A dispersion relation for defect CFT

TL;DR

This paper introduces a dispersion relation for defect conformal field theories that simplifies the calculation of two-point functions, enabling both reproduction of known results and derivation of new formulas at strong coupling.

Contribution

It provides a novel dispersion relation formula for defect CFTs that streamlines bootstrap calculations and yields new analytic results for supersymmetric Wilson lines.

Findings

Reproduced known results for monodromy defects in epsilon-expansion.

Derived new analytic formula for R-symmetry channel of operators in N=4 SYM.

Streamlined bootstrap calculations for defect CFTs.

Abstract

We present a dispersion relation for defect CFT that reconstructs two-point functions in the presence of a defect as an integral of a single discontinuity. The main virtue of this formula is that it streamlines explicit bootstrap calculations, bypassing the resummation of conformal blocks. As applications we reproduce known results for monodromy defects in the epsilon-expansion, and present new results for the supersymmetric Wilson line at strong coupling in $\mathcal{N}=4$ SYM. In particular, we derive a new analytic formula for the highest $R$-symmetry channel of single-trace operators of arbitrary length.