Bootstrapping line defects in AdS$_3$/CFT$_2$

TL;DR

This paper analyzes correlators along line defects in a specific AdS$_3$/CFT$_2$ setup, using conformal bootstrap and holographic methods to determine OPE coefficients and interpret their holographic significance.

Contribution

It provides the first bootstrap analysis of defect correlators in AdS$_3$/CFT$_2$ with mixed flux, deriving results dependent on only two OPE coefficients and confirming them holographically.

Findings

Bootstrap results depend on two OPE coefficients.

Holographic interpretation of unconstrained OPE coefficients.

Next-to-leading order strong-coupling calculations performed.

Abstract

We study correlators of insertions along 1/2 BPS line defects in the holographic dual to type IIB string theory in $AdS_3 \times S^3 \times T^4$ with mixed Ramond-Ramond and Neveu Schwarz-Neveu Schwarz three-form flux. These defects break the symmetries of the bulk CFT$_2$ as $PSU(1,1|2)^2\times SO(4) \rightarrow PSU(1,1|2)\times SU(2)$, defining displacement and tilt supermultiplets. We focus on the two-, three- and four-point functions of these supermultiplets, which we compute using analytic conformal bootstrap up to next-to-leading order in their strong-coupling expansion. We obtain a bootstrap result that only depends on two OPE coefficients. We perform a Witten diagram check of the bootstrap result, obtaining an holographic interpretation of the two OPE coefficients that are not constrained by the bootstrap procedure.