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Path Integral Approach to String Theory on AdS_3

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Nobuyuki Ishibashi (KEK), Kazumi Okuyama (KEK), Yuji Satoh (Tsukuba)

High Energy Physics - Theory · Submitted 17 May 2000

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim By an appropriate change of the normalization of the primary fields, our results coincide with those by Teschner, which were obtained by using the bootstrap approach.

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arXiv IDhep-th/0005152 (version 3)
Pith IDUXNQDCJQ, Pith's permanent record of this paper and its review
CitationKazumi Okuyama (KEK), Nobuyuki Ishibashi (KEK), Yuji Satoh (Tsukuba). "Path Integral Approach to String Theory on AdS_3." arXiv:hep-th/0005152 (2000). https://pith.science/paper/UXNQDCJQ
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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,560 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.11 · human participants 0.01 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.12 · compares with prior results 0.98 · mentions code or data availability 0.02.

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arXiv listing abstract v3. Results and the main claim are underlined; .

Using the path integral approach, we discuss the correlation functions of the $SL(2,\bfC)/SU(2)$ WZW model, which corresponds to the string theory on the Euclidean $AdS_3$. We obtain the two- and three-point functions for generic primary fields in closed forms. By an appropriate change of the normalization of the primary fields, our results coincide with those by Teschner, which were obtained by using the bootstrap approach. The supergravity results are also obtained in the semi-classical limit.

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 Using the path integral approach, we discuss the correlation functions of the $SL(2,\bfC)/SU(2)$ WZW model, which corresponds to the string theory on the Euclidean $AdS_3$. contribution 0.78 0.86 0.10 asserted 0.96
s1 We obtain the two- and three-point functions for generic primary fields in closed forms. result 0.97 0.96 0.42 asserted 1.00
s2 By an appropriate change of the normalization of the primary fields, our results coincide with those by Teschner, which were obtained by using the bootstrap approach. result 0.54 0.79 0.28 asserted 1.00
s3 The supergravity results are also obtained in the semi-classical limit. result 0.98 0.81 0.09 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

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Original abstract

Using the path integral approach, we discuss the correlation functions of the $SL(2,\bfC)/SU(2)$ WZW model, which corresponds to the string theory on the Euclidean $AdS_3$. We obtain the two- and three-point functions for generic primary fields in closed forms. By an appropriate change of the normalization of the primary fields, our results coincide with those by Teschner, which were obtained by using the bootstrap approach. The supergravity results are also obtained in the semi-classical limit.

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5 arXiv papers cite this in 5 sentences

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  • The $z_i-$dependent factor of the three-point correlation function of primary fields[ To be precise, the $^0_0$ conservation law implies that the three-point correlation function of $$ primary fields vanish unless $j_1+j_2+j_3=0.$ To remedy this one replaces at least on of the fields $Φ(v_k,j|z)$ with the “primary field in the izospin basis”, $Φ(x|z) = Φ(e^x^-_0v_k,j|z), x∈ℂ.$ ] $Φ(v_k,j_i|z_i)$, $i=1,2,3,$ is universal (its form follows from the global conformal invariance) and the essential information this function carries has the form of the three-point structure constant, a function of the level $k$ and weights $j_i.$ Structure constants of the Liouville theory were computed in [ref] and the structure constants of the $H^+_3 = SL(2,ℂ)/SU(2)$ coset model (with its underlying $$ chiral symmetry algebra) were determined by the bootstrap method in [ref] and by path integral methods in [

    Decomposition of ${\widehat{\mathfrak{sl}_2}}_{,k} \ \oplus \ {\widehat{\mathfrak{sl}_2}}_{,1}$ highest weight representations for generic level $k$ and equivalence between two dimensional CFT models · Introduction · 0.87

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