Hitchin Systems in $${\mathcal N}=2$$ Field Theory

Neitzke, Andrew

doi:10.1007/978-3-319-18769-3_3

Cited by 13 publications

(17 citation statements)

References 79 publications

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“…M H of solutions to the self-duality equations on C g,n (see [24] for a review). This space has a hyperkähler structure, and in one of its complex structures it can be identified with the moduli space M flat of complex flat connections.…”

Section: Introductionmentioning

confidence: 99%

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

Coman

Gabella

Teschner³

2015

J. High Energ. Phys.

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Non-perturbative aspects of N = 2 supersymmetric gauge theories of class S are deeply encoded in the algebra of functions on the moduli space M flat of flat SL(N )-connections on Riemann surfaces. Expectation values of Wilson and 't Hooft line operators are related to holonomies of flat connections, and expectation values of line operators in the low-energy effective theory are related to Fock-Goncharov coordinates on M flat . Via the decomposition of UV line operators into IR line operators, we determine their noncommutative algebra from the quantization of Fock-Goncharov Laurent polynomials, and find that it coincides with the skein algebra studied in the context of Chern-Simons theory. Another realization of the skein algebra is generated by Verlinde network operators in Toda field theory. Comparing the spectra of these two realizations provides non-trivial support for their equivalence. Our results can be viewed as evidence for the generalization of the AGT correspondence to higher-rank class S theories.

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Section: Introductionmentioning

confidence: 99%

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

Coman

Gabella

Teschner³

2015

J. High Energ. Phys.

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“…Instead, consider T in the background R 4 where we only turn on the Ω-deformation with parameter 1 = . This is sometimes called the Nekrasov-Shatashvili limit.…”

Section: Effective Twisted Superpotentialmentioning

confidence: 99%

“…as the eigenvalue corresponding to the eigenline l α j . 4 The other half of the parameters, say τ 1 , . .…”

Section: Higher Length-twist Coordinatesmentioning

confidence: 99%

“…It may be interpreted as a generating function of a Lagrangian submanifold L 0 relating the Coulomb parameters a to the dual Coulomb parameters a D = ∂ a F 0 . For theories of class S this integrable system is a Hitchin system associated to C [2,3,4].…”

Section: Introductionmentioning

confidence: 99%

“…The reason for only fixing a framing at the maximal punctures and maximal boundaries of C will become clear in §6, where we also discuss framings at other types of punctures and boundaries 4. A rationale for the slightly odd conventions is given in §8 5.…”

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confidence: 99%

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Higher length-twist coordinates, generalized Heun’s opers, and twisted superpotentials

Hollands

Kidwai

2018

Advances in Theoretical and Mathematical Physics

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In this paper we study a proposal of Nekrasov, Rosly and Shatashvili that describes the effective twisted superpotential obtained from a class S theory geometrically as a generating function in terms of certain complexified length-twist coordinates, and extend it to higher rank. First, we introduce a higher rank analogue of Fenchel-Nielsen type spectral networks in terms of a generalized Strebel condition. We find new systems of spectral coordinates through the abelianization method and argue that they are higher rank analogues of the Nekrasov-Rosly-Shatashvili Darboux coordinates. Second, we give an explicit parametrization of the locus of opers and determine the generating functions of this Lagrangian subvariety in terms of the higher rank Darboux coordinates in some specific examples. We find that the generating functions indeed agree with the known effective twisted superpotentials. Last, we relate the approach of Nekrasov, Rosly and Shatashvili to the approach using quantum periods via the exact WKB method.It can be shown that any (E, ∇) admits at most one oper structure, and thus we can indeed identify opers with a subspace of M flat (C, SL(K)).More concretely, any SL(K) oper can locally be written as a Kth order linear differential operator 18) 2 Class S geometry Fix a positive integer K, sometimes called the "rank", and a possibly punctured Riemann surface C. We equip the Riemann surface with a collection

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The (2, 0) superalgebra, null M-branes and Hitchin’s system

Kucharski

Lambert

Owen

2017

J. High Energ. Phys.

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We present an interacting system of equations with sixteen supersymmetries and an SO(2) × SO(6) R-symmetry where the fields depend on two space and one null dimensions that is derived from a representation of the six-dimensional (2, 0) superalgebra. The system can be viewed as two M5-branes compactified on S 1 − ×T 2 or equivalently as M2-branes on R + × R 2 , where ± refer to null directions. We show that for a particular choice of fields the dynamics can be reduced to motion on the moduli space of solutions to the Hitchin system. We argue that this provides a description of intersecting null M2-branes and is also related by U-duality to a DLCQ description of four-dimensional maximally supersymmetric Yang-Mills.

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Hitchin Systems in $${\mathcal N}=2$$ Field Theory

Cited by 13 publications

References 79 publications

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

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

Higher length-twist coordinates, generalized Heun’s opers, and twisted superpotentials

The (2, 0) superalgebra, null M-branes and Hitchin’s system

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