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Article Dans Une Revue Physical Review Letters Année : 2015

$R^3$ index for four-dimensional $N=2$ field theories

Sergey Alexandrov
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Gregory W. Moore
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Boris Pioline

Résumé

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.
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hal-01157692 , version 1 (03-06-2021)

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Sergey Alexandrov, Gregory W. Moore, Andrew Neitzke, Boris Pioline. $R^3$ index for four-dimensional $N=2$ field theories. Physical Review Letters, 2015, 114 (12), pp.121601. ⟨10.1103/PhysRevLett.114.121601⟩. ⟨hal-01157692⟩
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