A bstract Galilean Conformal Algebra (GCA) arises as a controlled nonrelativistic limit of the relativistic conformal algebra. In this paper, we initiate the study of momentum space correlation functions in two-dimensional GCA. We derive and solve momentum space Ward identities to obtain two-point and three-point functions. However, relating them to position space correlation functions presents a challenge as Fourier transforms of the latter do not exist. This is resolved by analytically continuing the boost eigenvalues to imaginary values. In this regime, the Fourier transform of the position space two-point and three-point functions exist and match exactly with the momentum space two-point and three-point function obtained by solving the Ward identities.

Blow-up solutions for asymmetric sinh-Poisson equations on Riemann surfaces with boundary

For M\subset \mathbb{R}^{d\geq 3} a smooth, connected, compact d -dimensional submanifold with boundary, equipped with the standard metric, the Laplacian on \partial M is known to commute with the corresponding Dirichlet-to-Neumann map if and only if M is a ball. In this paper, we investigate the d=2 case and show that, surprisingly, there exists a one-parameter family of submanifolds of \mathbb{R}^{2} as above for which the boundary Laplacian and the Dirichlet-to-Neumann map commute, thus answering an open problem posed by Girouard, Karpukhin, Levitin, and Polterovich. We then classify all such Riemannian surfaces of genus 0 or whose boundary has k\geq 3 connected components.

We review the conservation laws of magnetohydrodynamics (MHD) in an expanding homogeneous and isotropic Universe that can be applied to the study of early Universe physics during the epoch of radiation domination. The conservation laws for a conducting perfect fluid with relativistic bulk velocities in an expanding background are presented (for the first time in their non-conservation form, i.e., as dynamical equations for the velocity and energy density fluid variables), extending previous results that apply in the limit of subrelativistic bulk motion. Furthermore, it is shown that the subrelativistic limit presents new corrections that have not been considered in previous work. We discuss the conformal invariance of the MHD equations for a radiation-dominated fluid and different types of scaling of the fluid variables that are relevant for other equations of state when the bulk velocity is subrelativistic. In particular, we review the super-comoving coordinates that have been proposed for matter-dominated fluids and present this choice of coordinates for any constant equation of state. First-order fluid dynamics to include imperfect relativistic fluids and the scaling of the transport coefficients with temperature in the early Universe are presented. We review the propagation of sound waves, Alfvén waves, and magnetosonic waves in the early Universe plasma. The Boris correction for relativistic Alfvén speeds is presented and adapted for early Universe applications. This review is an extension, including new results, of part of the lectures presented at the minicourse “Simulations of Early Universe Magnetohydrodynamics” lectured by A. Roper Pol and J. Schober at EPFL, as part of the six-week program “Generation, evolution, and observations of cosmological magnetic fields” at the Bernoulli Center in May 2024.

Topological singular lines in three-dimensional parameter space-nodal lines and exceptional lines-are fundamental to wave physics and hold promise for advanced photonic control. However, their observation, especially in the optical regime, has been hindered by the challenge of constructing the required parameter space without complex structural engineering. Here, we demonstrate that the scattering matrix of a simple two-dimensional photonic crystal provides such a parameter space through frequency and in-plane momenta, enabling the first observation of chiral exceptional lines in the visible regime. Using high-precision momentum-space Mueller matrix spectroscopy, we map these lines and reveal their key topological features, including self-intersecting Riemann surfaces, phase vortices, and polarization half-vortices, with distinct responses to left- and right-handed circular polarizations. The exceptional lines exhibit characteristic square-root eigenvalue splitting and extend continuously across the frequency-momentum space, demonstrating their topological robustness. This achievement establishes a robust platform for investigating non-Hermitian topological physics at visible frequencies, opening pathways for chiral light-matter interactions, polarization-selective devices, and advanced sensing applications.

A bstract We discuss the marginal $$ \sqrt{T\overline{T}} $$ T T ¯ deformation of massless scalar field theories in two dimensions from a dynamical perspective. The operator flow equations for such deformations induce a particular Legendre Transformation between flowed Lagrangians and flowed Hamiltonians. The marginal deformation does not change the conformal symmetries of the theory, until some special points in the moduli space are reached, and the relativistic conformal algebra smoothly changes to the Carrollian conformal (equivalently BMS) one. We investigate this change of symmetry from both configuration space and phase space point of view, while keeping the notion of Legendre Transformation unchanged during the flow. By expanding the actions, in the extreme limits of the flow parameter, we recover the usual “Electric” Carroll theory and further uncover a novel “Magnetic” counterpart. We discuss the intriguing geometric understanding of such dynamical maps for the deformed theories, and also provide a concrete example for the same from a deformed string theory in flat space.

Abstract This paper investigates traversable wormhole solutions within the framework of f (Q, T ) gravity by incorporating conformal symmetry and employing a Lorentzian distribution to model the matter sources. The study considers different equations of state, such as traceless and barotropic forms, to explore their impact on the viability of wormhole solutions. A comprehensive analysis of the effects of the model parameters on the wormhole geometry and its physical properties is carried out. The findings reveal that the resulting shape function satisfies all the necessary wormhole conditions. Importantly, certain scenarios are identified where the wormhole can be supported by non-exotic matter, highlighting the physical plausibility of such solutions within modified gravity.

A third-order operator with periodic coefficients is an L-operator in the Lax pair for the Boussinesq equation on a circle. The projection of the divisor of the Floquet solution poles for this operator coincides with the spectrum of the three-point Dirichlet problem. The sign of the norming constant of the three-point problem determines the sheet of the Riemann surface on which the pole lies. We solve the inverse problem for a third-order operator with three-point Dirichlet conditions when the spectrum and norming constant are known. We construct a mapping from the set of coefficients to the set of spectral data and prove that this mapping is an analytic bijection in the neighborhood of zero.

Several morphological parameters such as aortic neck length, angulation, or centerline curvature have previously been evaluated to define "hostile" anatomies that predispose to poor outcomes after endovascular aneurysm repair. In this study, we present a new method for classifying aneurysm morphologies using their conformal structures. The conformal structure of a surface is determined by its Riemannian metric, and conformal mappings between surfaces with complex topologies preserve their conformal structures. To classify aneurysm shapes, the aortic aneurysm is first segmented from CT scans and represented as a discrete surface. Next, holomorphic differential forms are computed based on the discrete Hodge Theory. The aneurysm surface can be conformally mapped onto a pair of planar rectangles with an aortic bifurcation point by integrating a special holomorphic differential. This canonical configuration gives the conformal invariants, or "conformal fingerprints," which can then be used to classify aneurysm morphologies. This novel methodology shows promise in providing an improved understanding of aneurysm morphologies, which can aid in better predicting and managing potential complications after endovascular aneurysm repair.

Riemannian surfaces with horizontal twistor lifts in pseudohyperbolic spaces

Abstract In this study, we develop the inverse scattering transform of the focusing Lakshmanan-Porsezian-Daniel equation with a one-sided nonzero boundary condition, where the asymptotic amplitude tends to zero on one side at spatial infinity while remaining nonzero on the other. For the direct scattering problem, single-valued eigenfunctions are rigorously defined, and their analyticity, symmetries, and asymptotic behavior are rigorously analyzed. Furthermore, the Marchenko integral equations and the Riemann-Hilbert problems (both right and left) on a single sheet of scattering variable are constructed and utilized to formulate the inverse problem. Additionally, a proper uniformization variable is defined to formulate both the direct and inverse scattering problems, which maps the two-sheeted Riemann surface of the spectral parameter onto a single complex plane. Ultimately, the time evolutions of the eigenfunctions are derived, revealing the nontrivial time dependence of the scattering data.

Abstract Non-spherical wrist manipulators are widely used in industrial settings, yet they lack effective inverse kinematics solutions. Current methods primarily rely on numerical iteration, which suffers from limitations such as sensitivity to initial values and convergence issues. Meanwhile, algebraic elimination methods require complex elimination techniques to obtain analytical solutions, restricting their practical engineering application. To address the limitations of these existing approaches, this paper innovatively proposes a novel analytical method based on conformal geometric algebra theory. The core of this method lies in utilizing the geometric characteristics of the manipulator to establish a polynomial equation for one of the joint variables, after which the remaining joint angles are solved according to the joint angle solution methodology. The correctness of the proposed method was verified using three sets of joint angles. Additionally, a comparative analysis with the Dixon elimination method was conducted using 100 sets of arbitrary initial joint angles. Example validation demonstrates that the proposed method exhibits significant advantages in computation time, solution completeness, and numerical accuracy, thereby providing a new theoretical tool and practical framework for the inverse kinematics analysis of robotic manipulators.

In previous work, all finite simple groups that act with fixity 4 have been classified. In this article we investigate which ones of these groups act faithfully on a compact Riemann surface of genus at least 2 with fixity four in total and in such a way that fixity 4 is exhibited on at least one orbit.

A bstract The dilaton, a pseudo-Nambu-Goldstone boson (pNGB) of broken scale invariance, is an appealing ultralight dark matter (DM) candidate. Its mass is protected by conformal invariance and it can be searched for in tabletop experiments. However, contrary to standard pNGBs of internal symmetries, the dilaton generically has a large non-derivative self-coupling, leading to radiative contributions to its mass of the order of its decay constant. Hence typical ultralight dilatons should also have sub-eV decay constants, which would incur significant deviations from standard DM behavior at structure formation times, in severe tension with observations. Therefore, a fine-tuning is required to generate a hierarchy between the mass and the decay constant. In this work, we consider whether supersymmetry (SUSY) can be used to protect this hierarchy from quantum corrections. To ensure an ultralight dilaton mass robust against realistic SUSY-breaking contributions, we must consider a novel dilaton stabilization mechanism. The observed DM abundance can be produced by the misalignment mechanism for dilaton masses ranging from 10 −11 to 1 eV. Unfortunately, irreducible SUSY-breaking corrections due to gravity restrict the couplings between the dilaton and the Standard Model to be extremely small, beyond the reach of any current or proposed experiments. Our work demonstrates that constructing a consistent model of ultralight dilaton DM is quite involved.

A bstract (1+1)d QFTs provide a tractable arena for understanding the emergence of hydrodynamics in thermal states. At high temperatures this process is governed by the weak breaking of conformal symmetry, and so in this limit many features of the hydrodynamic theory that emerges have been argued to be universal. In this paper we study aspects of the stress tensor thermal two-point function in holographic QFTs of this kind and show that they are consistent with the universal hydrodynamic theory proposed to apply at late times. Specifically, we identify the locations of the ‘pole skipping’ points in momentum space at which there is an intersection of poles and zeroes of this two-point function in holographic QFTs. Although these points lie outside the regime where the hydrodynamic theory is controlled, we show that their locations are consistent with those found by resumming the hydrodynamic derivative expansion near the lightcone. For example, this resummation of the universal hydrodynamics correctly predicts the butterfly velocity of holographic theories.

A bstract Previous investigations of the three-body dynamics of B mesons have shown that no Efimov effect arises in systems composed of three B and B * mesons. This implies that the properties of such three-body systems can be described reliably within nonrelativistic effective field theory (NREFT) with short-range interactions using only two-body input, as three-body forces are strongly suppressed. In this work, we present leading-order predictions for the three-body point production rates of systems consisting of three B and B * mesons. These predictions provide a novel way to experimentally probe the $$ {B}^{\left(\ast \right)}-{\overline{B}}^{\left(\ast \right)} $$ B ∗ − B ¯ ∗ interactions, which play a crucial role in the hadronic-molecule interpretation of the $$ {T}_{b\overline{b}1}(10610) $$ T b b ¯ 1 10610 and $$ {T}_{b\overline{b}1}(10650) $$ T b b ¯ 1 10650 states. Moreover, they provide a way to test the approximate conformal symmetry predicted for such systems at low energies experimentally.

Classification of uniformly bounded simple Lie conformal algebras with upper bound one

On Galois theory of cluster algebras: general and that from Riemann surfaces

Blow-up solutions for general Toda systems on Riemann surfaces

We unify and advance a host of works on iterated function systems of holomorphic self-maps of hyperbolic Riemann surfaces. Our foremost result is a generalisation to left iterated function systems of an unpublished and little known theorem of Heins on iteration in the unit disc. Applications abound -- to work of Benini et al. on transcendental dynamics, to the theory of hyperbolic steps of holomorphic maps, and to left semiconjugacy in the unit disc. We extend other work of Benini et al. and Ferreira on relatively compact left iterated function systems, and we prove a hyperbolic distance inequality for holomorphic maps that generalises a theorem of Bracci, Kraus, and Roth. Additionally, we strengthen results of the first author and Christodoulou on left iterated function systems, removing the need for Bloch domains, and we answer an open question from their work. Finally, we establish a version of the Heins theorem for right iterated functions systems, and we generalise theorems of Beardon and Kuznetsov on right iterated function systems in relatively compact semigroups of holomorphic maps.