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

A large class of N=2 quantum field theories admits a BPS quiver description and the study of their BPS spectra is then reduced to a representation theory problem. In such theories the coupling to a line defect can be modelled by framed quivers. The associated spectral problem characterises the line defect completely. Framed BPS states can be thought of as BPS particles bound to the defect. We identify the framed BPS degeneracies with certain enumerative invariants associated ...

We study the BPS particle spectrum of five-dimensional superconformal field theories (SCFTs) on $\mathbb{R}^4\times S^1$ with one-dimensional Coulomb branch, by means of their associated BPS quivers. By viewing these theories as arising from the geometric engineering within M-theory, the quivers are naturally associated to the corresponding local Calabi-Yau threefold. We show that the symmetries of the quiver, descending from the symmetries of the Calabi-Yau geometry, togethe...

BPS quivers for N=2 SU(N) gauge theories are derived via geometric engineering from derived categories of toric Calabi-Yau threefolds. While the outcome is in agreement of previous low energy constructions, the geometric approach leads to several new results. An absence of walls conjecture is formulated for all values of N, relating the field theory BPS spectrum to large radius D-brane bound states. Supporting evidence is presented as explicit computations of BPS degeneracies...

Using recent results on BPS quiver theory, we develop a group theoretical method to describe the quiver mutations encoding the quantum mechanical duality relating the spectra of distinct quivers. We illustrate the method by computing the BPS spectrum of the infinite weak chamber of some examples of N=2 supersymmetric gauge models without and with quark hypermultiplets.

We explore BPS quivers for D=5 theories, compactified on a circle and geometrically engineered over local Calabi-Yau 3-folds, for which many of known machineries leading to (refined) indices fail due to the fine-tuning of the superpotential. For Abelian quivers, the counting reduces to a geometric one, but the technically challenging $L^2$ cohomology proved to be essential for sensible BPS spectra. We offer a mathematical theorem to remedy the difficulty, but for non-Abelian ...

It was observed recently, that the low energy effective action of the four-dimensional supersymmetric theories may be obtained as a certain limit of M Theory. From this point of view, the BPS states correspond to the minimal area membranes ending on the M Theory fivebrane. We prove that for the configuration, corresponding to the SU(2) Super Yang-Mills theory, the BPS spectrum is correctly reproduced, and develop techniques for analyzing the BPS spectrum in more general cases...

We study systematically the BPS spectra of N=2 SYM coupled to half--hypermultiplets, the basic example being E_7 SYM coupled to a half--hyper in the 56 irrepr. In order to do this, we determine the BPS quivers with superpotential of such N=2 models using a new technique we introduce. The computation of the BPS spectra in the various chambers is then reduced to the Representation Theory of the resulting quivers. We use the quiver description to study the BPS spectrum at both s...

Four dimensional N=1 theories are engineered by compactifying six dimensional (2,0) theory on a Riemann surface with regular punctures. A generalized Hitchin's equation involving two Higgs fields is proposed as the BPS equation for N=1 compactification. The puncture is interpreted as the singular boundary condition of this equation, and regular puncture is shown to be labeled by a nilpotent commuting pair. In this paper, we focus on a subset of regular puncture which is descr...

We introduce and explore the relation between quivers and 3-manifolds with the topology of the knot complement. This idea can be viewed as an adaptation of the knots-quivers correspondence to Gukov-Manolescu invariants of knot complements (also known as $F_K$ or $\hat{Z}$). Apart from assigning quivers to complements of $T^{(2,2p+1)}$ torus knots, we study the physical interpretation in terms of the BPS spectrum and general structure of 3d $\mathcal{N}=2$ theories associated ...

We consider N=2 superconformal theories defined on a 3+1 dimensional hyperplane intersection of two sets of M5 branes. These theories have (tensionless) BPS string solitons. We use a dual supergravity formulation to deduce some of their properties via the AdS/CFT correspondence.