title: R^{3} index for four-dimensional (N)=2 field theories.
abstract: In theories with N=2 supersymmetry on R^{3,1}, supersymmetric bound states can decay across walls of marginal stability in the space of Coulomb branch parameters, leading to discontinuities in the BPS indices Ω(γ,u). We consider a supersymmetric index I which receives contributions from 1/2-BPS states, generalizing the familiar Witten index Tr(-1)^{F}e^{-βH}. We expect I to be smooth away from loci where massless particles appear, thanks to contributions from the continuum of multiparticle states. Taking inspiration from a similar phenomenon in the hypermultiplet moduli space of N=2 string vacua, we conjecture a formula expressing I in terms of the BPS indices Ω(γ,u), which is continuous across the walls and exhibits the expected contributions from single particle states at large β. This gives a universal prediction for the contributions of multiparticle states to the index I. This index is naturally a function on the moduli space after reduction on a circle, closely related to the canonical hyperkähler metric and hyperholomorphic connection on this space.
authors: Laboratoire Charles Coulomb, CNRS UMR 5221, Université Montpellier 2, F-34095 Montpellier, France.
authors: Sergei
authors: S
authors: Alexandrov
authors: NHETC and Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08855-0849, USA.
authors: Gregory W
authors: GW
authors: Moore
authors: Department of Mathematics, University of Texas at Austin, Austin, Texas 78712-1202, USA.
authors: Andrew
authors: A
authors: Neitzke
authors: CERN Dep PH-TH, 1211 Geneva 23, Switzerland.|Sorbonne Universités, UPMC Univ. Paris 06, UMR 7589, LPTHE, F-75005 Paris, France.
authors: Boris
authors: B
authors: Pioline