Noppadol Mekareeya

Coulomb branch Hilbert series and Hall-Littlewood polynomials

A bstractThere has been a recent progress in understanding the chiral ring of 3d N

Coulomb branch and the moduli space of instantons

mathcal{N}

Hilbert series for moduli spaces of instantons on ℂ2/ℤ n

= 4 superconformal gauge theories by explicitly constructing an exact generating function (Hilbert series) counting BPS operators on the Coulomb branch. In this paper we introduce Coulomb branch Hilbert series in the presence of background magnetic charges for flavor symmetries, which are useful for computing the Hilbert series of more general theories through gluing techniques. We find a simple formula of the Hilbert series with background magnetic charges for Tρ(G) theories in terms of Hall-Littlewood polynomials. Here G is a classical group and ρ is a certain partition related to the dual group of G. The Hilbert series for vanishing background magnetic charges show that Coulomb branches of Tρ(G) theories are complete intersections. We also demonstrate that mirror symmetry maps background magnetic charges to baryonic charges.

T-branes, Anomalies and Moduli Spaces in 6D SCFTs

A bstractWe evaluate the Coulomb branch Hilbert series of mirrors of three dimensional Sicilian theories, which arise from compactifying the 6d (2, 0) theory with symmetry G on a circle times a Riemann surface with punctures. We obtain our result by gluing together the Hilbert series for building blocks Tρ(G), where ρ is a certain partition related to the dual group of G, which we evaluated in a previous paper. The result is expressed in terms of a class of symmetric functions, the Hall-Littlewood polynomials. As expected from mirror symmetry, our results agree at genus zero with the superconformal index prediction for the Higgs branch Hilbert series of the Sicilian theories and extend it to higher genus. In the A1 case at genus zero, we also evaluate the Coulomb branch Hilbert series of the Sicilian theory itself, showing that it only depends on the number of external legs.

Mirror symmetry in three dimensions via gauged linear quivers

A bstractThe moduli space of instantons on ℂ2 for any simple gauge group is studied using the Coulomb branch of N=4

\mathcal{N}\ge 2

mathcal{N}=4