ABCD of Instantons

By N. Nekrasov, S. Shadchin. 2004

213 citations recorded by the source corpus.

We solve = 2 supersymmetric Yang-Mills theories for an arbitrary classical gauge group, i.e. SU(N), SO(N), Sp(N). In particular, we derive the prepotential of the low-energy effective theory, and the corresponding Seiberg-Witten curves. We manage to do this without resolving singularities of the compactified instanton moduli spaces.

Subfields: Nuclear and High Energy Physics, Political Science and International Relations

View Paper: https://www.semanticscholar.org/paper/8fa19e91044cb408aeffd02feb15a4727c0af385

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In Nuclear and High Energy Physics

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Citations in the corpus

Non-Lagrangian theories from brane junctions (2013, background): “generating functions counting holomorphic functions on the Higgs branch [83–86].”
Liouville Correlation Functions from Four-Dimensional Gauge Theories (2009, background): “elation precise. – 17 – 6. Calculate directly Nekrasov’s partition function for SU(2) quivers, rather than for U(2) quivers. This should be possible by treating SU(2) as either SO(3) or as Sp(1), cf. [18, 19] 7. Obtain Nekrasov’s partition function when the gauge group SU(2)1×SU(2)2 × SU(2)3 couples”
Obstructions to the Existence of Sasaki–Einstein Metrics (2006, methodology): “using the character formula in [41] and taking the limit as in (2.”
5-dim superconformal index with enhanced En global symmetry (2012, methodology): “45) The instanton index I inst for U(N) gauge group can be read off from [33, 34] in which the 4d Nekrasov’s partition functions are written as the contour integral formula over the Cartan subalgebra of U(k) gauge group of the instanton moduli space.”
Counting BPS operators in gauge theories: quivers, syzygies and plethystics (2006, background): “[37] as well as an earlier result in [36]).”
Sasaki–Einstein Manifolds and Volume Minimisation (2006, background): “(44)Similar computations in related contexts have appeared before in [64, 65, 66].”
The Hilbert series of the one instanton moduli space (2010, background): “, [7, 8, 9, 10, 11] for explicit constructions); there is no known such construction, however, for the exceptional groups.”
Quantization of Integrable Systems and Four Dimensional Gauge Theories (2009, background): “We do it for the case of the N = 2 theory (the relativistic case is studied analogously, along the lines of [47, 48]).”
General instanton counting and 5d SCFT (2014, background): “Instanton partition functions for the pure N = 2 theories with classical gauge groups were studied in [16], with generalizations [17] to matter hypermultiplets in some representations.”
Vortex Counting and Lagrangian 3-Manifolds (2010, background): “, wm), its character has the form (see [22] for a very nice exposition in the context of the equivariant instanton counting):”