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arXiv · hep-th/0701063

Counting Gauge Invariants: the Plethystic Program

Bo Feng·Amihay Hanany·Yang-Hui He
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Abstract

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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Bo Feng, Amihay Hanany, Yang-Hui He. 2007-03-04. Counting Gauge Invariants: the Plethystic Program. https://doi.org/10.1088/1126-6708%2F2007%2F03%2F090

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