We study the ring of functions on the (classical and quantized) phase space of 2-dimensional BF theory with the gauge group GLN coupled to 1-dimensional quantum mechanics with global symmetry GLK. These functions are gauge-invariant local observables of the coupled system. We first construct the classical phase space of this system and describe its ring of functions, as well as their large-N limit. We next compute the Hilbert series of these algebras for finite N and in the large-N limit. We then study the quantization of this phase space and the deformation quantization of its ring of functions, elaborate its relation to the Yangian, and construct its coproduct. Finally, we identify these quantized algebras with the quantized Coulomb branch algebras of certain 3d N = 4 quiver gauge theories.
We establish boundedness and polynomial decay results for the Teukolsky system in the exterior spacetime of very slowly rotating and strongly charged sub-extremal Kerr-Newman black holes, with a focus on axially symmetric solutions. The key step in achieving these results is deriving a physical-space Morawetz estimate for the associated generalized Regge-Wheeler system, without relying on spherical harmonic decomposition.
A new notion of quasilocal mass is defined for generic, compact, two dimensional, spacelike surfaces in four dimensional spacetimes with negative cosmological constant. The definition is spinorial and based on work for vanishing cosmological constant by Penrose and Dougan Mason. Furthermore, this mass is non-negative, equal to the Misner-Sharp mass in spherical symmetry, equal to zero for every generic surface in AdS, has an appropriate form for gravity linearised about AdS and has an appropriate limit for large spheres in asymptotically AdS spacetimes.
Using the vertex model approach for braid representations, we compute polynomials for spin-1 placed on hyperbolic knots up to 15 crossings. These polynomials are referred to as 3-colored Jones polynomials or adjoint Jones polynomials. Training a subset of the data using a fully connected feedforward neural network, we predict the volume of the knot complement of hyperbolic knots from the adjoint Jones polynomial or its evaluations with 99.34% accuracy. A function of the adjoint Jones polynomial evaluated at the phase q = e 15 predicts the volume with nearly the same accuracy as the neural network. From an analysis of 2-colored and 3-colored Jones polynomials, we conjecture the best phase for ncolored Jones polynomials, and use this hypothesis to motivate an improved statement of the volume conjecture. This is tested for knots for which closed form expressions for the n-colored Jones polynomial are known, and we show improved convergence to the volume.
