Abstract
The Römelsberger index on S 3 × \( \mathbb{R} \) serves as a powerful test for conjectured dualities, relying on the claim that this object is an RG-invariant. In this work we support this claim by showing that the singularities suggested by Witten of “states moving in from infinity” are excluded on S 3 ×\( \mathbb{R} \). In addition, we provide an application of the Römelsberger index, in the form of a constraint on the RG flow of supersymmetric theories. The constraint, which applies for asymptotically free theories with unbroken supersymmetry and non-anomalous R-symmetry, is the following: if the R-charges of the chiral multiplets in the UV theory are q i ∈ (0, 2) and the IR theory can be described as a free theory of chiral bound states, then the R-charges of these bound states, \( {\tilde{q}}_j \) , are constrained such that \( {\tilde{q}}_j\in \left(0,2\right) \). We thus provide a proof of a weak version of a conjecture proposed by Intriligator. We mention some applications of this result.
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ArXiv ePrint: 1311.0487
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Gerchkovitz, E. Constraints on the R-charges of free bound states from the Römelsberger index. J. High Energ. Phys. 2014, 71 (2014). https://doi.org/10.1007/JHEP07(2014)071
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DOI: https://doi.org/10.1007/JHEP07(2014)071