Marginal operators from celestial diamonds

A bstract For a given conformal field theory (CFT), one can deform it via the addition of a marginal operator to the spectrum. In two dimensions, when the added operator has conformal weights $$ h=\overline{h}=1 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>h</mml:mi> <mml:mo>=</mml:mo> <mml:mover> <mml:mi>h</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> </mml:math> , conformal symmetry is not broken and the resulting theory is a distinct CFT. Studying such marginal operators for celestial CFTs allows for a geometric understanding of the space of allowed boundary theories dual to quantum field theories (QFT) in bulk asymptotically flat spacetimes. In traditional holographic examples, a marginal deformation on the boundary corresponds to a vacuum transition in the bulk theory. We affirm this in celestial CFTs which requires a general definition of marginal operators as composite celestial operators via pairs that live at distinct corners of celestial memory and Goldstone diamonds.