dS/CFT and the operator product expansion

TL;DR

This paper explores how conformal invariance and operator product expansions extend to dS/CFT correspondence, revealing that certain representations lead to singularities preventing conventional field theory realization.

Contribution

It generalizes conformal invariance and OPE relations to principal and complementary series representations relevant for dS/CFT, and analyzes their implications.

Findings

Conformal invariance constrains two and three-point functions.

Constructs conformal partial wave expansions for new representations.

Shows these representations cause essential singularities in CFTs.

Abstract

Global conformal invariance determines the form of two and three-point functions of quasi-primary operators in a conformal field theory, and generates nontrivial relations between terms in the operator product expansion. These ideas are generalized to the principal and complementary series representations, which play an important role in the conjectured dS/CFT correspondence. The conformal partial wave expansions are constructed for these representations which in turn determine the operator product expansion. This leads us to conclude that conformal field theories containing such representations have essential singularities, so cannot be realized as conventional field theories.