The omega deformation, branes, integrability and Liouville theory
By N. Nekrasov, E. Witten. 2010
278 citations recorded by the source corpus.
We reformulate the Ω-deformation of four-dimensional gauge theory in a way that is valid away from fixed points of the associated group action. We use this reformulation together with the theory of coisotropic A-branes to explain recent results linking the Ω-deformation to integrable Hamiltonian systems in one direction and Liouville theory of two-dimensional conformal field theory in another direction.
Subfields: Geometry and Topology, Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/8a28be3efaf7d59ed5ef73dd16c453fe43132027
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Citations in the corpus
- SUSY gauge theories on squashed three-spheres (2011, result): “g S-duality transformation acting on conformal blocks. By replacing the round metric of the wall S3 by a squashed one, one obtains the kernels for general b. Also, the AGT relation was interpreted in [22] as the equivalence between the space of supersymmetric ground states of 4D N = 2 gauge theories”
- BPS/CFT correspondence: non-perturbative Dyson-Schwinger equations and qq-characters (2015, background): “This function plays an important role in quantization of the symplectic manifold P and the Bethe/gauge correspondence [89, 96, 90, 87, 86].”
- Quantum geometry of refined topological strings (2011, methodology): “2 Ω-Deformation of N = 2, d = 4 Theories The so-called Ω-background for four-dimensional N = 2 supersymmetric theory, where the parameters ǫ1,2 correspond to the equivariant U(1)×U(1) action on the Euclidean space-time C ∼= R, has been considered in [1, 24, 25], based on earlier work [26, 27].”
- Vortex Counting and Lagrangian 3-Manifolds (2010, background): “34) was studied earlier by Braverman and Etingof [23] and, more recently, by Nekrasov and Shatashvili [24] in connection to quantum integrable systems (see also [14,19]).”
- Knot Invariants from Four-Dimensional Gauge Theory (2011, background): “It has been argued [63] that the S-duality between these two branes is important in understanding the AGT correspondence [64] as well as recent developments relating supersymmetric gauge theory and integrable systems [65].”
- Framed BPS states (2010, unknown): “While the sequence (2.13) is split it is not naturally split — reflecting the possibility of the Witten effect — so if we consider local systems (e.g. over the coupling constant space or the ζ plane C∗) then (2.13) can be nontrivial.”
- General Argyres-Douglas theory (2012, methodology): “Since these theories do not have a Lagrangian, one need to use some other methods to find the Nekrasov partition function, the method described in [59] should be helpful if we have good coordinates for the moduli space of flat connection in the presence of irregular singularity.”
- A& B model approaches to surface operators and Toda thoeries (2010, background): “It would be interesting to explore the relation of the β-ensemble quantization to the recent work [41] (see also [42]), where it was proposed and tested in some examples, that given a classical integrable system associated with a N = 2 gauge theory, its quantization is provided by the Nekrasov equiv”
- Y-system for scattering amplitudes (2010, background): “This connection between a four dimensional supersymmetric theory and two dimensional quantum integrable models is in the spirit of [28].”
- Quantum Geometry and Quiver Gauge Theories (2013, background): “[8], one with the generating function W(a) and another, with the generating function −W(a).”
- Wall-crossing in coupled 2d-4d systems (2011, methodology): “As described in [52], the defect at the tip of the cigar requires boundary conditions which describe branes in the sigma model.”