BPS Quivers and Spectra of Complete N=2 Quantum Field Theories

We conjecture a precise relationship between the Schur limit of the superconformal index of four-dimensional $\mathcal{N}=2$ field theories, which counts local operators, and the spectrum of BPS particles on the Coulomb branch. We verify this conjecture for the special case of free field theories, $\mathcal{N}=2$ QED, and $SU(2)$ gauge theory coupled to fundamental matter. Assuming the validity of our proposal, we compute the Schur index of all Argyres-Douglas theories. Our a...

We give a unified description of all BPS states of M-theory compactified on $T^5$ in terms of the five-brane. We compute the mass spectrum and degeneracies and find that the $SO(5,5,Z)$ U-duality symmetry naturally arises as a T-duality by assuming that the world-volume theory of the five-brane itself is described by a string theory. We also consider the compactification on $S^1/Z_2 \times T^4$, and give a new explanation for its correspondence with heterotic string theory by...

We study the gauge/gravity duality for theories with four dimensional ${\cal N}=2$ supersymmetries. We consider the large class of generalized quiver field theories constructed recently by one of us (D.G.). These field theories can also be viewed as the IR limit of M5 branes wrapping a Riemann surface with punctures. We give a prescription for constructing the corresponding geometries and we discuss a few special cases in detail. There is a precise match for various quantitie...

We apply ideas that have appeared in the study of D-branes on Calabi-Yau compactifications to the derivation of the BPS spectrum of field theories. In particular, we identify an orbifold point whose fractional branes can be thought of as ``partons'' of the BPS spectrum of N=2 pure SU(N) SYM. We derive the BPS spectrum and lines of marginal stability branes near that orbifold, and compare our results with the spectrum of the field theories.

A supersymmetric quantum mechanical model is constructed for BPS states bound to surface operators in five dimensional SU(r) gauge theories using D-brane engineering. This model represents the effective action of a certain D2-brane configuration, and is naturally obtained by dimensional reduction of a quiver $(0,2)$ gauged linear sigma model. In a special stability chamber, the resulting moduli space of quiver representations is shown to be virtually smooth and isomorphic to ...

We consider the low-energy limit of the two-dimensional theory on multiple M2-branes suspended between a flat M5-brane and a curved M5-brane. We argue that it is described by an $\mathcal{N}=(2,2)$ supersymmetric Landau-Ginzburg model with the superpotential determined by the shape of the curved M5-branes, which flows in the low-energy limit to a Kazama-Suzuki coset model. We provide evidence by studying ground states and BPS spectra of the systems.

We relate a number of results in the theory of flat surfaces to BPS spectra of a class of 4d $\mathcal{N}=2$ supersymmetric quantum field theories arising from M5 branes wrapped on Riemann surfaces -- $A_1$ class S theories. In particular, we apply classic results of Eskin and Masur, which determine the asymptotic growth of geodesic counts at large length on flat surfaces, as well as more recent progress in the mathematics literature, to determine the large mass asymptotics o...

We review M-theory description of 4d N=2 SQCD. Configurations of M-theory fivebranes relevant to describe the moduli spaces of the Coulomb and Higgs branches are studied using the Taub-NUT geometry. Minimal area membranes related with the BPS states of N=2 SQCD are given explicitly. They almost saturate the BPS bounds. The deviation from the bounds is due to their boundary condition constrained by the fivebrane. The electric-magnetic duality at the baryonic branch root is als...

We describe a simple method for determining the strong-coupling BPS spectrum of four dimensional N=2 supersymmetric Yang-Mills theory. The idea is to represent the magnetic monopoles and dyons in terms of D-brane boundary states of a non-compact d=2 N=2 Landau-Ginzburg model. In this way the quantum truncated BPS spectrum at the origin of the moduli space can be directly mapped to the finite number of primary fields of the superconformal minimal models.

The BPS spectrum of many 4d N=2 theories may be seen as the (categorical) Galois cover of the BPS spectrum of a different 4d N=2 model. The Galois group G acts as a physical symmetry of the covering N=2 model. The simplest instance is SU(2) SQCD with N_f=2 quarks, whose BPS spectrum is a Z_2-cover of the BPS spectrum of pure SYM. More generally, N=2 SYM with simply--laced gauge group admits Z_k-covers for all k; e.g. the Z_2-cover of SO(8) SYM is SO(8) SYM coupled to two copi...