Christopher Beem

Infinite Chiral Symmetry in Four Dimensions

We describe a new correspondence between four-dimensional conformal field theories with extended supersymmetry and two-dimensional chiral algebras. The meromorphic correlators of the chiral algebra compute correlators in a protected sector of the four-dimensional theory. Infinite chiral symmetry has far-reaching consequences for the spectral data, correlation functions, and central charges of any four-dimensional theory with

The

{\mathcal{N}=2}

Superconformal Bootstrap

N=2 superconformal symmetry.

Four-dimensional SCFTs from M5-branes

In this long overdue second installment, we continue to develop the conformal bootstrap program for 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 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 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.

N=4Superconformal Bootstrap

We implement the conformal bootstrap for N=4 superconformal field theories in four dimensions. The consistency of the four-point function of the stress-energy tensor multiplet imposes significant upper bounds for the scaling dimensions of unprotected local operators as functions of the central charge of the theory. At the threshold of exclusion, a particular operator spectrum appears to be singled out by the bootstrap constraints. We conjecture that this extremal spectrum is that of N=4 supersymmetric Yang-Mills theory at an S-duality invariant value of the complexified gauge coupling.

Holomorphic Blocks in Three Dimensions

A bstractWe engineer a large new set of four-dimensional

The

\mathcal{N} = 1

{\mathcal N}=2

superconformal field theories by wrapping M5-branes on complex curves. We present new supersymmetric AdS5 M-theory backgrounds which describe these fixed points at large N, and then directly construct the dual four-dimensional CFTs for a certain subset of these solutions. Additionally, we provide a direct check of the central charges of these theories by using the M5-brane anomaly polynomial. This is a companion paper which elaborates upon results reported in [1].