相关论文: De Rham model for string topology
We give a new proof of the string topology structure of a compact oriented surface of genus g greater than or equal to 2, using elementary algebraic topology. This reproves the result of Vaintrob.
A formula for the full nonperturbative topological string free energy was recently proposed by Hattab and Palti \cite{HP24a}. In this work, we extend their result to the refined topological string theory. We demonstrate that the proposed…
A few observations concerning topological string theories at the string-tree level are presented: (1) The tree-level, large phase space solution of an arbitrary model is expressed in terms of a variational problem, with an ``action'' equal,…
We study the application of IBL-infinity-algebras to string topology and explicitly compute the case of spheres. This involves finding a Green kernel and computing integrals associated to trivalent ribbon graphs, which are similar to…
Inferring topological and geometrical information from data can offer an alternative perspective on machine learning problems. Methods from topological data analysis, e.g., persistent homology, enable us to obtain such information,…
Degree one twisting of Deligne cohomology, as a differential refinement of integral cohomology, was established in previous work. Here we consider higher degree twists. The Rham complex, hence de Rham cohomology, admits twists of any odd…
We propose a duality between the complex Liouville string and a two-matrix integral. The complex Liouville string is defined by coupling two Liouville theories with complex central charges $c = 13 \pm i \lambda$ on the worldsheet. The…
Graph Signal Processing deals with the problem of analyzing and processing signals defined on graphs. In this paper, we introduce a novel filtering method for graph-based signals by employing ideas from topological data analysis. We begin…
We show how conformal field theory topological defects can relate solutions of open string field theory for different boundary conditions. To this end we generalize the results of Graham and Watts to include the action of defects on…
This thesis presents several new insights on the interface between mathematics and theoretical physics, with a central role for fermions on Riemann surfaces. First of all, the duality between Vafa-Witten theory and WZW models is embedded…
We attempt to review all trustworthy and well-controlled de Sitter compactifications of string theory.
A continuous cohomology theory for topological quandles is introduced, and compared to the algebraic theories. Extensions of topological quandles are studied with respect to continuous 2-cocycles, and used to show the differences in second…
In this thesis we probe various interactions between toric geometry and string theory. First, the notion of a top was introduced by Candelas and Font as a useful tool to investigate string dualities. These objects torically encode the local…
Using intersection theory in the context of Hilbert manifolds and geometric homology we show how to recover the main operations of string topology built by M. Chas and D. Sullivan. We also study and build an action of the homology of…
We consider the in-plane motion of elastic strings on tree-like network, observed from the 'leaves'. We investigate the inverse problem of recovering not only the physical properties i.e. the 'optical lengths' of each string, but also the…
Using light cone string field theory we derive recursion relations for closed string correlation functions and scattering amplitudes which hold to all orders in perturbation theory. These results extend to strings in a plane wave…
We survey some results on toric topology.
The tensionless limit of classical string theory may be formulated as a topological theory on the world-sheet. A vector density carries geometrical information in place of an internal metric. It is found that path-integral quantization…
In this short paper, we use Tannakian reconstruction techniques to prove a result that explains how to reconstruct the stacky approach to de Rham cohomology from the classical theory algebraic de Rham cohomology via an application of the…
The network topology can be described by the number of nodes and the interconnections among them. The degree of a node in a network is the number of connections it has to other nodes and the degree distribution is the probability…