City Research Online

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

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


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 archiveprefix: arXiv primaryclass: hep-th
Subjects: Q Science > QC Physics
Departments: School of Science & Technology > Mathematics
SWORD Depositor:
[thumbnail of 0608050v2.pdf]
Text - Accepted Version
Download (508kB) | Preview


Add to AnyAdd to TwitterAdd to FacebookAdd to LinkedinAdd to PinterestAdd to Email


Downloads per month over past year

View more statistics

Actions (login required)

Admin Login Admin Login