Wilson Loops and Chiral Correlators on Squashed Spheres

Abstract

After a very brief recollection of how my scientific collaboration with Ugo started, in this talk I will present some recent results obtained with localization: the deformed gauge theory partition function $Z(\vec{\tau }|q)$ and the expectation value of circular Wilson loops $W$ on a squashed four-sphere will be computed. The partition function is deformed by turning on ${\tau }_J\mathrm{tr}{\Phi }^J$ interactions with $\Phi$ the $\mathcal{N}=2$ superfield. For the $\mathcal{N}=4$ theory SUSY gauge theory exact formulae for $Z$ and $W$ in terms of an underlying $U(N)$ interacting matrix model can be derived thus replacing the free Gaussian model describing the undeformed $\mathcal{N}=4$ theory. These results will be then compared with those obtained with the dual CFT according to the AGT correspondence. The interactions introduced previously are in fact related to the insertions of commuting integrals of motion in the four-point CFT correlator and the chiral correlators are expressed as $\tau$-derivatives of the gauge theory partition function on a finite $\Omega$-background.

talk delivered at the conference "Interactions between Geometry and Physics", Guaraja, Sao Paulo, August 17-22, 2015

References in corpus (6)

• Supersymmetric Wilson loops on S^3
• Deforming SW curve
• Gauge theories on Omega-backgrounds from non commutative Seiberg-Witten curves
• Instanton calculus in R-R background and the topological string
• Six-dimensional supersymmetric gauge theories, quantum cohomology of instanton moduli spaces and gl(N) Quantum Intermediate Long Wave Hydrodynamics
• Moore-Read Fractional Quantum Hall wavefunctions and SU(2) quiver gauge theories

Cited by in corpus (6)

• Two-point Correlators in N=2 Gauge Theories
• A slow review of the AGT correspondence
• A Solvable Deformation of Quantum Mechanics
• Conformal field theories on deformed spheres, anomalies, and supersymmetry
• Partition functions of non-Lagrangian theories from the holomorphic anomaly
• Wilson loop and its correlators in the limit of large coupling constant