Noncommutative (A)dS and Minkowski spacetimes from quantum Lorentz subgroups

The complete classification of classical r-matrices generating quantum deformations of the (3+1)-dimensional (A)dS and Poincar ́e groups such that their Lorentz sector is a quantum sub-group is presented. It is found that there exists three classes of such r-matrices, one of them being a novel two-parametric one. The (A)dS and Minkowskian Poisson homogeneous spaces corresponding to these three deformations are explicitly constructed in both local and ambient coordinates. Their quantization is performed, thus giving rise to the associated noncommutative spacetimes, that in the Minkowski case are naturally expressed in terms of quantum null-plane coordinates, and they are always defined by homogeneous quadratic algebras. Finally, non-relativistic and ultra-relativistic limits giving rise to novel Newtonian and Carrollian noncommutative spacetimes are also presented.

The light-ray OPE and conformal colliders

We derive a nonperturbative, convergent operator product expansion (OPE) for null-integrated operators on the same null plane in a CFT. The objects appearing in the expansion are light-ray operators, whose matrix elements can be computed by the generalized Lorentzian inversion formula. For example, a product of average null energy (ANEC) operators has an expansion in the light-ray operators that appear in the stress-tensor OPE. An important application is to collider event shapes. The light-ray OPE gives a nonperturbative expansion for event shapes in special functions that we call celestial blocks. As an example, we apply the celestial block expansion to energy-energy correlators in $$ \mathcal{N} $$ N = 4 Super Yang-Mills theory. Using known OPE data, we find perfect agreement with previous results both at weak and strong coupling, and make new predictions at weak coupling through 4 loops (NNNLO).

Endpoint contributions to excited-state modular Hamiltonians

We compute modular Hamiltonians for excited states obtained by perturbing the vacuum with a unitary operator. We use operator methods and work to first order in the strength of the perturbation. For the most part we divide space in half and focus on perturbations generated by integrating a local operator J over a null plane. Local operators with weight n ≥ 2 under vacuum modular flow produce an additional endpoint contribution to the modular Hamiltonian. Intuitively this is because operators with weight n ≥ 2 can move degrees of freedom from a region to its complement. The endpoint contribution is an integral of J over a null plane. We show this in detail for stress tensor perturbations in two dimensions, where the result can be verified by a conformal transformation, and for scalar perturbations in a CFT. This lets us conjecture a general form for the endpoint contribution that applies to any field theory divided into half-spaces.

Differences in the Head Roll Test, Bow and Lean Test, and Null Plane between Persistent and Transient Geotropic Direction-Changing Positional Nystagmus

Background: Persistent geotropic direction-changing positional nystagmus (DCPN) has the characteristics of cupulopathy, but its underlying pathogenesis is not known. We investigated the relationship of the results of the head roll test, bow and lean test, and side of the null plane between persistent and transient geotropic DCPN to determine the lesion side of persistent geotropic DCPN and understand its mechanism. Methods: We enrolled 25 patients with persistent geotropic DCPN and 41 with transient geotropic DCPN. We compared the results of the head roll test, bow and lean test, and side of the null plane between the two groups. Results: The rates of bowing and leaning nystagmus were significantly higher in the persistent DCPN group. Only 16.0% of the persistent DCPN patients had stronger nystagmus in the head roll test and the null plane on the same side. The rates of the direction of bowing nystagmus in the bow and lean test and stronger nystagmus in the head roll test on the same side were also significantly lower in persistent DCPN than in transient DCPN. Conclusion: It was difficult to determine the lesion side in persistent geotropic DCPN using the direction of stronger nystagmus in the head roll test and null plane when the direction of the stronger nystagmus and null plane were opposite. Further study is needed to understand the position of the cupula according to head rotation and the anatomical position in persistent geotropic DCPN.