A dispersion relation for defect CFT

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.

30 pages, 1 figure

References in corpus (5)

• Mellin amplitudes for $Ad{S}_5\times S^5$
• Bootstrap equations for $\mathcal{N}=4$ SYM with defects
• $\epsilon$-Expansion in Critical ${\varphi }^3$-Theory on Real Projective Space from Conformal Field Theory
• Mixed Correlator Dispersive CFT Sum Rules
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• Holographic Wilson Loop One-point Functions in ABJM Theory