16,436 research outputs found
Instantons on Calabi-Yau cones
The Hermitian Yang-Mills equations on certain vector bundles over Calabi-Yau
cones can be reduced to a set of matrix equations; in fact, these are Nahm-type
equations. The latter can be analysed further by generalising arguments of
Donaldson and Kronheimer used in the study of the original Nahm equations.
Starting from certain equivariant connections, we show that the full set of
instanton equations reduce, with a unique gauge transformation, to the
holomorphicity condition alone.Comment: v2: 26 pages, accepted in Nucl.Phys.B, added 6 references, improved
discussion, added Yang-Mills with torsio
Coulomb branches for rank 2 gauge groups in 3d N=4 gauge theories
The Coulomb branch of 3-dimensional N=4 gauge theories is the space of bare
and dressed BPS monopole operators. We utilise the conformal dimension to
define a fan which, upon intersection with the weight lattice of a GNO-dual
group, gives rise to a collection of semi-groups. It turns out that the unique
Hilbert bases of these semi-groups are a sufficient, finite set of monopole
operators which generate the entire chiral ring. Moreover, the knowledge of the
properties of the minimal generators is enough to compute the Hilbert series
explicitly. The techniques of this paper allow an efficient evaluation of the
Hilbert series for general rank gauge groups. As an application, we provide
various examples for all rank two gauge groups to demonstrate the novel
interpretation.Comment: v2: 98 pages, 30 figures, 34 tables, 1 appendix, matches JHEP versio
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