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.
Highlights
In theories with N 1⁄4 2 supersymmetry on R3;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 Ωðγ; uÞ
Taking inspiration from a similar phenomenon in the hypermultiplet moduli space of N 1⁄4 2 string vacua, we conjecture a formula expressing I in terms of the BPS indices Ωðγ; uÞ, which is continuous across the walls and exhibits the expected contributions from single particle states at large β
BPS indices and the Witten index.—In four-dimensional field theories on R3;1 with N 1⁄4 2 supersymmetry, the spectrum of BPS states in general strongly depends on the value of the Coulomb branch parameters
Summary
In theories with N 1⁄4 2 supersymmetry on R3;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 Ωðγ; uÞ. Taking inspiration from a similar phenomenon in the hypermultiplet moduli space of N 1⁄4 2 string vacua, we conjecture a formula expressing I in terms of the BPS indices Ωðγ; uÞ, which is continuous across the walls and exhibits the expected contributions from single particle states at large β.
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