相关论文: Orbifold String Topology

Recently, there is an explosive growth of activities to understand stringy properties of orbifolds. In this article, we survey some of recent developments.

We describe the topological Hochschild homology of ring spectra that arise as Thom spectra for loop maps f: X->BF, where BF denotes the classifying space for stable spherical fibrations. To do this, we consider symmetric monoidal models 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…

We use recently obtained 2-loop string coupling constants to analyze a class of string models based on orbifold compactification. Assuming weak coupling at the string scale and single-scale unification leads to restrictions on the spectrum…

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 show that the mod $\ell$ cohomology of any finite group of Lie type in characteristic $p$ different from $\ell$ admits the structure of a module over the mod $\ell$ cohomology of the free loop space of the classifying space $BG$ of the…

Let M be a smooth, simply-connected, closed oriented manifold, and LM the free loop space of M. Using a Poincare duality model for M, we show that the reduced equivariant homology of LM has the structure of a Lie bialgebra, and we construct…

We develop some basic properties of the open string on the symmetric product which is supposed to describe the open string field theory in discrete lightcone quantization (DLCQ). After preparing the consistency conditions of the twisted…

The virtual cohomology of an orbifold is a ring structure on the cohomology of the inertia orbifold whose product is defined via the pull-push formalism and the Euler class of the excess intersection bundle. In this paper we calculate the…

Let $M$ be a connected, closed oriented manifold. Let $\omega\in H^m(M)$ be its orientation class. Let $\chi(M)$ be its Euler characteristic. Consider the free loop fibration $\Omega M\buildrel{i}\over\hookrightarrow…

We introduce BV-algebra structures on the homology of the space of framed long knots in $\mathbb{R}^n$ in two ways. The first one is given in a similar fashion to Chas-Sullivan's string topology. The second one is defined on the Hochschild…

In these lectures, we review the physics of time-dependent orbifolds of string theory, with particular attention to orbifolds of three-dimensional Minkowski space. We discuss the propagation of free particles in the orbifold geometries,…

In this expository paper written for physicists and geometers we introduce the notions of TQFT and of orbifold. Then we survey the construction of TQFT's originating from orbifolds such as Chen-Ruan theory and Orbifold String Topology.

We study topological string theory on elliptically fibered Calabi-Yau threefolds using mirror symmetry. We compute higher genus topological string amplitudes and express these in terms of polynomials of functions constructed from the…

In this paper we use trivial defects to define global taffy-like operations on string worldsheets, which preserve the field theory. We fold open and closed strings on a space X into open strings on products of multiple copies of X, and…

Chen and Ruan's orbifold cohomology of the symmetric product of a complex manifold is calculated. An isomorphism of rings (up to a change of signs) $H_{orb}^*(X^n/S_n;\complex) \cong H^*(X^{[n]};\complex)$ between the orbifold cohomology of…

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 show that relations in Homflypt type skein theory of an oriented $3$-manifold $M$ are induced from a $2$-groupoid defined from the fundamental $2$-groupoid of a space of singular links in $M$. The module relations are defined by…

This thesis is almost entirely devoted to studying string theory backgrounds characterized by simple geometrical and integrability properties. The archetype of this type of system is given by Wess-Zumino-Witten models, describing string…

Superstrings and topological strings with supermanifolds as target space play a central role in the recent developments in string theory. Nevertheless the rules for higher-genus computations are still unclear or guessed in analogy with…