$(2,2)$ Scattering and the Celestial Torus

Abstract

Analytic continuation from Minkowski space to $(2,2)$ split signature spacetime has proven to be a powerful tool for the study of scattering amplitudes. Here we show that, under this continuation, null infinity becomes the product of a null interval with a celestial torus (replacing the celestial sphere) and has only one connected component. Spacelike and timelike infinity are time-periodic quotients of AdS${}_3$. These three components of infinity combine to an $S^3$ represented as a toric fibration over the interval. Privileged scattering states of scalars organize into $SL(2,\mathbb{R}{)}_L\times SL(2,\mathbb{R}{)}_R$ conformal primary wave functions and their descendants with real integral or half-integral conformal weights, giving the normally continuous scattering problem a discrete character.

19 pages, 1 figure

References in corpus (21)

• Perturbative Gauge Theory As A String Theory In Twistor Space
• New Recursion Relations for Tree Amplitudes of Gluons
• AdS3 Black Holes and a Stringy Exclusion Principle
• Quantum Gravity In De Sitter Space
• Flat Space Amplitudes and Conformal Symmetry of the Celestial Sphere
• A Conformal Basis for Flat Space Amplitudes
• On Tree Amplitudes in Gauge Theory and Gravity
• A holographic reduction of Minkowski space-time
• The S-Matrix in Twistor Space
• Conformally Soft Theorem in Gauge Theory
• Celestial amplitudes and conformal soft theorems
• Symmetries of Celestial Amplitudes
• Scattering Amplitudes
• BMS Group at Spatial Infinity: the Hamiltonian (ADM) approach
• Conformally Soft Theorem In Gravity
• Loop amplitudes in gauge theories: modern analytic approaches
• On-Shell Recursion Relations for Generic Theories
• BMS Symmetry of Celestial OPE
• Scattering Amplitudes and BCFW Recursion in Twistor Space
• MHV Gluon Scattering Amplitudes from Celestial Current Algebras
• Notes on Conformal Soft Theorems and Recursion Relations in Gravity

Cited by in corpus (48)

• Holographic Symmetry Algebras for Gauge Theory and Gravity
• Celestial Operator Product Expansions and ${\mathrm{w}}_{1+\infty }$ Symmetry for All Spins
• AdS Witten Diagrams to Carrollian Correlators
• Top-down holography in an asymptotically flat spacetime
• Conformal Block Expansion in Celestial CFT
• Carrollian and celestial spaces at infinity
• Lectures on Celestial Holography
• Celestial operator products from the worldsheet
• Celestial Amplitudes as AdS-Witten Diagrams
• State-Operator Correspondence in Celestial Conformal Field Theory
• Elements of Celestial Conformal Field Theory
• Ambidextrous light transforms for celestial amplitudes
• Celestial $w_{1+\infty }$ Symmetries from Twistor Space
• Three-point energy correlators and the celestial block expansion
• Celestial Dual Superconformal Symmetry, MHV Amplitudes and Differential Equations
• Black Holes in Klein Space
• Subsubleading soft graviton symmetry and MHV graviton scattering amplitudes
• Deforming Soft Algebras for Gauge Theory
• Soft Scalars and the Geometry of the Space of Celestial CFTs
• Null geodesics, causal structure, and matter accretion in Lorentzian-Euclidean black holes
• Four-point correlators of light-ray operators in CCFT
• Celestial Locality and the Jacobi Identity
• Celestial Leaf Amplitudes
• (Chiral) Virasoro invariance of the tree-level MHV graviton scattering amplitudes
• Celestial amplitudes in an ambidextrous basis
• Celestial Geometry
• Supersymmetric celestial OPEs and soft algebras from the ambitwistor string worldsheet
• Correlators of Four Light-Ray Operators in CCFT
• Chaos in Celestial CFT
• All-order celestial OPE from on-shell recursion
• w(1+infinity) and the Celestial Sphere
• Spectral representation in Klein space: simplifying celestial leaf amplitudes
• Celestial Klein Spaces
• Celestial IR divergences and the effective action of supertranslation modes
• Currents in Celestial CFT
• $\widehat{s{l}_2}$ symmetry of ${\mathbb{R}}^{1,3}$ gravity
• Celestial OPE blocks
• Celestial Quantum Error Correction II: From Qudits to Celestial CFT
• Notes on self-dual gravity
• Entanglement Rényi entropies in celestial holography
• Celestial Eikonal Amplitudes in the Near-Horizon Region
• Diamonds in Klein geometry
• Celestial Holography
• Celestial Quantum Error Correction I: Qubits from Noncommutative Klein Space
• Quantum field theory in flat spacetime with multiple time directions
• Modular Flow of Celestial Conformal Field Theory
• NS-NS Spacetimes from Amplitudes
• Celestial Feynman Rules for Scalars