%0 Journal Article %1 Benvenuti:2006qr %A Benvenuti, Sergio %A Feng, Bo %A Hanany, Amihay %A He, Yang-Hui %D 2006 %K imported %T Counting BPS operators in gauge theories: Quivers, syzygies and plethystics %U http://arxiv.org/abs/hep-th/0608050 %X 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 $N ınfty$ 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.

@article{Benvenuti:2006qr, 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.}, added-at = {2011-03-12T05:52:28.000+0100}, author = {Benvenuti, Sergio and Feng, Bo and Hanany, Amihay and He, Yang-Hui}, biburl = {https://www.bibsonomy.org/bibtex/2bd038e6e724a1ee3b20ebb9f54978673/corneliu}, eprint = {hep-th/0608050}, file = {0608050.pdf:0608050.pdf:PDF}, interhash = {2b229b095cdf54a1688ecc9f08a9277f}, intrahash = {bd038e6e724a1ee3b20ebb9f54978673}, keywords = {imported}, slaccitation = {%%CITATION = HEP-TH 0608050;%%}, timestamp = {2011-03-12T05:52:30.000+0100}, title = {{C}ounting {BPS} operators in gauge theories: {Q}uivers, syzygies and plethystics}, url = {http://arxiv.org/abs/hep-th/0608050}, year = 2006 }