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Friday, September 23rd 2016

12:30 pm:

This talk consists of two parts. In the first part, we discuss indices of 5d superconformal field theories (SCFTs) with emphasis on indices of 1d operators. We construct an index for BPS operators supported on a ray in 5d SCFTs with exceptional global symmetries. We compute the E_n representations (for n=2,\dots,7) of operators of low spin, thus verifying that while the expression for the index is only SO(2n-2)\timesU(1) invariant, the index itself exhibits the full E_n symmetry (at least up to the order we expanded). The ray operators we studied in 5d can be viewed as generalizations of operators constructed in a Yang-Mills theory with fundamental matter by attaching an open Wilson line to a quark. For n\le 7, in contrast to local operators, they carry nontrivial charge under the \mathbb{Z}_{9-n}\subset E_n center of the global symmetry. In the second part, we discuss an on going project of bootstrapping 5d SCFTs. We consider the four point function of the 1/2 BPS operators. We discuss the crossing symmetry and the superconformal blocks of the four point function. We present some preliminary results on the bounds of the operator dimensions and OPE coefficients obtained from analyzing the crossing equation numerically.

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