Abstract
In this work we initiate the conformal bootstrap program for ${\mathcal N}=2$ superconformal field theories in four dimensions. We promote an abstract operator-algebraic viewpoint in order to unify the description of Lagrangian and non-Lagrangian theories, and formulate various conjectures concerning the landscape of theories. We analyze in detail the four-point functions of flavor symmetry current multiplets and of ${\mathcal N}=2$ chiral operators. For both correlation functions we review the solution of the superconformal Ward identities and describe their superconformal block decompositions. This provides the foundation for an extensive numerical analysis discussed in the second half of the paper. We find a large number of constraints for operator dimensions, OPE coefficients, and central charges that must hold for any ${\mathcal N}=2$ superconformal field theory.
Highlights
In this work we initiate the conformal bootstrap program for four-dimensional conformal field theories with N = 2 supersymmetry
We find a large number of constraints for operator dimensions, Operator Product Expansion (OPE) coefficients, and central charges that must hold for any N = 2 superconformal field theory
The moment map four-point function is related to the flavor symmetry of the theory, and we focus on the cases of su(2) and e6
Summary
In this work we initiate the conformal bootstrap program for four-dimensional conformal field theories with N = 2 supersymmetry These theories are extraordinarily rich, both physically and mathematically, and have been studied intensively from many viewpoints. The class S construction of [10, 11] gives rise to an enormous landscape of theories, most of which resist description by conventional Lagrangian field theoretic techniques Despite this abundance, the current catalog seems fairly structured, and one may reasonably suspect that a complete classification of N = 2 superconformal field theories (SCFTs) will be possible. In many examples we know, e.g., the central charges (including flavor central charges), the spectrum of protected operators, and some OPE coefficients associated with protected operators This partial knowledge can be used as input for a numerical bootstrap analysis.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
