Counting Gauge Invariants: the Plethystic Program

Details Counting Gauge Invariants: the Plethystic Program Counting Gauge Invariants: the Plethystic Program

2007-01-08

arxiv.org/abs/hep-th/0701063v2

JHEP 0703:090,2007

Physics

High Energy Physics

High Energy Physics - Theory

51 pages, 2 figures; refs updated, typos corrected

Scientific paper

10.1088/1126-6708/2007/03/090

We propose a programme for systematically counting the single and multi-trace gauge invariant operators of a gauge theory. Key to this is the plethystic function. We expound in detail the power of this plethystic programme for world-volume quiver gauge theories of D-branes probing Calabi-Yau singularities, an illustrative case to which the programme is not limited, though in which a full intimate web of relations between the geometry and the gauge theory manifests herself. We can also use generalisations of Hardy-Ramanujan to compute the entropy of gauge theories from the plethystic exponential. In due course, we also touch upon fascinating connections to Young Tableaux, Hilbert schemes and the MacMahon Conjecture.

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