Spectral representation in Klein space: simplifying celestial leaf amplitudes

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.

arXiv comment43 pages, 3 figures, typos and minor errors corrected, matches journal version to appear in JHEP

References in corpus (28)

• Large N Field Theories, String Theory and Gravity
• Direct Proof Of Tree-Level Recursion Relation In Yang-Mills Theory
• On BMS Invariance of Gravitational Scattering
• MHV Vertices And Tree Amplitudes In Gauge Theory
• Writing CFT correlation functions as AdS scattering amplitudes
• Semiclassical Virasoro Symmetry of the Quantum Gravity S-Matrix
• Flat Space Amplitudes and Conformal Symmetry of the Celestial Sphere
• Asymptotic Symmetries of Yang-Mills Theory
• A Conformal Basis for Flat Space Amplitudes
• On Tree Amplitudes in Gauge Theory and Gravity
• A holographic reduction of Minkowski space-time
• Spinning AdS Propagators
• Gluon Amplitudes as 2d Conformal Correlators
• Celestial holography meets twisted holography: 4d amplitudes from chiral correlators
• Conformal Basis, Optical Theorem, and the Bulk Point Singularity
• $(2,2)$ Scattering and the Celestial Torus
• Top-down holography in an asymptotically flat spacetime
• Unitarity Methods in AdS/CFT
• Celestial Amplitudes as AdS-Witten Diagrams
• Elements of Celestial Conformal Field Theory
• Celestial holography on Kerr-Schild backgrounds
• The Celestial Chiral Algebra of Self-Dual Gravity on Eguchi-Hanson Space
• Celestial Liouville Theory for Yang-Mills Amplitudes
• Physics of the Analytic S-Matrix
• Deforming Soft Algebras for Gauge Theory
• Six-Point Conformal Blocks in the Snowflake Channel
• Bulk locality from the celestial amplitude
• Celestial Leaf Amplitudes

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