H3+-WZNW correlators from Liouville theory

Ribault, Sylvain; Teschner, J.

doi:10.1088/1126-6708/2005/06/014

Cited by 125 publications

(280 citation statements)

References 31 publications

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“…However, the two realizations seem to be distinct for quiver gauge theories, already for gauge theories with two SU(2) factors. Nevertheless, it is known that affine sl(2) correlation functions and Liouville correlation functions with degenerate field insertions are related [55,56]. In this map the number of degenerate field insertions (2d defect surface operators) is larger than the number expected for the description of a 4d defect surface operator, that couple to all the gauge group factors in the quiver.…”

Section: Jhep01(2011)045 6 Summary and Outlookmentioning

confidence: 95%

Affine sl(N)conformal blocks from $ \mathcal{N} = 2 $ SU(N) gauge theories

Kozçaz

Pasquetti

Passerini

et al. 2011

J. High Energ. Phys.

115

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Recently Alday and Tachikawa [1] proposed a relation between conformal blocks in a two-dimensional theory with affine sl(2) symmetry and instanton partition functions in four-dimensional conformal N = 2 SU(2) quiver gauge theories in the presence of a certain surface operator. In this paper we extend this proposal to a relation between conformal blocks in theories with affine sl(N ) symmetry and instanton partition functions in conformal N = 2 SU(N ) quiver gauge theories in the presence of a surface operator. We also discuss the extension to non-conformal N = 2 SU(N ) theories.

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Section: Jhep01(2011)045 6 Summary and Outlookmentioning

confidence: 95%

Affine sl(N)conformal blocks from $ \mathcal{N} = 2 $ SU(N) gauge theories

Kozçaz

Pasquetti

Passerini

et al. 2011

J. High Energ. Phys.

115

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“…Conversely, as far as the relation between both maps is not trivial, as it is emphasized in Ref. 29, our way of proving the connection between violating winding correlators and conserving winding correlators turns out to be an ingenious trick. The conciseness of such a deduction becomes particularly evident once one gets familiarized with the complicated definition of the action of spectral flow operator in the x basis.…”

Section: Discussionmentioning

confidence: 93%

“…This map, different from that employed in Ref. 14 to prove the crossing symmetry in SL͑2,C͒ /SU͑2͒, was discovered by Stoyanovsky some years ago, 28 and it was further developed by Ribault and Teschner 29 and Ribault. 30,31 In Refs.…”

mentioning

confidence: 87%

“…19 If this "second map" is used, the four-point function reached in the WZNW side is one that contains four nonwinding states, enabling us to relate winding violating processes in AdS 3 with their conservative analogs. However, this is not the whole story since, unlike the SRT map, [28][29][30] the FZ map involves a nondiagonal correspondence between the quantum numbers of both Liouville and WZNW sides. Hence, besides the appropriate combination of the SRT and the FZ maps, a sort of a "diagonalization procedure" is also required in order to present the result in a clear form.…”

Section: B Overviewmentioning

confidence: 99%

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Note on Z2 symmetries of the Knizhnik-Zamolodchikov equation

Giribet

2007

Journal of Mathematical Physics

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Boundary states, extended symmetry algebra, and module structure for certain rational torus models J. Math. Phys. 43, 6085 (2002) We continue the study of hidden Z 2 symmetries of the four-point sl͑2͒ k KnizhnikZamolodchikov equation initiated by Giribet ͓Phys. Lett. B 628, 148 ͑2005͔͒. Here, we focus our attention on the four-point correlation function in those cases where one spectral flowed state of the sector = 1 is involved. We give a formula that shows how this observable can be expressed in terms of the four-point function of non spectral flowed states. This means that the formula holding for the winding violating four-string scattering processes in AdS 3 has a simple expression in terms of the one for the conservative case, generalizing what is known for the case of three-point functions, where the violating and the nonviolating structure constants turn out to be connected one to each other in a similar way. What makes this connection particularly simple is the fact that, unlike what one would naively expect, it is not necessary to explicitly solve the five-point function containing a single spectral flow operator to this end. Instead, nondiagonal functional relations between different solutions of the Knizhnik-Zamolodchikov equation turn out to be the key point for this short path to exist. Considering such functional relation is necessary but it is not sufficient; besides, the formula also follows from the relation existing between correlators in both Wess-Zumino-Novikov-Witten ͑WZNW͒ and Liouville conformal theories.

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“…QGL is a generalization of the usual Geometric Langlands duality, in the sense that in a certain "classical" limit the former reduces to the latter. 1 For a review of QGL and its relation to Conformal Field Theory see [3]; for some physical manifestations of QGL see [16,6].…”

Section: Introductionmentioning

confidence: 99%

Gauge Theory, Mirror Symmetry, and the Geometric Langlands Program

Kapustin

2008

Homological Mirror Symmetry

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Abstract. Montonen-Olive duality implies that the categories of A-branes on the moduli spaces of Higgs bundles on a Riemann surface C for groups G and L G are equivalent. We reformulate this as a statement about categories of B-branes on the quantized moduli spaces of flat connections for groups G C and L G C . We show that it implies the statement of the Quantum Geometric Langlands duality with a purely imaginary "quantum parameter" which is proportional to the inverse of the Planck constant of the gauge theory. The ramified version of the story is also considered.

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H₃⁺-WZNW correlators from Liouville theory

Cited by 125 publications

References 31 publications

Affine sl(N)conformal blocks from $ \mathcal{N} = 2 $ SU(N) gauge theories

Affine sl(N)conformal blocks from $ \mathcal{N} = 2 $ SU(N) gauge theories

Note on Z2 symmetries of the Knizhnik-Zamolodchikov equation

Gauge Theory, Mirror Symmetry, and the Geometric Langlands Program

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