Slava Rychkov

Solving the 3D Ising Model with the Conformal Bootstrap

We study the constraints of crossing symmetry and unitarity in general 3D conformal field theories. In doing so we derive new results for conformal blocks appearing in four-point functions of scalars and present an efficient method for their computation in arbitrary space-time dimension. Comparing the resulting bounds on operator dimensions and product-expansion coefficients in 3D to known results, we find that the 3D Ising model lies at a corner point on the boundary of the allowed parameter space. We also derive general upper bounds on the dimensions of higher spin operators, relevant in the context of theories with weakly broken higher spin symmetries.

Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents

We use the conformal bootstrap to perform a precision study of the operator spectrum of the critical 3d Ising model. We conjecture that the 3d Ising spectrum minimizes the central charge

Spinning Conformal Blocks

c

Central Charge Bounds in 4D Conformal Field Theory

c in the space of unitary solutions to crossing symmetry. Because extremal solutions to crossing symmetry are uniquely determined, we are able to precisely reconstruct the first several

EPFL Lectures on Conformal Field Theory in D>= 3 Dimensions

\mathbb {Z}_2

The

Z2-even operator dimensions and their OPE coefficients. We observe that a sharp transition in the operator spectrum occurs at the 3d Ising dimension