BPS Counting Research Articles

Counting chiral operators in quiver gauge theories

We discuss in detail the problem of counting BPS gauge invariant operators in the chiral ring of quiver gauge theories living on D-branes probing generic toric CY singularities. The computation of generating functions that include counting of baryonic operators is based on a relation between the baryonic charges in field theory and the Kahler moduli of the CY singularities. A study of the interplay between gauge theory and geometry shows that given geometrical sectors appear more than once in the field theory, leading to a notion of ``multiplicities. We explain in detail how to decompose the generating function for one D-brane into different sectors and how to compute their relevant multiplicities by introducing geometric and anomalous baryonic charges. The Plethystic Exponential remains a major tool for passing from one D-brane to arbitrary number N of D-branes. Explicit formulae are given for few examples, including 3/3, 0, and dP1.

D1/D5 systems in string theories

We propose CFT descriptions of the D1/D5 system in a class of freely acting Z_2 orbifolds/orientifolds of type IIB theory, with sixteen unbroken supercharges. The CFTs describing D1/D5 systems involve N=(4,4) or N=(4,0) sigma models on $(R^3\times S^1\times T^4\times (T^4)^N/S_N)/Z_2$, where the action of Z_2 is diagonal and its precise nature depends on the model. We also discuss D1(D5)-brane states carrying non-trivial Kaluza-Klein charges. The resulting multiplicities for two-charge bound states are shown to agree with the predictions of U-duality. We raise a puzzle concerning the multiplicities of three-charge systems, which is generically present in all vacuum configurations with sixteen unbroken supercharges studied so far, including the more familiar type IIB on K3 case: the constraints put on BPS counting formulae by U-duality are apparently in contradiction with any CFT interpretation. We argue that the presence of RR backgrounds appearing in the symmetric product CFT may provide a resolution of this puzzle.