Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2006-08-07
JHEP 0711:050,2007
Physics
High Energy Physics
High Energy Physics - Theory
59+1 pages, 7 Figures
Scientific paper
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.
Benvenuti Sergio
Feng Bo
Hanany Amihay
He Yang-Hui
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