Extends celestial RSVW formalism to minitwistor superspace to build tree-level N^k-MHV leaf amplitudes in planar N=4 SYM and gives dynamical realizations via Wilson operators on algebraic cycles and a minitwistor sigma model.
Spectral representation in Klein space: simplifying celestial leaf amplitudes
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abstract
In this paper, we explore the spectral representation in Klein space, which is the split $(2,2)$ signature flat spacetime. The Klein space can be foliated into Lorentzian $\mathrm{AdS}_3 /\mathbb{Z}$ slices, and its identity resolution has continuous and discrete parts. We calculate the identity resolution and the Plancherel measure in these slices. Using the foliation of Klein space into the slices, the identity resolution, and the Plancherel measure in each slice, we compute the spectral representation of the massive bulk-to-bulk propagator in Klein space. It can be expressed as the sum of the product of two massive (or tachyonic) conformal primary wavefunctions, with both continuous and discrete parts, and sharing a common boundary coordinate. An interesting point in Klein space is that, since the identity resolution has discrete and continuous parts, a new type of conformal primary wavefunction naturally arises for the massive (or tachyonic) case. For the conformal primary wavefunctions, both the discrete and continuous parts involve integrating over the common boundary coordinate and the real (or imaginary) mass. The conformal dimension is summed in the discrete part, whereas it is integrated in the continuous part. The spectral representation in Klein space is a computational tool to derive conformal block expansions for celestial amplitudes in Klein space and its building blocks, called celestial leaf amplitudes, by integrating the particle interaction vertex over a single slice of foliation.
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Authors construct canonical and path-integral quantizations for QFT in Klein space using extra modes, deriving correlation functions that match Minkowski space via analytical continuation.
A uniformly moving charge's field is a static Coulomb field in geodesic-centered coordinates, and in AdS the same construction yields a closed-form field with exact antipodal covariance whose null-fringe limits give flat-space antipodal matching.
citing papers explorer
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A Celestial Description of Planar Super-Yang-Mills Theory
Extends celestial RSVW formalism to minitwistor superspace to build tree-level N^k-MHV leaf amplitudes in planar N=4 SYM and gives dynamical realizations via Wilson operators on algebraic cycles and a minitwistor sigma model.
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QFT in Klein space
Authors construct canonical and path-integral quantizations for QFT in Klein space using extra modes, deriving correlation functions that match Minkowski space via analytical continuation.
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Li\'enard--Wiechert fields in AdS and flat-space antipodal matching from geodesic-centered Coulombic data
A uniformly moving charge's field is a static Coulomb field in geodesic-centered coordinates, and in AdS the same construction yields a closed-form field with exact antipodal covariance whose null-fringe limits give flat-space antipodal matching.
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