%0 Journal Article
%T $R^3$ index for four-dimensional $N=2$ field theories
%+ Laboratoire Charles Coulomb (L2C)
%+ NHETC
%+ University of Texas at Austin [Austin]
%+ CERN Theoretical Physics Department
%A Alexandrov, Sergey
%A Moore, Gregory W.
%A Neitzke, Andrew
%A Pioline, Boris
%Z 7 pages; v2: introduction expanded, minor corrections, differs from published version in PRL in that supplemental material is included as an Appendix. Réf Journal: Phys. Rev. Lett. 114, 121601 (2015)
%< avec comité de lecture
%Z L2C:15-071
%@ 0031-9007
%J Physical Review Letters
%I American Physical Society
%V 114
%N 12
%P 121601
%8 2015
%D 2015
%Z 1406.2360
%R 10.1103/PhysRevLett.114.121601
%Z Physics [physics]/High Energy Physics - Theory [hep-th]Journal articles
%X In theories with $N=2$ supersymmetry on $R^{3,1}$, BPS bound states can decay across walls of marginal stability in the space of Coulomb branch parameters, leading to discontinuities in the BPS indices $\Omega(\gamma,u)$. We consider a supersymmetric index $I$ which receives contributions from 1/2-BPS states, generalizing the familiar Witten index $Tr (-1)^F e^{-\beta H}$. We expect $I$ to be smooth away from loci where massless particles appear, thanks to contributions from the continuum of multi-particle 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 $\Omega(\gamma,u)$, which is continuous across the walls and exhibits the expected contributions from single particle states at large $\beta$. This gives a universal prediction for the contributions of multi-particle 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 hyperk\"ahler metric and hyperholomorphic connection on this space.
%G English
%2 https://hal.science/hal-01157692/document
%2 https://hal.science/hal-01157692/file/1406.2360%20%281%29.pdf
%L hal-01157692
%U https://hal.science/hal-01157692
%~ CNRS
%~ L2C
%~ MIPS
%~ UNIV-MONTPELLIER
%~ UM-2015-2021