed structure constants, [equation] which can be found in [ref] .","intent_p":0.81,"contests_p":null}]},{"kind":"comparison","label":"Compares with it","papers":14,"sentences":22,"quotes":[{"arxiv_id":"1007.2720","title":"Worldsheet four-point functions in AdS(3)/CFT(2)","url":"/paper/1007.2720","section":"Moduli integration and integral over $h$","sentence":"This should be compared with the $x$ dependence of the corresponding boundary four-point function, which is $x^H-H_1-H_2$ (see e.g. (4.2) in [ref] ), where $H$ denotes the corresponding spacetime conformal weights.","intent_p":0.93,"contests_p":null},{"arxiv_id":"1511.07256","title":"Notes on the SL(2,R) CFT","url":"/paper/1511.07256","section":"Introduction","sentence":"As is suggested by the results in [ref] , and unlike in the treatment of the OPE of the corresponding string amplitudes given in [ref] , it will be found that all continuous and discrete spectral flow sectors which are permitted by the selection rules have finite and non-vanishing OPE coefficients for some range of values of the \\(j\\) quantum number.","intent_p":0.86,"contests_p":null},{"arxiv_id":"1912.09754","title":"Winding modes and the reflection symmetry in AdS$_3$","url":"/paper/1912.09754","section":"Final remarks","sentence":"Indeed, while vertex operators in the former are built upon a specific lowest-weight state by means of translations in $x$-space, a single vertex in the latter gives rise to both $𝒟^+_J$ and $𝒟^-_J$, as stated in [ref] and already stressed below Eq. [ref].","intent_p":0.86,"contests_p":null},{"arxiv_id":"2208.00978","title":"On spectrally flowed local vertex operators in AdS$_3$","url":"/paper/2208.00978","section":"The $y$ variable and point-splitting","sentence":"Consequently, we find that these results exactly match the properties described in [ref] , proving that Eq. 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