Celestial Conformal Primaries in Effective Field Theories

Prahar Mitra (U of Amsterdam)

Apr 03. 2024, 11:30 — 12:00

Scattering amplitudes in $d+2$ dimensions can be recast as correlators of conformal primary operators in a putative holographic CFT$_d$ by working in a basis of boost eigenstates instead of momentum eigenstates. It has been shown previously that conformal primary operators with $\Delta \in \frac{d}{2} + i {\mathbb R}$ form a basis for massless one-particle representations. In this paper, we consider more general conformal primary operators with $\Delta \in {\mathbb C}$ and show that completeness, normalizability, and consistency with CPT implies that we must restrict the scaling dimensions to either $\Delta \in \frac{d}{2} + i {\mathbb R}$ or $\Delta \in {\mathbb R}$. Unlike those with $\Delta \in \frac{d}{2} + i {\mathbb R}$, the conformal primaries with $\Delta \in {\mathbb R}$ can be constructed without knowledge of the UV and can therefore be defined in effective field theories. With additional analyticity assumptions, we can restrict $\Delta \in 2 - \mzz_{\geq0}$ or $\Delta \in \frac{1}{2}-\mzz_{\geq0}$ for bosonic or fermionic operators, respectively.

Further Information
Venue:
ESI Schrödinger and Boltzmann Lecture Hall
Associated Event:
Carrollian Physics and Holography (Thematic Programme)
Organizer(s):
Andrea Campoleoni (U of Mons)
Laura Donnay (SISSA, Trieste)
Stefan Fredenhagen (U of Vienna)
Daniel Grumiller (TU Vienna)