Related papers: Deformation of string topology into homotopy skein…
Perturbative estimates suggest that extended topological defects such as cosmic strings emit few particles, but numerical simulations of the fields from which they are constructed suggest the opposite. In this paper we study the decay of…
We show, using a theorem of Milnor and Margulis, that string theory on compact negatively curved spaces grows new effective dimensions as the space shrinks, generalizing and contextualizing the results in hep-th/0510044. Milnor's theorem…
Configuration space integrals have in recent years been used for studying the cohomology of spaces of (string) knots and links in $\mathbb{R}^n$ for $n>3$ since they provide a map from a certain differential algebra of diagrams to the…
We analyze the $G$-skein theory invariants of the 3-torus $T^3$ and the two-torus $T^2$, for the groups $G = GL_N, SL_N$ and for generic quantum parameter. We obtain formulas for the dimension of the skein module of $T^3$, and we describe…
This paper is based on my talks (`Skein modules with a cubic skein relation: properties and speculations' and `Symplectic structure on colorings, Lagrangian tangles and its applications') given in Kyoto (RIMS), September 11 and September 18…
The string vertices of closed string field theory are subsets of the moduli spaces of punctured Riemann surfaces that satisfy a geometric version of the Batalin-Vilkovisky master equation. We present a homological proof of existence of…
We study the coupling of the closed string to the open string in the topological B-model. These couplings can be viewed as gauge invariant observables in the open string field theory, or as deformations of the differential graded algebra…
A new two dimensional $\mathcal{N}=(0,2)$ Supersymmetric Non-Linear Sigma Model describes the dynamics of internal moduli of the BPS semi-local vortex string supported in four dimensional $\mathcal{N}=2$ SQED. While the core of these…
In this thesis, we study the properties of String theory amplitudes within the framework of Intersection Theory (IT) for twisted (co)homology, which, as recently proposed, offered a novel approach to analyze relations between scattering…
We discuss links in thickened surfaces. We define the Khovanov-Lipshitz-Sarkar stable homotopy type and the Steenrod square for the homotopical Khovanov homology of links in thickened surfaces with genus$>1$. A surface means a closed…
It is generally known that the holomorphic anomaly equations in topological string theory reflect the quantum mechanical nature of the topological string partition function. We present two new results which make this assertion more precise:…
In this short note, we argue that directed homotopy can be given the structure of generalized modules, over particular monoids. This is part of a general attempt for refoundation of directed topology.
We briefly review the present status of string theory from the viewpoint of its implications on the short-distance space-time structure and black hole physics. Special emphases are given on two closely related issues in recent developments…
A new approach to the quantization of Chern-Simons theory has been developed in recent papers of the author. It uses a "simulation" of the moduli space of flat connections modulo the gauge group which reveals to be related to a lattice…
We couple Chern-Simons gauge theory to 3-dimensional topological gravity with the aim of investigating its quantum topological invariance. We derive the relevant BRST rules and Batalin-Vilkovisky action. Standard BRST transformations of the…
Infinite-dimensional Grassmannian manifold contains moduli spaces of Riemann surfaces of all genera. This well known fact leads to a conjecture that non-perturbative string theory can be formulated in terms of Grassmannian. We present new…
We study photon geodesics in topological solitons that have the same asymptotic properties as Schwarzschild black holes. These are coherent states in string theory corresponding to pure deformations of spacetime through the dynamics of…
In this paper we study the topology of the cobordism category of open and closed strings. This is a 2-category in which the objects are compact one-manifolds whose boundary components are labeled by an indexing set (the set of "D-branes"),…
Perturbative string amplitudes are correctly derived from the string geometry theory, which is one of the candidates of a non-perturbative formulation of string theory. In order to derive non-perturbative effects rather easily, we formulate…
We give some remarks on twisted determinant line bundles and Chern-Simons topological invariants associated with real hyperbolic manifolds. Index of a twisted Dirac operator is derived. We discuss briefly application of obtained results in…