We propose a three-dimensional field theory construction that realizes the vertex algebras associated with the intermediate Lie algebras and the related C2 -cofinite minimal W-algebras of the Deligne-Cvitanovi? (DC) series as boundary algebras. The construction is based on the minimal three-dimensional N=4 superconformal field theory coupled to a topological field theory. For a Neumann-type boundary condition compatible with the topological A-twist, the algebra of boundary local operators realizes the minimal W-algebra W-h boolean OR/6(g,fmin) . While this boundary condition is not deformable to the B-twist, we argue that a holomorphic-topological ( HTB ) twist instead realizes the level-one affine algebras of the intermediate Lie algebras, providing a uniform three-dimensional origin for these vertex algebra structures.
The double-scaling limit of the SYK (DSSYK) model is known to possess an underlying Uq(su(1,1)) quantum group symmetry. In this paper, we provide, for the first time, a von Neumann algebraic quantum group-theoretical description of the degrees of freedom and the dynamics of the DSSYK model. In particular, we construct the operator-algebraic quantum Gauss decomposition for the von Neumann algebraic quantum group SUq(1,1)& rtimes;Z2 , i.e. the q-deformation of the normaliser of SU(1,1) in SL(2,C) , and derive the Casimir action on its quantum homogeneous spaces. We then show that the dynamics on quantum AdS2,q space reduces to that of the DSSYK model. Furthermore, we argue that the extension of the global symmetry group to its normaliser is not only necessary for a consistent definition of the locally compact quantum group, but that, moreover, the reduction to the DSSYK model works exclusively at the level of the normaliser. The von Neumann algebraic description is shown to give a natural restriction on the allowed quantised coordinates, elegantly ensuring length positivity and non-negative integer chord numbers. Lastly, we make remarks on the correlation function related to the strange series representation, which is argued to interpolate between the AdS and dS regions of our q-homogeneous space.
In this paper, we establish existence for a class of semi-linear hyperbolic equations in 3+1 dimensions that satisfy the bounded weak null condition. We propose a conformal compactification of the future directed null-cone on Minkowski spacetime, which enables us to establish the existence of solutions to the wave equation in a neighbourhood of future null infinity. For fixed ρ _0>0 , the corresponding physical solution is constructed in a neighbourhood of future null infinity restricted to a slab of retarded time. Using this framework, we formulate a conformal symmetric hyperbolic Fuchsian system of equations. The existence of solutions to this Fuchsian system follows from an application of the existence theory developed in [1], and [2].
Based on the Decay and Fission Conjecture, we provide a classification of unitary quivers whose 3d N=4 Coulomb branches exhibit isolated singularities. This yields the complete list of isolated conical symplectic singularities that can arise in this way. In the process, we identify three new families of stable quivers: two giving rise to previously unknown isolated symplectic singularities, and one offering a novel realization of a known family.
This paper introduces a new scattering theory with asymptotic completeness for the Boltzmann equation in the L^∞ setting close to the vacuum. We investigate the long-time behavior of solutions to the Boltzmann equation using a new estimate for the Maxwellian distribution.
