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Asymptotic Symmetries and Detectors: Part 2
Examines recent breakthroughs in celestial holography and light-ray operators to test the universality of W-infinity and S-algebra symmetries beyond tree-level soft theorems.
Lecture guide · Written by AI from the lecture. For the lecture’s own words, open the Transcript tab.
Presents recent results on the universality and algebraic structure of asymptotic and celestial symmetries, specifically examining S-algebras and W-infinity symmetries from the perspective of light-ray operators in conformal field theories. The speaker discusses different derivations, contrasting ambient 4D CFT approaches, linearized gauge field equations, and light-sheet commutators to understand how these symmetries constrain scattering amplitudes and correlation functions.
This lecture assumes
- Asymptotic Symmetriestaught in Asymptotic Symmetries and Detectors: Part 1 at 0:20
- Celestial Holographytaught in de Sitter Quantum Cosmology: Part 1 at 46:50 and 2 more
- Soft Theoremstaught in Asymptotic Symmetries and Detectors: Part 1 at 0:53
Key Takeaways
- Leading soft theorems are tied to asymptotic symmetries like BMS and Kac-Moody symmetries through specific boundary conditions and charge conservation.
- Higher-order soft theorems can be systematically organized into towers of soft modes, which form algebraic structures such as the S-algebra and W-infinity symmetry.
- Light-ray operators defined on a null sheet in a CFT provide an alternative framework to study these symmetries via stress tensor commutators and operator product expansions.
- Unitarity and specific spectrum conditions, such as twist gaps or the absence of light neutral scalars, constrain the right-hand side of stress tensor commutators on a light sheet.
Concepts Explained9
Antipodal matching—The identification of fields or data at opposite points on the celestial sphere, linking past and future null infinity.
Celestial OPE—The operator product expansion of celestial operators living on the celestial sphere, which encodes bulk scattering information.
Kazmouti Symmetry—A symmetry of the celestial OPEs arising from the subleading soft theorems.
Linearized equations of motion for gauge fields in AdS—Equations describing the behavior of linearized gauge field components and their derivatives under special conformal generators.
Examples, Proofs & Derivations
Works & Sources Cited13
Paper
1810.05706—Cordoba and Shou, cited for light-ray operators and BMS algebra in CFTs.
Paper
2105.14346—Strominger, cited for celestial symmetry results.
Paper
2512.15973—Himwich and Pate, cited for celestial holography results.
Paper
2601.00096—Sharma, Strominger, Tripathi, and Wid, cited for recent results on W infinity and soft theorems.
Paper
2603.26459—Strominger and Mei, cited for bulk CFT light-sheet and operator analyses.