dS/CFT from Defect

TL;DR

This paper explores the connection between dS/CFT correspondence and defect operators by performing a Wick rotation, revealing new symmetry properties and deriving integral identities for correlators in the presence of defects.

Contribution

It introduces a global defect operator to reproduce two-point functions and derives integral identities, providing a unified framework for defect-including CFT observables.

Findings

PT symmetry is spontaneously broken in certain CFT$_2$ vacua.

A nonstandard adjoint action for CFT$_d$ generators is established.

Integral identities for bulk and defect correlators are derived.

Abstract

We perform a Wick rotation and analytic continuation from global AdS$_{d+1}$ to static dS$_{d+1}$, yielding CFT$_d$ generators with a nonstandard adjoint action tied to dS bulk coordinates. To reproduce the real-scalar two-point function, we introduce a global defect operator that twists the inner product. We further show that $PT$ symmetry is spontaneously broken in CFT$_2$ vacua with a central charge having an imaginary part. Finally, we derive integral identities for bulk and defect correlators, providing a unified framework for computing CFT$_d$ observables in the presence of global and local defects.