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Results for “Associative Rings and Algebras”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Local Poincaré algebra from quantum chaos

The local two-dimensional Poincaré algebra near the horizon of an eternal AdS black hole, or in proximity to any bifurcate Killing horizon, is generated by the Killing flow and outward null translations on the horizon. In holography, this local Poincaré algebra is reflected as a pair of unitary flows in the boundary Hilbert space whose generators under modular flow grow and decay exponentially with a maximal Lyapunov exponent. This is a universal feature of many geometric vacua of quantum gravity. To explain this universality, we show that a two-dimensional Poincaré algebra emerges in any quantum system that has von Neumann subalgebras associated with half-infinite modular time intervals (modular future and past subalgebras) in a limit analogous to the near-horizon limit. In ergodic theory, quantum dynamical systems with future or past algebras are called quantum K-systems. The surprising statement is that modular K-systems are always maximally chaotic. Interacting quantum systems in the thermodynamic limit and large N theories above the Hawking-Page phase transition are examples of physical theories with future/past subalgebras. We prove that the existence of (modular) future/past von Neumann subalgebras also implies a second law of (modular) thermodynamics and the exponential decay of (modular) correlators. We generalize our results from the modular flow to any dynamical flow with a positive generator and interpret the positivity condition as quantum detailed balance.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Generalized symmetries of the graviton

We find the set of generalized symmetries associated with the free graviton theory in four dimensions. These are generated by gauge invariant topological operators that violate Haag duality in ring-like regions. As expected from general QFT grounds, we find a set of “electric” and a dual set of “magnetic” topological operators and compute their algebra. To do so, we describe the theory using phase space gauge-invariant electric and magnetic dual variables constructed out of the curvature tensor. Electric and magnetic fields satisfy a set of constraints equivalent to the ones of a stress tensor of a 3d CFT. The constraints give place to a group $\mathbb{R}^{20}$ of topological operators that are charged under space-time symmetries. Finally, we discuss similarities and differences between linearized gravity and tensor gauge theories that have been introduced recently in the context of fractonic systems in condensed matter physics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Commuting Line Defects At $q^N$ = 1

Here, we explain the physical origin of a curious property of algebras $\mathcal{A}_{\mathfrak{q}}$ which encode the rotation-equivariant fusion ring of half-BPS line defects in four-dimensional $\mathcal{N}$ = 2 supersymmetric quantum field theories. These algebras are a quantization of the algebras of holomorphic functions on the three-dimensional Coulomb branch of the SQFTs, with deformation parameter log $\mathfrak{q}$. They are known to acquire a large center, canonically isomorphic to the undeformed algebra, whenever $\mathfrak{q}$ is a root of unity. We give a physical explanation of this fact. We also generalize the construction to characterize the action of this center in the $\mathcal{A}_{\mathfrak{q}}$-modules associated to three-dimensional $\mathcal{N}$ = 2 boundary conditions. Finally, we use dualities to relate this construction to a construction in the Kapustin–Witten twist of four-dimensional $\mathcal{N}$ = 4 gauge theory. These considerations give simple physical explanations of certain properties of quantized skein algebras and cluster varieties, and quantum groups, when the deformation parameter is a root of unity.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Soft algebras for leaf amplitudes

Celestial MHV amplitudes are comprised of non-distributional leaf amplitudes associated to an AdS3 leaf of a foliation of flat spacetime. It is shown here that the leaf amplitudes are governed by the same infinite-dimensional soft ‘S-algebra’ as their celestial counterparts. Moreover, taking the soft limit of the smooth three-point MHV leaf amplitude yields a nondegenerate minus-minus two-point leaf amplitude. The two- and three-point MHV leaf amplitudes are used to compute the plus-minus-minus leaf operator product coefficients.

79 ASTRONOMY AND ASTROPHYSICS↗