The Hilbert series of the one instanton moduli space

By S. Benvenuti, A. Hanany, Noppadol Mekareeya. 2010

181 citations recorded by the source corpus.

The moduli space of k G-instantons on $ {\mathbb{R}^4} $ for a classical gauge group G is known to be given by the Higgs branch of a supersymmetric gauge theory that lives on Dp branes probing D(p + 4) branes in Type II theories. For p = 3, these (3 + 1) dimensional gauge theories have $ \mathcal{N} = 2 $ supersymmetry and can be represented by quiver diagrams. The F and D term equations coincide with the ADHM construction. The Hilbert series of the moduli spaces of one instanton for classical gauge groups is easy to compute and turns out to take a particularly simple form which is previously unknown. This allows for a G invariant character expansion and hence easily generalisable for exceptional gauge groups, where an ADHM construction is not known. The conjectures for exceptional groups are further checked using some new techniques like sewing relations in Hilbert Series. This is applied to Argyres-Seiberg dualities.

Subfields: Mathematical Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/2ab64c934de5e0bb0a253dfb9e7cce4848d33091

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Citations in the corpus

Gauge Theories and Macdonald Polynomials (2011, methodology): “In [32] non-trivial very explicit expressions for the Higgs branch partition function of the SCFTs with exceptional flavor symmetry groups [27, 41] were conjectured.”
Comments on twisted indices in 3d supersymmetric gauge theories (2016, background): “Finally, we will argue that the genus-zero A- and B-twisted indices—the A- and Btwisted S(2)×S(1) partition functions [8]— with vanishing background fluxes are equal to the Coulomb and Higgs branch Hilbert series, respectively 4 [35, 36, 37, 38, 39, 40].”
Bootstrapping the superconformal index with surface defects (2012, background): “ form of a polynomial in t over the product of factors (1 tR Q i a f i ). In some cases, this specialization of the superconformal fugacities relates the index to the Hibert series (as dened e.g. in [42]) of the Higgs branch [23]. This relation was explored recently in [43, 44, 45]. { 13 { tR i Q i ”
On instantons as Kaluza-Klein modes of M5-branes (2011, methodology): “One may try to understand the above formula by the following attempt to directly count the BPS states in the instanton sigma model, generalizing [57].”