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Gauged Sigma-Models in Two Dimensions: November 3 – 7, 2014

Organized by Sergei Gukov, Nuno Romao, and Samson Shatashvili

Dates: November 3 – 7, 2014

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Gauged Sigma-Models in Two Dimensions


Time Title Presenters Video
8:30am Breakfast SCGP Cafe
9:30am Registration SCGP Lobby
10:45am Welcome
11:00am Bethe wavefunctions from gauged linear sigma models via Bethe/gauge correspondence Nikita Nekrasov video
12:00pm Lunch SCGP Cafe
2:00pm Microscopic GLSM Description of M2-brane Surface Operators and Sphere Partition Functions Jaume Gomis video
slides
3:00pm A quasi-topological gauged sigma model,  the geometric Langlands program, and knots Meng-Chwan Tan video
slides
4:00pm Tea Time
4:45pm Gravitating vortices Oscar Garcia-Prada video
slides


Time Title Presenters Video
8:30am Breakfast SCGP Cafe
9:30am Nonlinear vortices on nearly nodal curves Ignasi Mundet i Riera video
10:30am Coffee Break SCGP Cafe
11:00am The L^2 geometry of the space of P^1 vortex-antivortex pairs Martin Speight video
slides
12:00pm Lunch SCGP Cafe
1:00pm SCGP Weekly Talk: Vortex Equations and Invariants: A Survey Ignasi Mundet i Riera video
2:00pm Divisor Links Marcel Bokstedt video
3:00pm L^2-Betti Numbers and Particle Counting in a Gauged Nonlinear Sigma-Model Christian Wegner video
4:00pm Tea Time
4:45pm Gauged Witten Equation and Correlation Functions Guangbo Xu video


Time Title Presenters Video
8:30am Breakfast SCGP Cafe
9:30am The Verlinde algebra and its generalisations Anton Kapustin video
10:30am Coffee Break SCGP Cafe
11:00am Chiral rings in 2d (0,2) theories Eric Sharpe video
slides
12:00pm Lunch SCGP Cafe
2:00pm Exact solutions of 2d supersymmetric gauge theories Abhijit Gadde video
slides
3:00pm Branes and vortices Amihay Hanany video
4:00pm Tea Time
5:00pm Art Event: Wine and Cheese Reception SCGP Lobby
5:30pm Art Talk:  Colliding Worlds:  How Cutting-Edge Science is Redefining Contemporary Art Arthur Miller


Time Title Presenters Video
8:30am Breakfast SCGP Cafe
9:30am Mirror Symmetry and Gauged Linear Sigma Models Dave Morrison video
10:30am Coffe Break SCGP Cafe
11:00am Flipping out over vortices Chris Woodward video
slides
12:00pm Lunch SCGP Cafe
2:00pm Grade Restriction Rule for Rodland Model and Pfaffian/Grassmann Correspondence, via Hemisphere Partition Function Kentaro Hori videoUpdate
3:00pm Cluster Algebras from 2d Gauge Theories Francesco Benini video
slides
4:00pm Tea Time
6:00pm Workshop Banquet


Time Title Presenters Video
8:30am Breakfast SCGP Cafe
9:30am 3d N=4 Gauge Theory and Symplectic Duality Tudor Dimofte video
10:30am Coffee Break SCGP Cafe
11:00am Superconformal index and surface defects Lotte Hollands video
12:00pm Lunch SCGP Cafe
2:00pm BPS States, Knots, and Vortices Piotr Sulkowski No Video
3:00pm Equivariant Integration Over Hitchin Moduli Space Du Pei video
4:00pm Tea Time



Gauged sigma-models from Riemann surfaces to Kaehler targets have been an important ingredient in recent developments at the crossroads of quantum field theory, geometry and topology. Of particular interest are models that exhibit self-duality, since they are more amenable to rigorous treatment — they incorporate a rich mathematical structure reflecting the fact that they admit certain local extensions accommodating representations of the N=(2,2) supersymmetry algebra. Twisted versions of these supersymmetric models yield topological quantum field theories that are defined on arbitrary Riemann surfaces. The correlators of such theories are formally expressed through path integrals, but they localize to finite-dimensional integrals which have a rigorous formulation. The TQFTs obtained via an A-twist localize to the moduli space of solutions to the vortex equations, whose quantum observables are intimately related to gauged Gromov-Witten invariants constructed from the action on the target manifold. They realize the quantum equivariant cohomology ring of the group action on the target, in a generalization of the familiar framework for Gromov-Witten theory for pseudo-holomorphic maps from a complex curve to a symplectic manifold. When the target of the sigma-model is an equivariant Calabi-Yau manifold, one can also produce an alternative B-twist, whose correlators localize to the Kaehler quotient of the target. The potential of studying two-dimensional self-dual gauged sigma-models has already been vindicated by a number of recent breakthroughs, which we intend to showcase in this workshop.

This workshop is a part of the Fall 2014 program, Gauge Theory, Integrability, and Novel Symmetries of Quantum Field Theory, which is organized by Anton Kapustin, Nikita Nekrasov, Samson Shatashvili, Volker Schomerus, and Konstantin Zarembo. This program takes place from September 2 – December 19, 2014.

Gauged Sigma poster for web