Abstract
In threedimensional gauge theories, monopole operators create and destroy vortices. We explore this idea in the context of 3d N=4 gauge theories in the presence of an Omegabackground. In this case, monopole operators generate a noncommutative algebra that quantizes the Coulombbranch chiral ring. The monopole operators act naturally on a Hilbert space, which is realized concretely as the equivariant cohomology of a moduli space of vortices. The action furnishes the space with the structure of a Verma module for the Coulombbranch algebra. This leads to a new mathematical definition of the Coulombbranch algebra itself, related to that of BravermanFinkelbergNakajima. By introducing additional boundary conditions, we find a construction of vortex partition functions of 2d N=(2,2) theories as overlaps of coherent states (Whittaker vectors) for Coulombbranch algebras, generalizing work of BravermanFeiginFinkelbergRybnikov on a finite version of the AGT correspondence. In the case of 3d linear quiver gauge theories, we use brane constructions to exhibit vortex moduli spaces as handsaw quiver varieties, and realize monopole operators as interfaces between handsawquiver quantum mechanics, generalizing work of Nakajima.
Original language  English 

Pages (fromto)  803917 
Number of pages  103 
Journal  Advances in Theoretical and Mathematical Physics 
Volume  22 
Issue number  4 
DOIs  
Publication status  Published  5 Dec 2018 
Fingerprint
Dive into the research topics of 'Vortices and Vermas'. Together they form a unique fingerprint.Profiles

Tudor Dimofte
 School of Mathematics  Reader in Algebra, Geometry & Topology and related fields
Person: Academic: Research Active (Teaching)