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.
New formulas derived for anomaly cancellation using modular forms and E8 bundles.
New anomaly cancellation formulas for E8*E8*E8 gauge group.
New anomaly formulas from E8 bundles.
New anomaly formulas derived from bundles.
Formula derived for Lie algebra E8's bracket.
We present a geometric construction of the exceptional Lie algebras F4 and E8 starting from the round 8- and 15-spheres, respectively, inspired by the construction of the Killing superalgebra of a supersymmetric supergravity background. (There is no supergravity in the paper.)
The data required for heterotic string theory with gauge group G, which for anomaly cancellation reasons must either be E8 x E8 or Spin(32)/Z2, consist of the following: a ten-dimensional space-time X and a principal G-bundle P. The fields in the theory consist of: a metric on X, a connection on P and a B-field which i…
The compact exceptional Lie groups F4, E6, E7 and E8 have spinor groups as a subgroup as follows: E8 \supset Ss(16) \supset Spin(15) \supset Spin(14) \supset Spin(13), E7 \supset Spin(12) \supset Spin(11), E6 \supset Spin(10), F4 \supset Spin(9) \supset Spin(8) \supset Spin(7) \supset \cdot \cdot \cdot \supset Spin(1) …
In this note we revisit the subject of anomaly cancelation in string theory and M-theory on manifolds with String structure and give three observations. First, that on String manifolds there is no E8 x E8 global anomaly in heterotic string theory. Second, that the description of the anomaly in the phase of the M-theory…
We study isometric Lie group actions on the compact exceptional groups E6, E7, E8, F4 and G2 endowed with a biinvariant metric. We classify polar actions on these groups. We determine all isometric actions of cohomogeneity less than three on E6, E7, F4 and all isometric actions of cohomogeneity less than 20 on E8. More…
The strong symmetric genus of a finite group G is the smallest genus of a closed orientable topological surface on which G acts faithfully as a group of orientation preserving automorphisms. In this paper we complete the calculation of the strong symmetric genus for each finite Coxeter group excluding the group E8.
The higher gauge field in 11-dimensional supergravity -- the C-field -- is constrained by quantum effects to be a cocycle in some twisted version of differential cohomology. We argue that it should indeed be a cocycle in a certain twisted nonabelian differential cohomology. We give a simple and natural characterization…
Classifies real trivectors in 9D using Galois cohomology.
We consider geometric and analytical aspects of M-theory on a manifold with boundary Y. The partition function of the C-field requires summing over harmonic forms. When Y is closed Hodge theory gives a unique harmonic form in each de Rham cohomology class, while in the presence of a boundary the Hodge-Morrey-Friedrichs…
Using instanton Floer theory, extending methods due to Froyshov, we determine the definite lattices that arise from smooth 4-manifolds bounded by certain homology 3-spheres. For example, we show that for +1 surgery on the (2,5) torus knot, the only non-diagonal lattices that can occur are E8 and the indecomposable unim…
The notion of (Z/2Z) x (Z/2Z)-symmetric spaces is a generalization of classical symmetric spaces, where the group Z/2Z is replaced by (Z/2Z) x (Z/2Z). In this article, a classification is given of the (Z/2Z) x (Z/2Z)-symmetric spaces G/K where G is an exceptional compact Lie group or Spin(8), complementing recent resul…
Study monodromy factorizations for lines on del Pezzo surfaces.
Complete construction for Lie groups of types F4, E6, E7, E8.
New hyperKähler orbifolds of Kummer type discovered.
The study of quotient structures in multi-graded bundles, including double vector bundles.
Study of semi-principal bundles using group actions and wreath products.
Establishes a framework for stringor bundles, proving their canonical isomorphism to Stolz-Teichner's.
In this study, we generalize double tangent bundles to double jet bundles. We present a secondary vector bundle structure on a 1-jet of a vector bundle. We show that 1-jet of a vector bundle carries two vector bundle structures, namely primary and secondary structures. We also show that the manifold charts induced by p…
This paper shows vector bundles and differential bundles are equivalent in smooth manifolds.
Introduces Darboux-Lie derivative for fiber bundles.
On a complex manifold, a co-Higgs bundle is a holomorphic vector bundle with an endomorphism twisted by the tangent bundle. The notion of generalized holomorphic bundle in Hitchin's generalized geometry coincides with that of co-Higgs bundle when the generalized complex manifold is ordinary complex. Schwarzenberger's r…
A stratified bundle is a fibered space in which strata are classical bundles and in which attachment of strata is controlled by a structure category of fibers. Well known results on fibre bundles are shown to be true for stratified bundles; namely the pull back theorem, the bundle theorem and the principal bundle theor…
We define double principal bundles (DPBs), for which the frame bundle of a double vector bundle, double Lie groups and double homogeneous spaces are basic examples. It is shown that a double vector bundle can be realized as the associated bundle of its frame bundle. Also dual structures, gauge transformations and conne…
Proves every equivariant vector bundle over toric manifolds is a Klyachko bundle.
Categorical bundles provide a natural framework for gauge theories involving multiple gauge groups. Unlike the case of traditional bundles there are distinct notions of triviality, and hence also of local triviality, for categorical bundles. We study categorical principal bundles that are product bundles in the categor…
Symplectic fillings of prequantization bundles are shown to be disk bundles under certain conditions.
Identifies images of determinant morphism for specific co-Higgs bundles.
Bundling of graph edges (node-to-node connections) is a common technique to enhance visibility of overall trends in the edge structure of a large graph layout, and a large variety of bundling algorithms have been proposed. However, with strong bundling, it becomes hard to identify origins and destinations of individual…
The paper defines and explores vector bundles that can be turned and their properties.
Study projective flat vector bundles over Riemann surfaces using Wronskian line bundles.
The paper generalizes bundle gerbes over groupoids and their correspondence with PB groupoids.
Study geometric characterization of asymptotic pseudodifferential calculus on spinor bundles.
Generalizes Higgs bundles theory using a vector bundle twist.
Study of generalized vector bundles and their geometric tools.
The paper extends orthogonal decomposition results to hermitian Higgs bundles.
We present the notion of a filtered bundle as a generalisation of a graded bundle. In particular, we weaken the necessity of the transformation laws for local coordinates to exactly respect the weight of the coordinates by allowing more general polynomial transformation laws. The key examples of such bundles include af…
Introduces generalized principal bundles and connections, linking them to standard gauge theories.
Study proves existence of precotangent bundles for Grassmannians.
Investigates connections in Lie group bundles, focusing on geometric reduction.
Study of Pascal algebra matrices and their jet bundle map for vector bundles.
A bundle gerbe is constructed from an oriented smooth vector bundle of even rank with a fiberwise inner product, over a compact connected orientable smooth manifold with Riemannian metric. From a trivialization of the bundle gerbe is constructed an irreducible Clifford module bundle, a spinor bundle over the smooth fre…
We develop the theory of smooth principal bundles for a smooth group , using the framework of diffeological spaces. After giving new examples showing why arbitrary principal bundles cannot be classified, we define -numerable bundles, the smooth analogs of numerable bundles from topology, and prove that pulling ba…
In \cite{BR1}, \cite{BR2}, a parabolic determinant line bundle on a moduli space of stable parabolic bundles was constructed, along with a Hermitian structure on it. The construction of the Hermitian structure was indirect: The parabolic determinant line bundle was identified with the pullback of the determinant line b…