Darboux coordinates, Yang-Yang functional, and gauge theory

By N. Nekrasov, A. Rosly, S. Shatashvili. 2011

230 citations recorded by the source corpus.

The moduli space of flat SL2 connections on a punctured Riemann surface Σ with fixed conjugacy classes of the monodromies around the punctures is endowed with a system of holomorphic Darboux coordinates in which the generating function of the variety of SL2-opers is identified with the universal part of the effective twisted superpotential of the corresponding four-dimensional N=2 supersymmetric theory subject to the two-dimensional Ω-deformation. This allows defining the Yang-Yang functionals for the quantum Hitchin system in terms of the classical geometry of the moduli space of local systems for the dual gauge group and relating it to the instanton counting of the four-dimensional gauge theories in the rank-one case.

Subfields: Mathematical Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/943711ec266e0caaf4edac00caa1120b4b8c9414

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In Mathematical Physics

1. Sergei Gukov
2. Tudor Dimofte
3. D. Gaiotto
4. E. Witten
5. N. Nekrasov
6. K. Maruyoshi
7. C. Vafa
8. Marcos Mariño

In Nuclear and High Energy Physics

1. Sergei Gukov
2. Tudor Dimofte
3. D. Gaiotto
4. E. Witten
5. C. Vafa
6. N. Nekrasov
7. Marcos Mariño
8. Dan Xie

Citations in the corpus

• BPS/CFT correspondence: non-perturbative Dyson-Schwinger equations and qq-characters (2015, methodology): “in the AGT setup [2, 1] to assign the Xi(x)-observables to the non-intersecting loops on the curve C on which one compactifies the A1 (0,2)theory, which define the α-coordinates in the system of Darboux coordinates on the moduli space of SL2 local systems [87].”
• The Ω Deformed B-model for Rigid N = 2 Theories (2011, background): “parameter t collectively denotes flat coordinates on the vector multiplet moduli space, m the bare hypermultiplet masses, and ǫ1, ǫ2 are the equivariant rotation parameters acting on the four dimensional spacetime in the so-called Ω-background [3, 7].”
• Knot Invariants from Four-Dimensional Gauge Theory (2011, background): “The role of the S-duality between Bcc and Boper is more explicit in [66].”
• Wild quiver gauge theories (2011, background): “This should be obtained by analyzing the irregular conformal block in the ǫ2 → 0 limit [79, 80].”
• Entanglement Entropy at Large Central Charge (2013, background): “, then analytically continue n!1 where the monodromy problem can be solved analytically. xThe semiclassical block f also appears in other contexts, including the Bethe ansatz and 4d gauge theory. See [26, 27] and references therein. 14 4.1 Semiclassical k-point conformal blocks First we must show th”
• General Argyres-Douglas theory (2012, background): “It seems that the Darboux coordinates constructed in [61] can be generalized to our case once the cluster coordinates are known.”
• Isomonodromic Tau-Functions from Liouville Conformal Blocks (2014, methodology): “r), r= 1,...,n− 3 will be denoted as (σ,τ). We observe that the coordinates (σ,τ) are for n= 4 close relatives of the parameters used in [Ji]. They are also closely related to the coordinates used in [NRS]. 2.3 Isomonodromic deformations and tau-function Let us briefly recall the well-known relations”
• Gauge Theories Labelled by Three-Manifolds (2011, background): “ersymmetric vacua, particularly as given by equations (5.3) with fWa sum of dilogarithm functions, is highly reminiscent of recent work relating eective 2d eld theories to quantum integrable systems [36, 37, 38]. For example, 3d N= 2 theories much like T M compactied on a circle are related to the X”
• Quantum Geometry and Quiver Gauge Theories (2013, background): “[8, 9], the twisted superpotential W(a,m; q, ǫ) of the effective two-dimensional theory is the sum: W(a,m; q, ǫ) = W(a,m; q, ǫ) +W(a,m; ǫ) (1.”
• Chern-Simons theory and S-duality (2011, methodology): “complex structure I. However, when restricted to the brane of opers they appear to coincide with the J-holomorphic coordinates i.7 Various aspects of the distinguished branes (2.33) were discussed in [15, 51, 56, 57, 42]. In the two-dimensional sigma-model on R I, the Hilbert space HN=2 1;2 (S3) is”