Related papers: Counterexamples in Levin-Wen string-net models, gr…
The 2+1 dimensional lattice models of Levin and Wen [PRB 71, 045110 (2005)] provide the most general known microscopic construction of topological phases of matter. Based heavily on the mathematical structure of category theory, many of the…
We develop a graphical calculus for monoidal categories equipped with twisted pivotal structures, which are a generalization of pivotal structures originating from the study of orientation structures in the context of the Cobordism…
We derive a Kontsevich-type matrix model for the c=1 string directly from the W-infinity solution of the theory. The model that we obtain is different from previous proposals, which are proven to be incorrect. Our matrix model contains the…
We consider N=1 supersymmetric U(N), SO(N), and Sp(N) gauge theories, with two-index tensor matter and added tree-level superpotential, for general breaking patterns of the gauge group. By considering the string theory realization and…
Levin-Wen models are microscopic spin models for topological phases of matter in (2+1)-dimension. We introduce a generalization of such models to (3+1)-dimension based on unitary braided fusion categories, also known as unitary premodular…
We prove the conjectured classification of topological phases in two spatial dimensions with gappable boundary, in a simplified setting. Two gapped ground states of lattice Hamiltonians are in the same quantum phase of matter, or…
String theory avoids the ultraviolet infinities that arise in trying to quantize gravity. It is also more predictive than conventional quantum field theory, one aspect of this being the way that it contributed to the emergence of the…
We present Voevodsky's construction of a model of univalent type theory in the category of simplicial sets. To this end, we first give a general technique for constructing categorical models of dependent type theory, using universes to…
Classical and quantum Chern-Simons with gauge group $\text{U}(1)^N$ were classified by Belov and Moore in \cite{belov_moore}. They studied both ordinary topological quantum field theories as well as spin theories. On the other hand a…
As observed recently by various people the topos $\mathbf{sSet}$ of simplicial sets appears as essential subtopos of a topos $\mathbf{cSet}$ of cubical sets, namely presheaves over the category $\mathbf{FL}$ of finite lattices and monotone…
We describe a completely algebraic axiom system for intertwining operators of vertex algebra modules, using algebraic flat connections, thus formulating the concept of a {\em tree algebra}. Using the Riemann-Hilbert correspondence, we…
This paper examines the string topology category of a manifold, defined by Blumberg, Cohen and Teleman. Since the string topology category is a subcategory of a compactly generated triangulated category, the machinery of stratification,…
Chern-Simons Theories with gauge super-groups appear naturally in string theory and they possess interesting applications in mathematics, e.g. for the construction of knot and link invariants. This paper is the first in a series where we…
We use finite group topological lattice gauge theory, also known as the quantum double model, as a lens to explore a notion of topological order enriched by a non-invertible symmetry. For invertible symmetry enriched topological order,…
It has been argued by Ishikawa and Kato that by making use of a specific bosonization, $c_M=1$ string theory can be regarded as a constrained topological sigma model. We generalize their construction for any $(p,q)$ minimal model coupled to…
Noncompact groups, similar to those that appeared in various supergravity theories in the 1970's, have been turning up in recent studies of string theory. First it was discovered that moduli spaces of toroidal compactification are given by…
We study the Wegner-Wilson loops in the string-net model of Levin and Wen in the presence of a string tension. The latter is responsible for a phase transition from a topological deconfined phase (weak tension) to a trivial confined phase…
{}From the ordinary tensile string we derive a geometric action for the tensionless ($T=0$) string and discuss its symmetries and field equations. The Weyl symmetry of the usual string is shown to be replaced by a global space-time…
Methods for predicting material properties often rely on empirical models or approximations that overlook the fundamental topological nature of quantum interactions. We introduce a topological framework based on string theory and graph…
We define a category $v\mathcal{T}$ of tangles diagrams drawn on surfaces with boundaries. On the one hand we show that there is a natural functor from the category of virtual tangles to $v\mathcal{T}$ which induces an equivalence of…