Bounds on N = 1 superconformal theories with global symmetries

Abstract: Recently, the conformal-bootstrap has been successfully used to obtain generic bounds on the spectrum and OPE coefficients of unitary conformal field theories. In practice, these bounds are obtained by assuming the existence of a scalar operator in the theory and analyzing the crossing-symmetry constraints of its 4-point function. In N = 1 superconformal theories with a global symmetry there is always a scalar primary operator, which is the top of the current multiplet. In this paper we analyze the crossing-symmetry constraints of the 4-point function of this operator for N = 1 theories with SU(N) global symmetry. We analyze the current-current OPE and write the superconformal blocks, generalizing the work of Fortin, Intriligator and Stergiou to the non-Abelian case. Moreover we find new contributions to the OPE which can appear both in the Abelian and non-Abelian cases. We then use these results to obtain lower bounds on the coefficient of the current 2-point function.