Alexandrov Sergei, Moore Gregory W, Neitzke Andrew, Pioline Boris
Laboratoire Charles Coulomb, CNRS UMR 5221, Université Montpellier 2, F-34095 Montpellier, France.
NHETC and Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08855-0849, USA.
Phys Rev Lett. 2015 Mar 27;114(12):121601. doi: 10.1103/PhysRevLett.114.121601. Epub 2015 Mar 23.
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.
在(R^{3,1})上具有(N = 2)超对称性的理论中，超对称束缚态可以在库仑分支参数空间中的边际稳定性壁上衰变，导致BPS指标(\Omega(\gamma, u))出现不连续性。我们考虑一个超对称指标(I)，它接收来自(1/2 - BPS)态的贡献，推广了熟悉的维滕指标(Tr(-1)^{F}e^{-\beta H})。由于多粒子态连续统的贡献，我们期望(I)在无质量粒子出现的轨迹之外是光滑的。从(N = 2)弦真空的超多重态模空间中的类似现象获得灵感，我们推测了一个用BPS指标(\Omega(\gamma, u))表示(I)的公式，该公式在壁上是连续的，并且在大(\beta)时展示了单粒子态的预期贡献。这给出了多粒子态对指标(I)贡献的通用预测。这个指标自然是在一个圆上约化后模空间上的函数，与该空间上的典范超凯勒度量和超全纯联络密切相关。
