Related papers: String geometry vs. spin geometry on loop spaces
In this paper, we show the existence of (co-oriented) contact structures on certain classes of $G_2$-manifolds, and that these two structures are compatible in certain ways. Moreover, we prove that any seven-manifold with a spin structure…
Free actions of finite groups on spheres give rise to topological spherical space forms. The existence and classification problems for space forms have a long history in the geometry and topology of manifolds. In this article, we present a…
The string topology coproduct on the homology of the free loop space of a closed manifold induces a string cobracket on $S^1$-equivariant homology. We give a complete computation of the string topology coproduct for surfaces of higher genus…
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…
It is shown that the Topological Massive and ``Self-dual'' theories, which are known to provide locally equivalent descriptions of spin 1 theories in 2+1 dimensions, have different global properties when formulated over topologically…
We determine spectral curves for the known spiky string solutions in AdS space in the limit of large angular momentum. We also construct generic multi-spike solutions in this limit and compute the corresponding spectral data. The resulting…
The homology of the free and the based loop space of a compact globally symmetric space can be studied through explicit cycles. We use cycles constructed by Bott and Samelson and by Ziller to study the string topology coproduct and the…
The roles that spin networks play in gauge theories, quantum gravity and topological quantum field theory are briefly described, with an emphasis on the question of the relationships among them. It is argued that spin networks and their…
The recent developments of the ``connection'' and ``loop'' representations have given the possibility to show that the two representation are equivalent and that it is possible to transform any result from one representation into the other.…
The aim of this paper is to explain the relationship between the (co)homology of the free loop space and the Hochschild homology of its singular cochain algebra. We introduce all the relevant technical tools, namely simplicial and cyclic…
The symmetries of string theory on ${\rm AdS}_3 \times {\rm S}^3 \times \mathbb{T}^4$ at the dual of the symmetric product orbifold point are described by a so-called Higher Spin Square (HSS). We show that the massive string spectrum in…
We discuss different formulations and approaches to string theory and $ 2d$ quantum gravity. The generic idea to get a unique description of {\it many} different string vacua altogether is demonstrated on the examples in $ 2d$ conformal,…
Higher spin gravity is an interesting toy model of stringy geometry. Particularly intriguing is the presence of higher spin gauge transformations that redefine notions of invariance in gravity: the existence of event horizons and…
Band topology is both constrained and enriched by the presence of symmetry. The importance of anti-unitary symmetries such as time reversal was recognized early on leading to the classification of topological band structures based on the…
These are notes of a series of lectures on mirror symmetry and topological string theory given at the Mathematical Sciences Center at Tsinghua University. The N=2 superconformal algebra, its deformations and its chiral ring are reviewed. A…
We investigate hetrotic string theory on special holonomy manifolds including exceptional holonomy G_2 and Spin(7) manifolds. The gauge symmetry is F_4 in a G_2 manifold compactification, and so(9) in a Spin(7) manifold compactification. We…
We verify that for a finite simplicial complex $X$ and for piecewise linear loops on $X$, the "thin" loop space is a topological group of the same homotopy type as the space of continuous loops. This turns out not to be the case for the…
String theory is a quantum theory that reproduces the results of General Relativity at long distances but is completely different at short distances. Mathematically, string theory is based on a very new -- and little understood -- framework…
Recently the $\text{SU}(2)$ spin-network states in loop quantum gravity is generalized to those of the corresponding affine Lie algebra. We show that if one literally starts from the full $\text{SL}(2,\mathbb{C})$ group, this procedure…
We investigate topological properties of the moduli space of spin structures over genus two curves. In particular, we provide a combinatorial description of this space and give a presentation of the (rational) cohomology ring via generators…