# Counting BPS Operators in Gauge Theories: Quivers, Syzygies and Plethystics

Benvenuti, S., Feng, B., Hanany, A. (2007). Counting BPS Operators in Gauge Theories: Quivers, Syzygies and Plethystics. Journal of High Energy Physics, 0711(050), doi: 10.1088/1126-6708/2007/11/050

## Abstract

We develop a systematic and efficient method of counting single-trace and multi-trace BPS operators with two supercharges, for world-volume gauge theories of $N$ D-brane probes for both $N \to \infty$ and finite $N$. The techniques are applicable to generic singularities, orbifold, toric, non-toric, complete intersections, et cetera, even to geometries whose precise field theory duals are not yet known. The so-called Plethystic Exponential'' provides a simple bridge between (1) the defining equation of the Calabi-Yau, (2) the generating function of single-trace BPS operators and (3) the generating function of multi-trace operators. Mathematically, fascinating and intricate inter-relations between gauge theory, algebraic geometry, combinatorics and number theory exhibit themselves in the form of plethystics and syzygies.

Publication Type: Article The original publication is available at http://iopscience.iop.org/1126-6708/2007/11/050/ archiveprefix: arXiv primaryclass: hep-th Q Science > QC Physics School of Mathematics, Computer Science & Engineering > Mathematics
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