Journal
JOURNAL OF HIGH ENERGY PHYSICS
Volume -, Issue 10, Pages -Publisher
SPRINGER
DOI: 10.1007/JHEP10(2020)183
Keywords
Conformal Field Theory; Supersymmetric Gauge Theory
Categories
Funding
- Simons Foundation [488657]
- Israel Science Foundation [2289/18, 1937/12]
- I-CORE Program of the Planning and Budgeting Committee
- Clore Scholars Programme
- BSF [2018204]
- Israel Science Foundation center for excellence grant
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We show that exactly marginal operators of Supersymmetric Conformal Field Theories (SCFTs) with four supercharges cannot obtain a vacuum expectation value at a generic point on the conformal manifold. Exactly marginal operators are therefore nilpotent in the chiral ring. This allows us to associate an integer to the conformal manifold, which we call the nilpotency index of the conformal manifold. We discuss several examples in diverse dimensions where we demonstrate these facts and compute the nilpotency index.
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