Study of higher spin Killing spinors on 3D manifolds, proving rigidity and providing explicit expressions.
problem Understanding higher spin Killing spinors on 3D manifolds.
method Definition and detailed study of higher spin Killing spinors in arbitrary dimension, focusing on 3D manifolds. Rigidity result and explicit expressions for 3-sphere and 3-hyperbolic space.
result Proved a rigidity result for 3D manifolds admitting higher spin Killing spinors and provided explicit expressions for these spinors.
The paper extends higher-order operators in higher spin spaces.
problem Generalizing higher-order operators in higher spin spaces.
method Constructing 3rd order fermionic and 4th order bosonic operators in higher spin spaces.
result Fundamental solutions and intertwining operators of 3rd order fermionic and 4th order bosonic operators are presented.
The paper classifies higher order fermionic and bosonic operators in spin spaces.
problem Understanding higher order conformally invariant differential operators.
method Using higher spin theory in Clifford analysis, constructing operators as generalizations of the Euclidean Dirac operator.
result These operators act on functions in homogeneous harmonic or monogenic polynomial spaces, and are classified as fermionic or bosonic based on spin.
Study of higher spin bundles on Klein surfaces, linking to singularity theory.
problem Understanding the structure of spaces of higher spin bundles on Klein surfaces.
method Analysis of topological invariants and quotient spaces of Euclidean spaces.
result Connected components of the space of higher spin bundles are homeomorphic to quotients of Euclidean spaces.
The paper constructs arbitrary order conformally invariant operators in higher spin spaces.
problem Classifying and constructing conformally invariant differential operators in higher spin spaces.
method Explicit expressions and convolution type operators, intertwining operators, and representation theory.
result Explicit expressions and properties of conformally invariant differential operators in higher spin spaces.
We present a generalization of the Clifford action for other representations spaces of Spin(n), which is called the Clifford homomorphism. Their properties extend to the ones for the higher spin Dirac operators on spin manifolds. In particular, we have general Bochner identities for them, and an eigenvalue estimate o…
Study centralizers of spin subalgebras in higher-dimensional spaces.
problem Understanding centralizers of spin subalgebras in complex algebraic structures.
method Analyzing the centralizers of isomorphic copies of spin subalgebras in specific Lie algebras.
result Determined centralizers of spin subalgebras in higher-dimensional spaces.
We prove that any connected component of the space of m-spin structures on compact Riemann surfaces with finite number of punctures and holes is homeomorphic to a quotient of the vector space R^d by a discrete group action. Our proof is based on the representation of the space of m-spin structures on a Riemann surface …
We review progress on the generalized Witten conjecture and some of its major ingredients. This conjecture states that certain intersection numbers on the moduli space of higher spin curves assemble into the logarithm of the tau function of a semiclassical limit of the r-th Gelfand-Dickey (or KdV_r) hierarchy. Addition…
We study 4-dimensional higher-derivative conformal higher spin (CHS) fields generalising Weyl graviton and conformal gravitino. They appear, in particular, as "induced" theories in the AdS/CFT context. We consider their partition function on curved Einstein-space backgrounds like (A)dS or sphere and Ricci-flat spaces. …
Finsler geometry connects to higher-spin fields and curved-space Fronsdal equations.
problem Eliminating non-transverse modes in Finsler dynamics for higher spins.
method Parameterizing Finsler geometry in terms of symmetric tensors, analyzing linear and nonlinear terms, and examining gauge transformations.
result Finsler dynamics leads to the curved-space Fronsdal equation for all spins, plus a Stueckelberg-like coupling.
The paper studies rational higher tangential structures from Lie groups, revealing systematic effects of variations.
problem Understanding higher tangential structures at the rational level and their connections to geometry.
method Defining and studying Spin-Fivebrane and Spin-Ninebrane structures, analyzing their spaces and gauge groups.
result Variations of higher structures systematically involve lower ones, with interesting effects revealed.
Dynamics of four-dimensional massless fields of all spins is formulated in the Siegel space of complex 4×4 symmetric matrices. It is shown that the unfolded equations of free massless fields, that have a form of multidimensional Schrodinger equations, naturally distinguish between positive- and negative-frequen…
The paper decomposes and analyzes the higher spin Laplace operator.
problem Understanding the properties and solutions of the higher spin Laplace operator.
method Decomposition into Rrita-Schwinger operators, proving conformal invariance, establishing integral formulas.
result Established a Borel-Pompeiu type formula and a Green type integral formula for the higher spin Laplace operator.
Extends spinor-horosphere correspondence to higher dimensions and new spinor types.
problem Constructing isomorphisms between spinors and horospheres in hyperbolic spaces.
method Generalizes Mathews' results to Lipschitz spinors and null multiflags in higher-dimensional hyperbolic spaces.
result Equivariant correspondence between two-component Lipschitz spinors and higher-dimensional horospheres.
Study on decay rates of higher derivatives for nonlinear Dirac equations.
problem Estimating decay rates of higher derivatives of solutions to nonlinear Dirac equations.
method Similar to Li and Zang's method, focusing on 'good' spin null form.
result Obtained decay rates of higher derivatives of solutions.
Study higher order fermionic and bosonic operators on cylinders and Hopf manifolds.
problem Understanding higher order higher spin operators on specific manifolds.
method Analysis of higher order operators on cylinders and Hopf manifolds.
result Construction of kernels for these operators on the studied manifolds.
Motivated by the description of N=1 M-theory compactifications to four-dimensions given by Exceptional Generalized Geometry, we propose a way to geometrize the M-theory fluxes by appropriately relating the compactification space to a higher-dimensional manifold equipped with a torsion-free structure. As a n…
We propose a formulation of a Lorentzian quantum geometry based on the framework of causal fermion systems. After giving the general definition of causal fermion systems, we deduce space-time as a topological space with an underlying causal structure. Restricting attention to systems of spin dimension two, we derive th…
Classifies components of abelian differentials over Teichmüller space.
problem Classifying components of strata of abelian differentials.
method Computing monodromy groups and determining finite generating sets for r-spin stabilizer subgroups. result Complete classification of strata components for g≥5. Positive energy theorems for spin initial data with charge in higher dimensions.
problem Establishing positive energy theorems for spin initial data with charge in dimensions n≥4. method Using a dominant energy condition and asymptotically flat ends, extending classical theorems.
result Extending classical positive energy theorems to spin initial data with charge.
Joyce constructed examples of compact eight-manifolds with holonomy Spin(7), starting with a Calabi-Yau four-orbifold with isolated singular points of a special kind. That construction can be seen as the gluing of ALE Spin(7)-manifolds to each singular point of the Calabi-Yau four-orbifold divided by an anti-holomorphi…
We study the higher spin Dirac operators on 3-dimensional manifolds and show that there exist two Laplace type operators for each associated bundle. Furthermore, we give lower bound estimations for the first eigenvalues of these Laplace type operators.
Explains conformal maps and holomorphic structures for surfaces in higher-dimensional Euclidean spaces.
problem Explains conformal maps and holomorphic structures for surfaces in higher-dimensional Euclidean spaces.
method Uses Clifford algebra and spin transforms to explain conformal maps and holomorphic structures.
result Calculates the degree of the spinor bundle associated with a conformal immersion and defines analogues of polar and bipolar surfaces.
Formulas for spectra of higher spin operators on sphere subbundles.
problem Finding spectra of higher spin operators on specific subbundles of spinor-valued tensors.
method Explicit formulas derived for spectra in both even and odd dimensions.
result Spectra formulas for higher spin operators and their squares.
The article studies spinor and tensor fields on curved spaces, deriving formulas and spectra.
problem Understanding spinor and tensor fields on curved spaces.
method Weitzenböck-type formulas, explicit factorization of Laplace operator, representation theory.
result Explicit factorization of the Laplace operator and spectra calculation on constant curvature spaces.
This is an introduction to the construction of higher-dimensional knots by spinning methods. Simple spinning of classical knots was introduced by E. Artin in 1926, and several generalizations have followed. These include twist spinning, superspinning or p-spinning, frame spinning, roll spinning, and deform spinning. We…
In this paper, we use localization algebras to study higher rho invariants of closed spin manifolds with positive scalar curvature metrics. The higher rho invariant is a secondary invariant and is closely related to positive scalar curvature problems. The main result of the paper connects the higher index of the Dirac …
We prove the genus zero part of the generalized Witten conjecture relating moduli spaces of spin curves to Gelfand-Dickey hierarchies. That is, we show that intersection numbers on the moduli space of stable r-spin curves assemble into a generating function which yields a solution of the semiclassical limit of the KdV_…
The abstract theorem is extended to higher genus surfaces.
problem Generalizing the web trace theorem to higher genus surfaces.
method Geometric derivation and spin geometry of embedded loops.
result Expansion of twisted Kasteleyn matrices for higher genus surfaces.
New Spin(7) manifolds created from Calabi-Yau bundles.
problem Creating complete non-compact Spin(7) manifolds.
method Building on T2-bundles over AC Calabi-Yau manifolds. result First known examples of complete toric Spin(7) manifolds.
The algebra of differential geometry operations on symmetric tensors over constant curvature manifolds forms a novel deformation of the sl(2,R) [semidirect product] R^2 Lie algebra. We present a simple calculus for calculations in its universal enveloping algebra. As an application, we derive generating functions for t…
We define (higher rank) spinorially twisted spin structures and deduce various curvature identites as well as estimates for the eigenvalues of the corresponding twisted Dirac operators.
The abstract discusses financial irreversibility using quantum mechanics and projective geometry.
problem Financial irreversibility and its limitations in trading strategies.
method Projective geometry and Taylor expansion of directed distance in quantum systems.
result Fundamental asymmetry under state exchange is a key factor in financial irreversibility.
The purpose of this note is introduce a new axiom (called the Descent Axiom) in the theory of r-spin cohomological field theories. This axiom explains the origin of gravitational descendants in this theory. Furthermore, the Descent Axiom immediately implies the Vanishing Axiom, explicating the latter (which has no a …
Compact gravity models yield tiny spin-two field masses.
problem Understanding the mass of spin-two fields in compactified gravity models.
method Relies on Bakry-Émery geometry, Cheeger constant, and synthetic Ricci lower bounds.
result Proves the existence of a spin-two field with very small mass under general assumptions.
Study of partially-massless higher-spin algebras in (A)dSd+1.
problem Understanding global symmetries of partially-massless higher-spin fields.
method Defined and quotiented ideals in the universal enveloping algebra of (A)dSd+1 isometries, derived bilinear forms, and used Howe duality. result Explicit calculation of bilinear forms revealing additional ideals for non-negative integer values of ℓ−d/2. The paper explores spin^h structures and their obstructions.
problem Understanding which manifolds are spin^h.
method Analyzing the fifth Stiefel-Whitney class and constructing generalised spin structures.
result Every compact orientable manifold of dimension 7 or lower is spin^h, and there are higher-dimensional manifolds that are not.
The Rosenberg index vanishes if a manifold admits a wide Riemannian band or cube-like domain.
problem Proving the Rosenberg index does not vanish for certain manifolds.
method Analyzing isometric immersions of wide Riemannian bands and cube-like domains on spin manifolds.
result Closed spin manifolds with infinite KO-width have non-vanishing Rosenberg index. In the background effective field theory of heterotic string theory, the Green-Schwarz anomaly cancellation mechanism plays a key role. Here we reinterpret it and its magnetic dual version in terms of differential twisted String- and differential twisted Fivebrane-structures that generalize the notion of Spin-structure…
We discuss twistor-like interpretation of the Sp(8) invariant formulation of 4d massless fields in ten dimensional Lagrangian Grassmannian Sp(8)/P which is the generalized space-time in this framework. The correspondence space C is SpH(8)/PH where SpH(8) is the semidirect product of Sp(8) with Heis…
Let M be a closed spin manifold of dimension at least three with a fixed topological spin structure. For any Riemannian metric, we can construct the associated Dirac operator. The spectrum of this Dirac operator depends on the metric of course. In 2005, Dahl conjectured that M can be given a metric, for which a finite …
We give a method of decomposing bundle-valued polynomials compatible with the action of the Lie group Spin(n), where important tools are Spin(n)-equivariant operators and their spectral decompositions. In particular, the top irreducible component is realized as an intersection of kernels of these operators.
Gravitational interactions of higher spin fields are generically plagued by inconsistencies. We present a simple framework that couples higher spins to a broad class of gravitational backgrounds (including Ricci flat and Einstein) consistently at the classical level. The model is the simplest example of a Yang--Mills d…
Study higher-order spin glass models for social network behavior with peer-group effects.
problem Modeling correlation phenomena on social networks with peer-group effects.
method Inference in higher-order Ising models to recover coefficients and peer-group effects.
result Strong concavity of log pseudo-likelihood implies statistical error rate of sqrt(d/n) for MPLE.
Study 3d N=1 vacua from M-theory compactification on Spin(7) space.
problem Quantum corrections in 3d N=1 vacua from M-theory compactification.
method Use Higgs bundles to analyze 3d N=1 vacua and track corrections.
result Topological anomalies are robust and calculable in 3d effective field theory.
We prove the vanishing of higher A-hat-genera, in the sense of Browder and Hsiang, on smooth manifolds with effective circle actions and with finite second and fourth homotopy groups
We find all m-spin structures on Klein surfaces of genus larger than one. An m-spin structure on a Riemann surface P is a complex line bundle on P whose m-th tensor power is the cotangent bundle of P. A Klein surface can be described by a pair (P,tau), where P is a Riemann surface and tau is an anti-holomorphic involut…