Celestial diamonds encode the structure of global conformal multiplets in 2D celestial CFT and offer a natural language for describing the conformally soft sector. The operators appearing at their left and right corners give rise to conformally soft factorization theorems, the bottom corners correspond to conserved charges, and the top corners to conformal dressings. We show that conformally soft charges can be expressed in terms of light ray integrals that select modes of the appropriate conformal weights. They reside at the bottom corners of memory diamonds, and ascend to generalized currents. We then identify the top corners of the associated Goldstone diamonds with conformal Faddeev-Kulish dressings and compute the sub-leading conformally soft dressings in gauge theory and gravity which are important for finding nontrivial central extensions. Finally, we combine these ingredients to speculate on 2D effective descriptions for the conformally soft sector of celestial CFT.

/pdf/revisiting-the-conformally-soft-sector-with-celestial-1k06qhh3g1.pdf

Revisiting the Conformally Soft Sector with Celestial Diamonds

A bstract The operator product expansion of massless celestial primary operators of arbitrary spin is investigated. Poincaré symmetry is found to imply a set of recursion relations on the operator product expansion coefficients of the leading singular terms at tree-level in a holomorphic limit. The symmetry constraints are solved by an Euler beta function with arguments that depend simply on the right-moving conformal weights of the operators in the product. These symmetry-derived coefficients are shown not only to match precisely those arising from momentum-space tree-level collinear limits, but also to obey an infinite number of additional symmetry transformations that respect the algebra of w 1+ ∞ . In tree-level minimally-coupled gravitational theories, celestial currents are constructed from light transforms of conformally soft gravitons and found to generate the action of w 1+∞ on arbitrary massless celestial primaries. Results include operator product expansion coefficients for fermions as well as those arising from higher-derivative non-minimal couplings of gluons and gravitons. 

/pdf/celestial-operator-product-expansions-and-w1-symmetry-for-5dkmj8o6.pdf

Celestial operator product expansions and w1+∞ symmetry for all spins

The soft limits of scattering amplitudes have been extensively studied due to their essential role in the computation of physical observables in collider physics. The universal factorisation that occurs in these kinematic limits has been shown to be related to conservation laws associated with asymptotic, or large, gauge symmetries. This connection has led to a deeper understanding of the symmetries of gauge and gravitational theories and to a reformulation of scattering amplitudes in a basis of boost eigenstates which makes manifest the two-dimensional global conformal symmetry of the celestial sphere. The recast, or celestial, amplitudes possess many of the properties of conformal field theory (CFT) correlation functions which has suggested a path towards a holographic description of asymptotically flat spacetimes. In this review we consider these interconnected developments in our understanding of soft theorems, asymptotic symmetries and CFT with a focus on the structure and symmetries of the celestial amplitudes and their holographic interpretation.

https://iopscience.iop.org/article/10.1088/1751-8121/ac9a40/pdf

The SAGEX review on scattering amplitudes Chapter 11: Soft Theorems and Celestial Amplitudes

In a recent paper, here referred to as part I, we considered the celestial four-gluon amplitude with one gluon represented by the shadow transform of the corresponding primary field operator. This correlator is ill-defined because it contains branch points related to the presence of conformal blocks with complex spin. In this work, we adopt a procedure similar to minimal models and construct a single-valued completion of the shadow correlator, in the limit when the shadow is “soft.” By following the approach of Dotsenko and Fateev, we obtain an integral representation of such a single-valued correlator. This allows inverting the shadow transform and constructing a single-valued celestial four-gluon amplitude. This amplitude is drastically different from the original Mellin amplitude. It is defined over the entire complex plane and has correct crossing symmetry, OPE and bootstrap properties. It agrees with all known OPEs of celestial gluon operators. The conformal block spectrum consists of primary fields with dimensions ∆ = m + iλ, with integer m ≥ 1 and various, but always integer spin, in all group representations contained in the product of two adjoint representations.

/pdf/conformal-blocks-from-celestial-gluon-amplitudes-part-ii-2qey37k8ud.pdf

Conformal blocks from celestial gluon amplitudes. Part II. Single-valued correlators

Goldilocks modes and the three scattering bases

The bulk-to-boundary dictionary for 4D celestial holography is given a new entry defining 2D boundary states living on oriented circles on the celestial sphere. The states are constructed using the 2D CFT state-operator correspondence from operator insertions corresponding to either incoming or outgoing particles which cross the celestial sphere inside the circle. The BPZ construction is applied to give an inner product on such states whose associated bulk adjoints are shown to involve a shadow transform. Scattering amplitudes are then given by BPZ inner products between states living on the same circle but with opposite orientations. 2D boundary states are found to encode the same information as their 4D bulk counterparts, but organized in a radically different manner.

/pdf/state-operator-correspondence-in-celestial-conformal-field-e3wbsi9y1y.pdf

State-operator correspondence in celestial conformal field theory

/pdf/state-operator-correspondence-in-celestial-conformal-field-mzqoaolem8.pdf

Erin Crawley

Papers

State-operator correspondence in celestial conformal field theory

State-Operator Correspondence in Celestial Conformal Field Theory