Related papers: String Topology for Embedding Spaces
We set up, purely in A-model terms, a novel formalism for the global solution of the open and closed topological A-model on toric Calabi-Yau threefolds. The starting point is to build on recent progress in the mathematical theory of open…
In this note, we first explain the equivalence between the interaction Hamiltonian of Green-Schwarz light-cone gauge superstring field theory and the twist field formalism known from matrix string theory. We analyze the role of the large N…
Symplectic invariants introduced in math-ph/0702045 can be computed for an arbitrary spectral curve. For some examples of spectral curves, those invariants can solve loop equations of matrix integrals, and many problems of enumerative…
We investigate the field theory of strings having as a target space an arbitrary discrete one-dimensional manifold. The existence of the continuum limit is guaranteed if the target space is a Dynkin diagram of a simply laced Lie algebra or…
We study properties of differential graded (dg) operads modulo weak equivalences, that is, modulo the relation given by the existence of a chain of dg operad maps inducing a homology isomorphism. This approach, naturally arising in string…
We use the computational power of rational homotopy theory to provide an explicit cochain model for the loop product and the string bracket of a 1-connected closed manifold M. We prove that the loop homology of M is isomorphic to the…
We show how to make a topological string theory starting from an $N=4$ superconformal theory. The critical dimension for this theory is $\hat c= 2$ ($c=6$). It is shown that superstrings (in both the RNS and GS formulations) and critical…
The purpose of this paper is to give applications of the Eilenberg-Moore type spectral sequence converging to the relative loop homology algebra of a Gorenstein space, which is introduced in the previous paper due to the authors. Moreover,…
Twenty years ago, Mumford initiated the systematic study of the cohomology ring of moduli spaces of Riemann surfaces. Around the same time, Harer proved that the homology of the mapping class groups of oriented surfaces is independent of…
We introduce cannibalistic classes for string bundles with values in $TMF$ with level structures. This allows us to compute the Morava $E$-homology of any map from the bordism spectrum $MString$ to $TMF$ with level structures.
What is the meaning of entanglement in a theory of extended objects such as strings? To address this question we consider the spatial entanglement between two intervals in the Gross-Taylor model, the string theory dual to two-dimensional…
String geometry theory is a candidate of the non-perturbative formulation of string theory. In order to determine the string vacuum, we need to clarify how superstring backgrounds are described in string geometry theory. In this paper, we…
We examine the extent to which the action for the membrane of M-theory (the eleven-dimensional construct which underlies and unifies all of the known string theories) simplifies in the so-called Open Membrane (OM) limit, a limit which lies…
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"),…
We investigate the physics of the E-string theory and its compactifications as well as their applications to four-dimensional topology. In particular, we compute the partition function of the topologically twisted theory on $M_4\times T^2$,…
We present a new approach to bootstrapping string-like theories by exploiting a local crossing symmetric dispersion relation and field redefinition ambiguities. This approach enables us to use mass-level truncation and to go beyond the dual…
Word embeddings aims to map sense of the words into a lower dimensional vector space in order to reason over them. Training embeddings on domain specific data helps express concepts more relevant to their use case but comes at a cost of…
Chas and Sullivan introduced string homology, which is the equivariant homology of the loop space with the $S^1$ action on loops by rotation. Craig Westerland computed the string homology for spheres with coefficients in $\mathbb{Z}…
We introduce a spectral embedding algorithm for finding proximal relationships between nodes in signed graphs, where edges can take either positive or negative weights. Adopting a physical perspective, we construct a Hamiltonian which is…
The partition function of the membrane is investigated. In particular, the case relevant to perturbative string theory of a membrane with topology $S^1 \times \Sigma$ is examined. The coupling between the string world sheet Euler character…