arXiv research

We introduce and illustrate a new approach to the unknotting problem via the dynamics of vortex strings in a nonlinear partial differential equation of reaction-diffusion type. To untangle a given knot, a Biot-Savart construction is used to initialize the knot as a vortex string in the FitzHugh-Nagumo equation. Remarka…

Reformulates compatibility condition for generalized metrics in string theory.

In this Part II of D(11), we introduce new objects: super-$C^k$-schemes and Azumaya super-$C^k$-manifolds with a fundamental module (or, synonymously, matrix super-$C^k$-manifolds with a fundamental module), and extend the study in D(11.1) ([L-Y3], arXiv:1406.0929 [math.DG]) to define the notion of `differentiable maps…

We show that there exists a natural Tulczyjew triple in the dynamics of objects for which the standard kinematic configuration space $TM$, i.e. the tangent bundle, is replaced with its $n$-th exterior power, i.e. the bundle of tangent $n$-vectors. In this framework, which is fully covariant, we geometrically derive pha…

Proves a unique connection for Born geometry.

A new method uses string method to explore diffusion models.

The paper analyzes the stability of an observer error in a vibrating string system.

In the paper, we study numerically the projections of the real exchange rate dynamics onto the string-like topology. Our approach is inspired by the contemporary movements in the string theory. The string map of data is defined here by the boundary conditions, characteristic length, real valued and the method of redist…

Summary of para-Hermitian geometry for T-duality in string theory.

The most general gauge-invariant marginal deformation of four-dimensional abelian BF-type topological field theory is studied. It is shown that the deformed quantum field theory is topological and that its observables compute, in addition to the usual linking numbers, smooth intersection indices of immersed surfaces wh…

We study warped compactifications of string/M theory with the help of effective potentials, continuing previous work of the last two authors and Michael R. Douglas presented in arXiv:1206.1885. The dynamics of the conformal factor of the internal metric, which is responsible for instabilities in these constructions, is…

The Lagrangian description of mechanical systems and the Legendre Transformation (considered as a passage from the Lagrangian to the Hamiltonian formulation of the dynamics) for point-like objects, for which the infinitesimal configuration space is TM, is based on the existence of canonical symplectic isomorphisms of d…

A model is developed to study the effectiveness of innovation and its impact on structure creation and structure change on agent-based societies. The abstract model that is developed is easily adapted to any particular field. In any interacting environment, the agents receive something from the environment (the other a…

The closed string model in the background gravity field is considered as a bi-Hamiltonian system in assumption that string model is the integrable model for particular kind of the background fields. The dual nonlocal Poisson brackets(PB), depending of the background fields and of their derivatives, are obtained. The in…

We propose a formulation of the term structure of interest rates in which the forward curve is seen as the deformation of a string. We derive the general condition that the partial differential equations governing the motion of such string must obey in order to account for the condition of absence of arbitrage opportun…

D-branes on noncommutative spaces mimic string theory, offering new insights into mirror symmetry.

We consider D-branes in string theory and address the issue of how to describe them mathematically as a fundamental object (as opposed to a solitonic object) of string theory in the realm in differential and symplectic geometry. The notion of continuous maps, $k$-times differentiable maps, and smooth maps from an Azuma…

By a conformal string in Euclidean space is meant a closed critical curve with non-constant conformal curvatures of the conformal arclength functional. We prove that (1) the set of conformal classes of conformal strings is in 1-1 correspondence with the rational points of the complex domain $\{q\in \mathbb{C} \,:\, 1/2…

Derives path integrals for perturbative strings on various backgrounds.

Topological string theory derived from string geometry for non-perturbative effects.

Identifies all perturbative vacua in bosonic string theory.

String backgrounds and D-branes do not possess the structure of Lorentzian manifolds, but that of manifolds with area metric. Area metric geometry is a true generalization of metric geometry, which in particular may accommodate a B-field. While an area metric does not determine a connection, we identify the appropriate…

We introduce a new action $S_{standard}^{(ρ,h; Φ,g,B,C)}$ for D-branes that is to D-branes as the Polyakov action is to fundamental strings. This `standard action' is abstractly a non-Abelian gauged sigma model --- based on maps $\varphi: (X^{\!A\!z},E;\nabla)\rightarrow Y$ from an Azumaya/matrix manifold $X^{\!A\!z}$ …

String geometry theory connects strings to space-time and finds string vacua.

Model explains yield curve dynamics using order flow shocks.

Derives path-integrals for superstrings on curved backgrounds using string geometry theory.

We investigate the Penrose limits of classical string and M-theory backgrounds. We prove that the number of (super)symmetries of a supergravity background never decreases in the limit. We classify all the possible Penrose limits of AdS x S spacetimes and of supergravity brane solutions. We also present the Penrose limi…

This paper classifies virtual string links up to cobordism using group theory.

Chiral string integrands simplify to ambitwistor string integrands in the tensionless limit.

Overwhelming majority of econometric models applied on a long term basis in the financial forex market do not work sufficiently well. The reason is that transaction costs and arbitrage opportunity are not included, as this does not simulate the real financial markets. Analyses are not conducted on the non equidistant d…

A virtual string can be defined as an equivalence class of planar diagrams under certain kinds of diagrammatic moves. Virtual strings are related to virtual knots in that a simple operation on a virtual knot diagram produces a diagram for a virtual string. In this paper we consider three operations on a virtual string …

A virtual string is a scheme of self-intersections of a closed curve on a surface. We study algebraic invariants of strings as well as two equivalence relations on the set of strings: homotopy and cobordism. We show that the homotopy invariants of strings form an infinite dimensional Lie group. We also discuss connecti…

Research extends Cahn's results on virtual strings to connected non-parallel strings.

New formulas link string bordism to integers.

There is an interpretation of open string field theory in algebraic topology. An interpretation of closed string field theory can be deduced from this open string theory to obtain as well the interpretation of open and closed string field theory combined.

Extended Alexander groups are used to define an invariant for open virtual strings. Examples of non-commuting open strings and a ribbon-concordance obstruction are given. An example is given of a slice virtual open string that is not ribbon. Definitions are extended to open n-strings.

Introduces holomorphic string algebroids and classifies them.

BOSS optimizes string inputs using string kernels and genetic algorithms.

String topology coproduct and Turaev cobracket computed for surfaces.

We present a finite-dimensional and smooth formulation of string structures on spin bundles. It uses trivializations of the Chern-Simons 2-gerbe associated to this bundle. Our formulation is particularly suitable to deal with string connections: it enables us to prove that every string structure admits a string connect…

We consider a dynamic market model of liquidity where unmatched buy and sell limit orders are stored in order books. The resulting net demand surface constitutes the sole input to the model. We prove that generically there is no arbitrage in the model when the driving noise is a stochastic string. Under the equivalent …

Paper shows string cobordism at 24 dims can be determined by elliptic genus.

The actions, anomalies, and quantization conditions allow the M2-brane and the M5-brane to support, in a natural way, structures beyond Spin on their worldvolumes. The main examples are twisted String structures. This also extends to twisted String^c structures, which we introduce and relate to twisted String structure…

Introduces string structures linking to loop spaces.

A new method for virtual homotopy classes of virtual strings.

Study topological G₂ and Spin(7) strings at 1-loop using double complexes.

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…

Abstract M5 branes on ADE singularities yields BPS spectrum and partition functions.