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Algebraic properties of the monopole formula · Around

2016

Algebraic properties of the monopole formula

Hanany, Amihay, Sperling, Marcus

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The monopole formula provides the Hilbert series of the Coulomb branch for a 3-dimensional N=4 gauge theory.

Employing the concept of a fan defined by the matter content, and summing over the corresponding collection of monoids, allows the following: firstly, we provide explicit expressions for the Hilbert series for any gauge group.
Secondly, we prove that the order of the pole at t=1 and t=infinity equals the complex or quaternionic dimension of the moduli space, respectively.
Thirdly, we determine all bare and dressed BPS monopole operators that are sufficient to generate the entire chiral ring.

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G. M. Ziegler, · 1995
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