Year: 2017
Type: article
Abstract: In this long overdue second installment, we continue to develop the conformal bootstrap program for $\mathcal{N}=4$ superconformal field theories (SCFTs) in four dimensions via an analysis of the correlation function of four stress-tensor supermultiplets. We review analytic results for this correlator and make contact with the SCFT/chiral algebra correspondence of Beem et al. [Commun. Math. Phys. 336, 1359 (2015)]. We demonstrate that the constraints of unitarity and crossing symmetry require the central charge $c$ to be greater than or equal to $3/4$ in any interacting $\mathcal{N}=4$ SCFT. We apply numerical bootstrap methods to derive upper bounds on scaling dimensions and operator product expansion coefficients for several low-lying, unprotected operators as a function of the central charge. We interpret our bounds in the context of $\mathcal{N}=4$ super Yang-Mills theories, formulating a series of conjectures regarding the embedding of the conformal manifold---parametrized by the complexified gauge coupling---into the space of scaling dimensions and operator product expansion coefficients. Our conjectures assign a distinguished role to points on the conformal manifold that are self-dual under a subgroup of the $S$-duality group. This paper contains a more detailed exposition of a number of results previously reported in Beem et al. [Phys. Rev. Lett. 111, 071601 (2013)] in addition to new results.
Language: Latvian
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2564566519