A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
The paper classifies higher order fermionic and bosonic operators in spin spaces.
Study of higher spin bundles on Klein surfaces, linking to singularity theory.
The paper decomposes and analyzes the higher spin Laplace operator.
The paper constructs arbitrary order conformally invariant operators in higher spin spaces.
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. …
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 of higher spin Killing spinors on 3D manifolds, proving rigidity and providing explicit expressions.
Maximal index vanishes for certain spin manifolds with positive scalar curvature.
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…
The purpose of this note is introduce a new axiom (called the Descent Axiom) in the theory of -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 …
Motivated by the description of 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…
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…
The paper extends higher-order operators in higher spin spaces.
We present a generalization of the Clifford action for other representations spaces of , 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 on decay rates of higher derivatives for nonlinear Dirac equations.
The article studies spinor and tensor fields on curved spaces, deriving formulas and spectra.
The paper studies rational higher tangential structures from Lie groups, revealing systematic effects of variations.
We present a Donaldson-Witten type field theory in eight dimensions on manifolds with holonomy. We prove that the stress tensor is BRST exact for metric variations preserving the holonomy and we give the invariants for this class of variations. In six and seven dimensions we propose similar theories on Calabi…
The first part of this text is a gentle exposition of some basic constructions and results in the extended prequantum theory of Chern-Simons-type gauge field theories. We explain in some detail how the action functional of ordinary 3d Chern-Simons theory is naturally localized ("extended", "multi-tiered") to a map on t…
Study 3d N=1 vacua from M-theory compactification on Spin(7) space.
Study connects manifold complexity to scalar curvature bounds.
Study higher order fermionic and bosonic operators on cylinders and Hopf manifolds.
Paper shows string cobordism at 24 dims can be determined by elliptic genus.
We classify higher-SPTs and their anomalies via cobordism theory.
Finsler geometry connects to higher-spin fields and curved-space Fronsdal equations.
Positive energy theorems for spin initial data with charge in higher dimensions.
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.
The Dirac operator for a manifold Q, and its chirality operator when Q is even dimensional, have a central role in noncommutative geometry. We systematically develop the theory of this operator when Q=G/H, where G and H are compact connected Lie groups and G is simple. An elementary discussion of the differential geome…
The paper proves a 'long neck principle' for Riemannian spin manifolds with positive scalar curvature.
Formulas for spectra of higher spin operators on sphere subbundles.
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…
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…
The Jones-Wenzl projectors play a central role in quantum topology, underlying the construction of SU(2) topological quantum field theories and quantum spin networks. We construct chain complexes whose graded Euler characteristic is the "classical" projector in the Temperley-Lieb algebra. We show that they are homotopy…
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 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 construct eta- and rho-invariants for Dirac operators, on the universal covering of a closed manifold, that are invariant under the projective action associated to a 2-cocycle of the fundamental group. We prove an Atiyah-Patodi-Singer index theorem in this setting, as well as its higher generalization. Applications …
The abstract theorem is extended to higher genus surfaces.
The paper defines higher invariants for groups of polynomial growth and proves their convergence.
In this article, we prove that on any compact spin manifold of dimension m congruent 0,6,7 mod 8, there exists a metric, for which the associated Dirac operator has at least one eigenvalue of multiplicity at least two. We prove this by catching the desired metric in a subspace of Riemannian metrics with a loop that is …
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_…
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.
Compact gravity models yield tiny spin-two field masses.
Extends spinor-horosphere correspondence to higher dimensions and new spinor types.
Study of partially-massless higher-spin algebras in (A)dS.
Topological field theory computes Arf invariant of r-spin surfaces.
The paper explores spin^h structures and their obstructions.
Dynamics of four-dimensional massless fields of all spins is formulated in the Siegel space of complex 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…
No chiral field theory for quantum spin chain limits.