Abstract
We apply the numerical bootstrap program to chiral operators in four-dimensional $$ \mathcal{N}=2 $$ SCFTs. In the first part of this work we study four-point functions in which all fields have the same conformal dimension. We give special emphasis to bootstrapping a specific theory: the simplest Argyres-Douglas fixed point with no flavor symmetry. In the second part we generalize our setup and consider correlators of fields with unequal dimension. This is an example of a mixed correlator and allows us to probe new regions in the parameter space of $$ \mathcal{N}=2 $$ SCFTs. In particular, our results put constraints on relations in the Coulomb branch chiral ring and on the curvature of the Zamolodchikov metric.
Highlights
Critical 3d Ising model, where the the low-lying spectrum was obtained in [2, 3] by studying the four-point function of the spin operator
We start with a brief introduction to chiral operators, and proceed to study the multiplets being exchanged in the OPE, as well as the superconformal blocks that capture the contributions of each superconformal family to the four-point function
In [11], the CFT data was constrained by obtaining an upper bound on the dimension of the first unprotected long scalar operator, and a lower bound on the central charge
Summary
We will set up the crossing symmetry equation for N = 2 chiral correlators of unequal dimension. This is an example of a mixed correlator, and will allow us to explore regions inaccessible with the single correlator bootstrap. The remarkable success of the mixed correlator bootstrap in three dimensions is one of the main motivations for considering mixed correlators in N = 2 SCFTs. We start with a brief introduction to chiral operators, and proceed to study the multiplets being exchanged in the OPE, as well as the superconformal blocks that capture the contributions of each superconformal family to the four-point function. The bootstrap for chiral correlators in three dimensions was studied in [18, 19]
Sign-in/Register to view highlights & summary 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 callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
