2019_EJRNL_PP_DAVID_POLAND_1.pdf
Terbatas Ratnasari
» ITB
Terbatas Ratnasari
» ITB
Conformal field theories have been long known to describe the fascinating universal physics of scale
invariant critical points. They describe continuous phase transitions in fluids, magnets, and numerous
other materials, while at the same time sit at the heart of our modern understanding of quantum field
theory. For decades it has been a dream to study these intricate strongly coupled theories
nonperturbatively using symmetries and other consistency conditions. This idea, called the conformal
bootstrap, saw some successes in two dimensions but it is only in the last ten years that it has been
fully realized in three, four, and other dimensions of interest. This renaissance has been possible due
to both significant analytical progress in understanding how to set up the bootstrap equations and the
development of numerical techniques for finding or constraining their solutions. These developments
have led to a number of groundbreaking results, including world-record determinations of critical
exponents and correlation function coefficients in the Ising and OðNÞ models in three dimensions.
This article will review these exciting developments for newcomers to the bootstrap, giving an
introduction to conformal field theories and the theory of conformal blocks, describing numerical
techniques for the bootstrap based on convex optimization, and summarizing in detail their
applications to fixed points in three and four dimensions with no or minimal supersymmetry.