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Differential equations are powerful tools in the study of correlation functions in conformal field theories (CFTs). Carrollian amplitudes behave as correlation functions of Carrollian CFT that holographically describes asymptotically flat spacetime. We derive linear differential equations satisfied by Carrollian MHV gluon and graviton amplitudes. We obtain non-distributional solutions for both the gluon and graviton cases. We perform various consistency checks for these differential equations, including compatibility with conformal Carrollian symmetries. 

It is shown that there exists a simple deformed version of Strominger’s infinite-dimensional w(1+infinity) algebra of soft graviton symmetries, which we conjecture to arise in spacetimes with a nonvanishing cosmological constant. The deformed algebra contains a subalgebra generating SO(1,4) or SO(2,3) symmetry groups of dS4 or AdS4, depending on the sign of the cosmological constant. The transformation properties of soft gauge symmetry currents under the deformed w(1+infinity) are also discussed. 

Carrollian holography is supposed to describe gravity in four-dimensional asymptotically flat space-time by the three-dimensional Carrollian CFT living at null infinity. We transform superstring scattering amplitudes into the correlation functions of primary fields of Carrollian CFT depending on the three-dimensional coordinates of the celestial sphere and a retarded time coordinate. The power series in the inverse string tension is converted to a whole tower of both UV and IR finite descendants of the underlying field-theoretical Carrollian amplitude. We focus on four-point amplitudes involving gauge bosons and gravitons in type I open superstring theory and in closed heterotic superstring theory at the tree-level. We also discuss the limit of infinite retarded time coordinates, where the string world-sheet becomes celestial. 

We propose a description of the gluon scattering amplitudes as the inverse Mellin transforms of the conformal correlators of light operators in two-dimensional Liouville theory tensored with WZW-like chiral currents on the celestial sphere. The dimensions of operators are Mellin dual to gluon light cone energies while their positions are determined by the gluon momentum directions. Tree-level approximation in Yang-Mills theory corresponds to the semiclassical limit of Liouville theory. By comparing subleading corrections, we find b^2=(8π^2)^{−1}b_0g^2(M), where b is the Liouville coupling constant, g(M) is the Yang Mills coupling at the renormalization scale M and b_0 is the one-loop coefficient of the Yang-Mills beta function. 

A bstract We discuss supersymmetric Yang-Mills theory coupled to dilatons in the framework of celestial holography. We show that in the presence of point-like dilaton sources, the CCFT operators associated with the gauge supermultiplet acquire a simple, factorized form. They factorize into the holomorphic (super)current part and the exponential “light” operators of Liouville theory, in the infinite central charge limit. The current sector exhibits (1,0) supersymmetry, thus implementing spacetime supersymmetry in CCFT. 

A bstract In celestial holography, four-dimensional scattering amplitudes are considered as two-dimensional conformal correlators of a putative two-dimensional celestial conformal field theory (CCFT). The simplest way of converting momentum space amplitudes into CCFT correlators is by taking their Mellin transforms with respect to light-cone energies. For massless particles, like gluons, however, such a construction leads to three-point and four-point correlators that vanish everywhere except for a measure zero hypersurface of celestial coordinates. This is due to the four-dimensional momentum conservation law that constrains the insertion points of the operators associated with massless particles. These correlators are reminiscent of Coulomb gas correlators that, in the absence of background charges, vanish due to charge conservation. We supply the background momentum by coupling Yang-Mills theory to a background dilaton field, with the (complex) dilaton source localized on the celestial sphere. This picture emerges from the physical interpretation of the solutions of the system of differential equations discovered by Banerjee and Ghosh. We show that the solutions can be written as Mellin transforms of the amplitudes evaluated in such a dilaton background. The resultant three-gluon and four-gluon amplitudes are single-valued functions of celestial coordinates enjoying crossing symmetry and all other properties expected from standard CFT correlators. We use them to extract OPEs and compare them with the OPEs extracted from multi-gluon celestial amplitudes without a dilaton background. We perform the conformal block decomposition of the four-gluon single-valued correlator and determine the dimensions, spin and group representations of the entire primary field spectrum of the Yang-Mills sector of CCFT. 

We introduce VISOR, a new dataset of pixel annotations and a benchmark suite for segmenting hands and active objects in egocentric video. VISOR annotates videos from EPIC-KITCHENS, which comes with a new set of challenges not encountered in current video segmentation datasets. Specifically, we need to ensure both short- and long-term consistency of pixel-level annotations as objects undergo transformative interactions, e.g. an onion is peeled, diced and cooked - where we aim to obtain accurate pixel-level annotations of the peel, onion pieces, chopping board, knife, pan, as well as the acting hands. VISOR introduces an annotation pipeline, AI-powered in parts, for scalability and quality. In total, we publicly release 272K manual semantic masks of 257 object classes, 9.9M interpolated dense masks, 67K hand-object relations, covering 36 hours of 179 untrimmed videos. Along with the annotations, we introduce three challenges in video object segmentation, interaction understanding and long-term reasoning. For data, code and leaderboards: http://epic-kitchens.github.io/VISOR 

A bstract 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.