Related papers: From 3D topological quantum field theories to 4D m…
In the framework of the Closed-Time-Path formalism, we show how topological defects may arise in Quantum Field Theory as result of a localized (inhomogeneous) condensation of particles. We demonstrate our approach on two examples; kinks in…
Quantum technologies offer the prospect to efficiently simulate sign-problem afflicted regimes in lattice field theory, such as the presence of topological terms, chemical potentials, and out-of-equilibrium dynamics. In this work, we derive…
It is believed that most (perhaps all) gapped phases of matter can be described at long distances by Topological Quantum Field Theory (TQFT). On the other hand, it has been rigorously established that in 1+1d ground states of gapped…
Gravitational theories with multiple scalar fields coupled to the metric and each other --- a natural extension of the well studied single-scalar-tensor theories --- are interesting phenomenological frameworks to describe deviations from…
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…
A modular tensor category $\mathcal{C}$ gives rise to a Reshetikhin-Turaev type topological quantum field theory which is defined on 3-dimensional bordisms with embedded $\mathcal{C}$-coloured ribbon graphs. We extend this construction to…
We investigate the most general gauging operations in 2+1 dimensional oriented field theories with finite symmetry groups, which correspond to gapped boundary conditions in 3+1 dimensional Dijkgraaf-Witten theory. The classification is…
In this paper we will present some ideas to use 3D topology for quantum computing extending ideas from a previous paper. Topological quantum computing used \textquotedblleft knotted\textquotedblright{} quantum states of topological phases…
3+1 dimensional topological phases can support loop-like excitations in addition to point-like ones, allowing for non-trivial loop-loop and point-loop braiding statistics not permitted to point-like excitations alone. Furthermore, these…
We discuss topological quantum field theories that compute topological invariants which depend on additional structures (or decorations) on three-manifolds. The $q$-series invariant $\hat{Z}(q)$ proposed by Gukov, Pei, Putrov and Vafa is an…
The surface/state correspondence suggests that the bulk co-dimensional two surface could be dual to the quantum state in the holographic conformal field theory(CFT). Inspired by the cutoff-AdS/$T\overline{T}$-deformed-CFT correspondence, we…
We construct non-semisimple $2+1$-TQFTs yielding mapping class group representations in Lyubashenko's spaces. In order to do this, we first generalize Beliakova, Blanchet and Geer's logarithmic Hennings invariants based on quantum…
We use a mix of field theoretic and holographic techniques to elucidate various properties of quantum entanglement entropy. In (3+1)-dimensional conformal field theory we study the divergent terms in the entropy when the entangling surface…
The study of gapped quantum many-body systems in three spatial dimensions has uncovered the existence of quantum states hosting quasiparticles that are confined, not by energetics but by the structure of local operators, to move along lower…
We show that reasonably well behaved 3d and 4D TQFts must contain certain algebraic structures. In 4D, we find both Hopf categories and trialgebras.
BF theory is a topological field theory that appears in different parts of theoretical physics and one of its important uses is in lower dimensional holography settings. While it can be defined as a dimensional reduction of 3D CS theory, it…
In this paper, we introduce the concept of 3-alterfolds with embedded separating surfaces. When the separating surface is decorated by a spherical fusion category, we obtain quantum invariants of 3-alterfold, which is consistent with many…
The formalism of the Rokhsar-Kivelson (RK) model has been frequently used to study topological phase transitions in 2D in terms of the deformed wavefunctions, which are RK-type wavefunctions. A key drawback of the deformed wavefunctions is…
A large class of quantum field theories on 1+1 dimensional Minkowski space, namely, certain integrable models, has recently been constructed rigorously by Lechner. However, the construction is very abstract and the concrete form of local…
As a point of departure it is suggested that Quantum Cosmology is a topological concept independent from metrical constraints. Methods of continuous topological evolution and topological thermodynamics are used to construct a cosmological…