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 N = 4 SYM. In particular, we derive a new analytic formula for the highest R-symmetry channel of single-trace operators of arbitrary length.

Interacting conformal scalar in a wedge

“…It would be interesting to generalise the approach presented recently in [25,26] to the wedge configuration to be able to understand how to systematise the study of one-and two-point functions. As a consequence, it would be interesting to further explore the connections found in [27] to more general cases, such as the one presented in this paper.…”

Further on the Aharonov-Bohm Green function: the coincidence limit

“…In a recent report, [1], it was shown, essentially just by a coordinate transformation, that an old contour integral expression for the Green function, G, of a free conformal scalar, φ, in the presence of an Aharonov-Bohm flux tube takes the form of an Appell F 1 function. 2 Expansion of this Green function, or correlator, in a Fourier series effectively provides its defect block expansion, of which several forms can be found, related by hypergeometric transformations.…”

“…This representation has also been derived on the basis of a dispersion relation for the correlator applied to a (generalised) free field by Barrat et al[2].…”