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arXiv · 1210.3605

BPS Degeneracies and Superconformal Index in Diverse Dimensions

Amer Iqbal·Cumrun Vafa
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Abstract

We present a unifying theme relating BPS partition functions and superconformal indices. In the case with complex SUSY central charges (as in N=2 in d=4 and N=(2,2) in d=2) the known results can be reinterpreted as the statement that the BPS partition functions can be used to compute a specialization of the superconformal indices. We argue that in the case with real central charge in the supersymmetry algebra, as in N=1 in d=5 (or the N=2 in d=3), the BPS degeneracy captures the full superconformal index. Furthermore, we argue that refined topological strings, which captures 5d BPS degeneracies of M-theory on CY 3-folds, can be used to compute 5d supersymmetric index including in the sectors with 3d defects for a large class of 5d superconformal theories. Moreover, we provide evidence that distinct Calabi-Yau singularities which are expected to lead to the same SCFT yield the same index.

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Amer Iqbal, Cumrun Vafa. 2015-12-21. BPS Degeneracies and Superconformal Index in Diverse Dimensions. https://doi.org/10.1103/physrevd.90.105031

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