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Counting Gauge Invariants: the Plethystic Program

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arxiv hep-th/0701063 v2 pith:36TVXRZX submitted 2007-01-08 hep-th

classification hep-th
keywords gaugeplethysticprogrammecountingtheoriestheorycalabi-yaucase
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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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Cited by 14 Pith papers

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