CERN Accelerating science

Article
Report number	arXiv:1406.2360 ; LPTA-14-023 ; CERN-PH-TH-2014-100 ; LPTA-14-023 ; CERN-PH-TH-2014-100
Title	$\mathbb R^3$ Index for Four-Dimensional $N=2$ Field Theories
Author(s)	Alexandrov, Sergei (Montpellier U.) ; Moore, Gregory W. (Rutgers U., Piscataway) ; Neitzke, Andrew (U. Texas, Austin (main)) ; Pioline, Boris (CERN ; UPMC, Paris (main))
Publication	2015-03-23
Imprint	09 Jun 2014
Number of pages	7
Note	7 pages; v2: introduction expanded, minor corrections, differs from published version in PRL in that supplemental material is included as an Appendix
In:	Phys. Rev. Lett. 114 (2015) 121601
DOI	10.1103/PhysRevLett.114.121601
Subject category	Particle Physics - Theory
Abstract	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.
Copyright/License	publication: © 2015-2025 The Author(s) (License: CC-BY-3.0) preprint: © 2014-2025 CERN (License: CC-BY-3.0)

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