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Alexandrov S, Moore GW, Neitzke A, et al. R^{3} index for four-dimensional (N)=2 field theories. Phys Rev Lett. 2015;114(12):121601doi: 10.1103/PhysRevLett.114.121601.
Alexandrov, S., Moore, G. W., Neitzke, A., & Pioline, B. (2015). R^{3} index for four-dimensional (N)=2 field theories. Physical review letters, 114(12), 121601. https://doi.org/10.1103/PhysRevLett.114.121601
Alexandrov, Sergei, et al. "R^{3} index for four-dimensional (N)=2 field theories." Physical review letters vol. 114,12 (2015): 121601. doi: https://doi.org/10.1103/PhysRevLett.114.121601
Alexandrov S, Moore GW, Neitzke A, Pioline B. R^{3} index for four-dimensional (N)=2 field theories. Phys Rev Lett. 2015 Mar 27;114(12):121601. doi: 10.1103/PhysRevLett.114.121601. Epub 2015 Mar 23. PMID: 25860732.
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Phys Rev Lett. 2015 Mar 27;114(12):121601. doi: 10.1103/PhysRevLett.114.121601. Epub 2015 Mar 23.

R^{3} index for four-dimensional (N)=2 field theories.

Physical review letters

Sergei Alexandrov, Gregory W Moore, Andrew Neitzke, Boris Pioline

Affiliations

  1. Laboratoire Charles Coulomb, CNRS UMR 5221, Université Montpellier 2, F-34095 Montpellier, France.
  2. NHETC and Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08855-0849, USA.
  3. Department of Mathematics, University of Texas at Austin, Austin, Texas 78712-1202, USA.
  4. CERN Dep PH-TH, 1211 Geneva 23, Switzerland.
  5. Sorbonne Universités, UPMC Univ. Paris 06, UMR 7589, LPTHE, F-75005 Paris, France.

PMID: 25860732 DOI: 10.1103/PhysRevLett.114.121601

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.

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