Bootstrapping SCFTs with Four Supercharges

Nikolay Bobev; Sheer El-Showk; Dalimil Mazac; Miguel F. Paulos

doi:10.1007/jhep08(2015)142

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arXiv · 1503.02081

Bootstrapping SCFTs with Four Supercharges

Nikolay Bobev·Sheer El-Showk·Dalimil Mazac·Miguel F. Paulos

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Abstract

We study the constraints imposed by superconformal symmetry, crossing symmetry, and unitarity for theories with four supercharges in spacetime dimension $2\leq d\leq 4$. We show how superconformal algebras with four Poincar\'{e} supercharges can be treated in a formalism applicable to any, in principle continuous, value of $d$ and use this to construct the superconformal blocks for any $d\leq 4$. We then use numerical bootstrap techniques to derive upper bounds on the conformal dimension of the first unprotected operator appearing in the OPE of a chiral and an anti-chiral superconformal primary. We obtain an intriguing structure of three distinct kinks. We argue that one of the kinks smoothly interpolates between the $d=2$, $\mathcal N=(2,2)$ minimal model with central charge $c=1$ and the theory of a free chiral multiplet in $d=4$, passing through the critical Wess-Zumino model with cubic superpotential in intermediate dimensions.

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Nikolay Bobev, Sheer El-Showk, Dalimil Mazac, Miguel F. Paulos. 2015-03-06. Bootstrapping SCFTs with Four Supercharges. https://doi.org/10.1007/jhep08(2015)142

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