Line operators in theories of class S $$ \mathcal{S} $$ , quantized moduli space of flat connections, and Toda field theory

Coman, Ioana; Gabella, Maxime; Teschner, J.

doi:10.1007/jhep10(2015)143

Cited by 28 publications

(46 citation statements)

References 136 publications

(330 reference statements)

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“…In the case c = N − 1, where the CFT/isomonodromy correspondence is expected to hold true, a definition of the general vertex operator for the W N -algebra was proposed in [30] by employing the isomonodromic tau functions and the corresponding 3-point Fuchsian systems. The elements of the basis of vertex operators are labeled in this approach by a finite number of moduli parameterizing the monodromy data [32,54,31,18]. For generic central charge, analogous definition is not available so far, but it is expected to be consistent with an action of the algebra of Verlinde loop operators on the space of 3-point conformal blocks, see recent work [19].…”

Section: Introductionmentioning

confidence: 99%

Higher-rank isomonodromic deformations and W-algebras

2019

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We construct the general solution of a class of Fuchsian systems of rank N as well as the associated isomonodromic tau functions in terms of semi-degenerate conformal blocks of W N -algebra with central charge c = N − 1. The simplest example is given by the tau function of the Fuji-Suzuki-Tsuda system, expressed as a Fourier transform of the 4-point conformal block with respect to intermediate weight. Along the way, we generalize the result of Bowcock and Watts on the minimal set of matrix elements of vertex operators of the W N -algebra for generic central charge and prove several properties of semi-degenerate vertex operators and conformal blocks for c = N − 1.

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Section: Introductionmentioning

confidence: 99%

Higher-rank isomonodromic deformations and W-algebras

2019

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“…Another extension of this work regards the study of other N = 2 models as for example class S-theories [16]. It should be interesting apply the results of [17][18][19], like the relation between the twisted character of the chiral algebra and the Lens space index, in order to reproduce the lattices and the S-duality structure obtained in [20][21][22][23][24][25][26][27][28]. Also the results of [29], investigating the geometric origin of the global properties from the 6d N = (1, 0) perspective, may be useful for the study of N = 2 models.…”

Section: Discussionmentioning

confidence: 99%

Lens space index and global properties for 4d $$ \mathcal{N} $$ = 2 models

Amariti¹,

Marcassoli²

2020

J. High Energ. Phys.

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The additional data necessary to univocally fix the gauge group for a given algebra are represented by the same charge lattices of mutually local Wilson and 't Hooft lines for both 4d N = 4 SYM and N = 2 elliptic models. Motivated by this equivalence in this paper we study the Lens space index of these N = 2 elliptic models. The index is indeed sensitive to the global properties and in the N = 4 case it is expected to coincide among S-dual models with different global properties, while it gives different results for models that lie in other S-duality orbits. Here by an explicit calculation we show that the same results hold for the N = 2 elliptic models as well.

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“…It was shown in [La1,La2,CGT] that the generators introduced above satisfy two algebraic relations of the form P i {L γ , γ ∈ π 1 (C 0,3 )} = 0, i = 1, 2.…”

Section: Moduli Spaces Of Flat Sl(3)-connectionsmentioning

confidence: 99%

Toda Conformal Blocks, Quantum Groups, and Flat Connections

Coman

Pomoni

Teschner

2019

Commun. Math. Phys.

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This paper investigates the relations between the Toda conformal field theories, quantum group theory and the quantisation of moduli spaces of flat connections. We use the free field representation of the W-algebras to define natural bases for spaces of conformal blocks of the Toda conformal field theory associated to the Lie algebra sl 3 on the three-punctured sphere with representations of generic type associated to the three punctures. The operator-valued monodromies of degenerate fields can be used to describe the quantisation of the moduli spaces of flat SL(3)-connections. It is shown that the matrix elements of the monodromies can be expressed as Laurent polynomials of more elementary operators which have a simple definition in the free field representation. These operators are identified as quantised counterparts of natural higher rank analogs of the Fenchel-Nielsen coordinates from Teichmüller theory. Possible applications to the study of the non-Lagrangian SUSY field theories are briefly outlined.

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Line operators in theories of class S $$ \mathcal{S} $$ , quantized moduli space of flat connections, and Toda field theory

Cited by 28 publications

References 136 publications

Higher-rank isomonodromic deformations and W-algebras

Higher-rank isomonodromic deformations and W-algebras

Lens space index and global properties for 4d $$ \mathcal{N} $$ = 2 models

Toda Conformal Blocks, Quantum Groups, and Flat Connections

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