OPE coefficients in Argyres-Douglas theories

The calculation of physical quantities in certain quantum field theories such as those of the Argyres-Douglas type is notoriously hard, due to the lack of a Lagrangian description. Here we tackle this problem following two alternative approaches. On the one hand, we use localization on the four-sphere to compute two-correlators and OPE coefficients in Argyres-Douglas superconformal theories. On the other hand, we use the conformal bootstrap machinery to put stringent bounds on such coefficients, only relying on the knowledge of central charge and conformal dimension of the operators. We compare the results obtained with these two methods and find good agreement for all rank-one cases and for the rank-two Argyres-Douglas theories (A(1), A(4)) and (A(1), A(5)), in the moduli space of pure SU(5) and SU(6) super Yang-Mills. We also apply our results from localization to obtain bounds on the dimensions of the lightest neutral unprotected operators of the CFTs.

Automated summary

This paper investigates the calculation of physical quantities in certain quantum field theories, specifically the Argyres-Douglas type. Two alternative approaches, localization and conformal bootstrap, are used to tackle this problem. The results show good agreement between the two methods in rank-one cases and the rank-two Argyres-Douglas theories, and the localization results provide bounds on the dimensions of the lightest neutral unprotected operators in CFTs.