Related papers: TQFT string operations in open-closed string topol…
We construct classical solutions of open string field theory which are not invariant under ordinary twist operation. From detailed analysis of the moduli space of the solutions, it turns out that our solutions become nontrivial at…
We revisit the role of loop and surface operators as order parameters for gapped phases of four-dimensional gauge theories. We show that in some cases surface operators are confined, and that this fact can be used to distinguish phases…
We construct two-dimensional non-commutative topological quantum field theories (TQFTs), one for each Hecke algebra corresponding to a finite Coxeter system. These TQFTs associate an invariant to each ciliated surface, which is a Laurent…
We construct a graph TQFT for the minus flavor of Heegaard Floer homology. Our graph TQFT extends Ozsv\'{a}th and Szab\'{o}'s TQFT for closed and connected 3-manifolds, and allows for cobordisms with disconnected ends. As an application, we…
In this paper, we use a topological quantum field theory (TQFT) to define families of new homology theories of a $2$-dimensional CW complex of a smooth closed surface. The dimensions of these homology groups can be used to count the number…
Topological quantum field theories (TQFT) encode properties of quantum states in the topological features of abstract manifolds. One can use the topological avatars of quantum states to develop intuition about different concepts and…
The paper contains the construction of a topological quantum field theory with corners that underlies the smooth topological quantum field theory of Lickorish. Among other things, a contraction formula for diagrams is proved, the presence…
Using covariant phase space formulations for the natural topological invariants associated with the world-surface in closed string theory, we find that certain Wilson loops defined on the world-surface and that preserve topological…
The paper is devoted to a description of quantum group structures in the geometric quantization of a self-interacting string field, which appear under a transition from a tree-level of the theory to the account of loop effects in…
The standard, gapped entanglement boundary condition in Chern Simons theory breaks the topological invariance of the theory by introducing a complex structure on the entangling surface. This produces an infinite dimensional subregion…
Dynamical quantum field theories (QFTs), such as those in which spacetimes are equipped with a metric and/or a field in the form of a smooth map to a target manifold, can be formulated axiomatically using the language of…
To understand what does Chern-Simons with compact Lie group(does not like Dijkgraaf-Witten model with finite group in 3d) attach to a point, we first give a construction of Topological Quantum Field Theory(TQFT) via Chern-Simons theory in…
In this paper we propose a naive construction of 2-dimensional extended topological quantum field theories (TQFTs), which can be further generalized to the higher-dimension extended TQFTs.
We prove that all open string theory disc amplitudes in a flat background obey Britto-Cachazo-Feng-Witten (BCFW) on-shell recursion relations, up to a possible reality condition on a kinematic invariant. Arguments that the same holds for…
Cobordism categories have played an important role in classical geometry and more recently in mathematical treatments of quantum field theory. Here we will compute localisations of two-dimensional discrete cobordism categories. This allows…
The topological string/spectral theory correspondence establishes a precise, non-perturbative duality between topological strings on local Calabi-Yau threefolds and the spectral theory of quantized mirror curves. While this duality has been…
Entanglement has long been the subject of discussion by philosophers of quantum theory, and has recently come to play an essential role for physicists in their development of quantum information theory. In this paper we show how the…
It has been found that surface operators have a significant role in AGT relation. This duality is an outstanding consequence of M-theory, but it is actually encoded into the brane web for which the topological string can work. From this…
We introduce a symmetric monoidal $\infty$-category $\mathrm{GrCob}$ of graph cobordisms between spaces, and use the homology of its morphism spaces to define string operations. Precisely, for an $E_\infty$-ring spectrum $R$ and an oriented…
This is an expanded and updated version of a talk given at the Conference on Topics in Geometry and Physics at the University of Southern California, November 6, 1992. It is a survey talk, aimed at mathematicians AND physicists, which…