2018/01/30 by Teleman, Constantin · 3 citations
#55N91 #81R05 #81R12 #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th)
paper · doi:10.48550/arxiv.1801.10124
I give a simple construction of certain Coulomb branches C3,4(G;E) of gauge theory in 3 and 4 dimensions defined by Nakajima et al. for a compact Lie group G and a polarisable quaternionic representation E. The manifolds C(G; 0) are abelian group schemes (over the bases of regular adjoint Gc-orbits, respectively conjugacy classes), and C(G;E) is glued together from two copies of C(G;0) shifted by a rational Lagrangian section εV, the Euler class of the index bundle of a polarisation V of E. Extending the interpretation of C3(G;0) as "classifying space" for topological 2D gauge theories, I characterise functions on C3(G;E) as operators on the equivariant quantum cohomologies of M× V, for all compact symplectic G-manifolds M. The non-commutative version has an analogous description in terms of the Γ-function of V, appearing to play the role of Fourier transformed J-function of the gauged linear Sigma-model V/G.