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 $N ınfty$ 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.
Users
Please
log in to take part in the discussion (add own reviews or comments).