An Analytic Approach to BCFT$_d$

Understand

We develop an analytic approach to Boundary Conformal Field Theory (BCFT), focussing on the two-point function of a general pair of scalar primary operators.

• The resulting crossing equation can be thought of as a vector equation in an infinite-dimensional space ${\cal V}$ of analytic functions of a single complex variable.
• We argue that in a unitary theory, functions in ${\cal V}$ satisfy a boundedness condition in the Regge limit.
• We identify a useful basis for ${\cal V}$, consisting of bulk and boundary conformal blocks with scaling dimensions which appear in OPEs of the mean field theory correlator.