The conformal bootstrap: Theory, numerical techniques, and applications

Four-Fermion Theory and the Conformal Bootstrap

We employ the conformal bootstrap to re-examine the problem of finding the critical behavior of four-Fermion theory at its strong coupling fixed point. Existence of a solution of the bootstrap equations indicates self-consistency of the assumption that, in space-time dimensions less than four, the renormalization group flow of the coupling constant of a four-Fermion interaction has a nontrivial...

BOOTSTRAP METHODS IN ECONOMETRICS: THEORY AND NUMERICAL PERFORMANCE by

History and Recent Developments in Techniques for Numerical Conformal Mapping

A brief outline is given of some of the main historical developments in the theory and practice of conformal mappings. Originating with the science of cartography, conformal mappings has given rise to many highly sophisticated methods. We emphasize the principles of mathematical discovery involved in the development of numerical methods, through several examples.

Conformal Field Theory, Boundary Conditions and Applications to String Theory

This is an introduction to two-dimensional conformal field theory and its applications in string theory. Modern concepts of conformal field theory are explained, and it is outlined how they are used in recent studies of D-branes in the strong curvature regime by means of CFT on surfaces with boundary.

Conformal bootstrap for the BFKL Pomeron

We calculate the interaction vertex of three BFKL states including the bare triple BFKL Pomeron coupling and discuss its relation with the correlation functions in two-dimensional conformal field theory. We construct the operator algebra of the fields interpolating the BFKL states and show that in the multi-color limit the vertex satisfies the constraints imposed by the conformal bootstrap on t...