Soft Scalars and the Geometry of the Space of Celestial CFTs

Abstract

Known examples of the holographic dictionary in asymptotically Anti-de Sitter spacetimes equate moduli spaces of bulk vacua with conformal manifolds in the dual quantum field theory. We demonstrate that the same identification holds for gravity in asymptotically flat spacetimes in any dimension, in accord with expectations derived from the celestial conformal field theory (CCFT) formalism. Soft limits of moduli scalars described by the sigma model are universal, and relate to parallel transport of $S$-matrix observables over the moduli space of bulk vacua. The leading "soft moduli operator" is the shadow transform of a dimension $\Delta =d$ marginal operator $M(x)$. The universal form of the soft limit guarantees that $M(x)$ acts as a marginal deformation in the CCFT${}_d$, and coherent states of the soft scalars correspond to finite deformations along the conformal manifold. This manifold typically has curvature, which is captured by the antisymmetric double-soft theorem and which reflects the Berry curvature in CCFT${}_d$. We also compute the Mellin-transformed four-point function in the sigma model and compare to a formula of Kutasov for the curvature of the conformal manifold.

21 pages

References in corpus (11)

• Effective Field Theories from Soft Limits
• Holographic Symmetry Algebras for Gauge Theory and Gravity
• Celestial Operator Product Expansions and ${\mathrm{w}}_{1+\infty }$ Symmetry for All Spins
• $(2,2)$ Scattering and the Celestial Torus
• Conformal Blocks from Celestial Gluon Amplitudes
• Shadows and Soft Exchange in Celestial CFT
• Geometric Soft Theorems
• Celestial Amplitudes as AdS-Witten Diagrams
• State-Operator Correspondence in Celestial Conformal Field Theory
• Elements of Celestial Conformal Field Theory
• Symmetry and Unification from Soft Theorems and Unitarity

Cited by in corpus (12)

• Bridging Carrollian and Celestial Holography
• From Celestial Correlators to AdS, and back
• Deforming Soft Algebras for Gauge Theory
• Revisiting the Shadow Stress Tensor in Celestial CFT
• Symmetries in Celestial CFT${}_d$
• Lorentz Symmetry and IR Structure of The BFSS Matrix Model
• $T\bar{T}$ deformed soft theorem
• $p$-Forms on the Celestial Sphere
• On the Definition of the Spin Charge in Asymptotically-Flat Spacetimes
• Real-time observables in de Sitter thermodynamics
• Loop corrections versus marginal deformation in celestial holography
• Double-soft limit and celestial shadow OPE from charge bracket