City Research Online

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
Additional Information:	The original publication is available at http://iopscience.iop.org/1126-6708/2007/11/050/ archiveprefix: arXiv primaryclass: hep-th
Subjects:	Q Science > QC Physics
Departments:	School of Science & Technology > Mathematics
SWORD Depositor:	Symplectic Administrator

Export

Downloads