Related papers: A cellular topological field theory
In this thesis I studied the Symanzik's method for the introduction of the boundary in a field theory and, specifically, I applied this method to three Topological Field Theories of the Shwartz type: the non-abelian Chern-Simons model, the…
Topological phases of matter can be classified by using Clifford algebras through Bott periodicity. We consider effective topological field theories of quantum Hall systems and topological insulators that are Chern-Simons and BF field…
It was recently discovered that fractional quantum Hall (FQH) states can be classified by the way ground state wave functions go to zero when electrons are brought close together. Quasiparticles in the FQH states can be classified in a…
We investigate the properties of foliated gauge fields and construct several foliated field theories in 3+1d that describe foliated fracton orders both with and without matter, including the recent hybrid fracton models. These field…
The goal of this work is to describe a categorical formalism for (Extended) Topological Quantum Field Theories (TQFTs) and present them as functors from a suitable category of cobordisms with corners to a linear category, generalizing 2d…
In this paper we consider the $q$-Brauer algebra over $R$ a commutative noetherian domain. We first construct a new basis for $q$-Brauer algebras, and we then prove that it is a cell basis, and thus these algebras are cellular in the sense…
In this paper, we construct the beta function in the functorial formulation of two-dimensional quantum field theories (FQFT). A key feature of this approach is the absence of ultraviolet divergences. We show that, nevertheless, in the FQFT…
Highest-weight representations of infinite dimensional Lie algebras and Hilbert schemes of points are considered, together with the applications of these concepts to partition functions, which are most useful in physics. Partition functions…
We construct an equivariant algebraic cobordism theory for schemes with an action by a linear algebraic group over a field of characteristic zero.
We show that it is possible to construct a quantum field theory that is invariant under the translation of the noncommutative parameter $\theta_{\mu\nu}$. This is realized in a noncommutative cohomological field theory. As an example, a…
We construct a certain `cobordism category' ${\cal D}$ whose morphisms are suitably decorated cobordism classes between similarly decorated closed oriented 1-manifolds, and show that there is essentially a bijection between…
Let G be a connected complex semisimple Lie group. Webster and Yakimov have constructed partitions of the double flag variety G/B x G/B_, where (B, B_) is a pair of opposite Borel subgroups of G, generalizing the Deodhar decompositions of…
A new topological field theory is constructed, which is characterized by cubic interactions similar to those of non-abelian Chern-Simons field theories, but still retains the simplicity of the abelian case. The perturbative expansion of…
The Arf-Brown invariant $\mathit{AB}(\Sigma)$ is an 8th root of unity associated to a surface $\Sigma$ equipped with a pin$^-$ structure. In this note we investigate a certain fully extended, invertible, topological quantum field theory…
The classical action for pure Yang--Mills gauge theory can be formulated as a deformation of the topological $BF$ theory where, beside the two-form field $B$, one has to add one extra-field $\eta$ given by a one-form which transforms as the…
We introduce Compositional Quantum Field Theory (CQFT) as an axiomatic model of Quantum Field Theory, based on the principles of locality and compositionality. Our model is a refinement of the axioms of General Boundary Quantum Field…
Floer field theory is a construction principle for e.g. 3-manifold invariants via decomposition in a bordism category and a functor to the symplectic category, and is conjectured to have natural 4-dimensional extensions. This survey…
We consider topological quantum mechanics as an example of topological field theory and show that its special properties lead to numerous interesting relations for topological corellators in this theory. We prove that the generating…
Boundary conformal field theory (BCFT) is the study of conformal field theory (CFT) on manifolds with a boundary. We can use conformal symmetry to constrain correlation functions of conformal invariant fields. We compute two-point and…
In this paper, we realize the algebra of $\mathbb{Z}_2$-relations, signed partition algebras and partition algebras as tabular algebras and prove the cellularity of these algebras using the method of \cite{GM1}. Using the results of Graham…