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→∞ 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.

Counting BPS Operators in Gauge Theories: Quivers, Syzygies and Plethystics / Benvenuti, S.; Feng, B.; Hanany, A.; He, Y. H.. - In: JOURNAL OF HIGH ENERGY PHYSICS. - ISSN 1029-8479. - 2007:11(2007), pp. 1-48. [10.1088/1126-6708/2007/11/050]

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

Benvenuti, S.;
2007-01-01

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→∞ 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.
2007
2007
11
1
48
050
https://arxiv.org/abs/hep-th/0608050
Benvenuti, S.; Feng, B.; Hanany, A.; He, Y. H.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/32135
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