Results 41 to 50 of about 210 (155)

Connectomes and properties of quantum entanglement

Journal of High Energy Physics, 2023
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 phenomena of quantum ...
Dmitry Melnikov
doaj   +1 more source

Genus bounds from unrolled quantum groups at roots of unity

Journal of the London Mathematical Society, Volume 112, Issue 5, November 2025.
Abstract For any simple complex Lie algebra g$\mathfrak {g}$, we show that the degrees of the “ADO” link polynomials coming from the unrolled restricted quantum group U¯qH(g)$\overline{U}^H_q(\mathfrak {g})$ at a root of unity give lower bounds to the Seifert genus of the link.
Daniel López Neumann, Roland van der Veen   +1 more
wiley   +1 more source

Formal languages and TQFTs with defects

Journal of Geometry and Physics
A construction that assigns a Boolean 1D TQFT with defects to a finite state automaton was recently developed by Gustafson, Im, Kaldawy, Khovanov, and Lihn. We show that the construction is functorial with respect to the category of finite state automata with transducers as morphisms.
Luisa Boateng, Matilde Marcolli
openaire   +2 more sources

The three‐dimensional Seiberg–Witten equations for 3/2$3/2$‐spinors: A compactness theorem

Mathematische Nachrichten, Volume 298, Issue 10, Page 3331-3375, October 2025.
Abstract The Rarita‐Schwinger–Seiberg‐Witten (RS–SW) equations are defined similarly to the classical Seiberg–Witten equations, where a geometric non–Dirac‐type operator replaces the Dirac operator called the Rarita–Schwinger operator. In dimension 4, the RS–SW equation was first considered by the second author (Nguyen [J. Geom. Anal. 33(2023), no. 10,
Ahmad Reza Haj Saeedi Sadegh, Minh Lam Nguyen   +1 more
wiley   +1 more source

Is Einstein‐Cartan Theory Coupled to Light Fermions Asymptotically Safe?

Journal of Gravity, Volume 2013, Issue 1, 2013., 2013
The difference between Einstein′s general relativity and its Cartan extension is analyzed within the scenario of asymptotic safety of quantum gravity. In particular, we focus on the four‐fermion interaction which distinguishes the Einstein‐Cartan theory from its Riemannian limit.
Eckehard W. Mielke, Kazuharu Bamba
wiley   +1 more source

Integrality for TQFTs

Duke Mathematical Journal, 2004
We discuss ways that the ring of coefficients for a TQFT can be reduced if one restricts somewhat the allowed cobordisms. When we apply these methods to a TQFT associated to SO(3) at an odd prime p, we obtain a functor from a somewhat restricted cobordism category to the category of free finitely generated modules over a ring of cyclotomic integers :Z [
openaire   +3 more sources

Mixed-state TQFTs

, 2021
In this short note, we propose a generalization of Atiyah type TQFTs from pure states to mixed states in the sense that the Hilbert space of pure states associated to a space manifold is replaced by a quantum coherent space related to density matrices. Atiyah type TQFT is a symmetric monoidal functor from the Bord category of manifolds to the category ...
Zini, Modjtaba Shokrian, Wang, Zhenghan
openaire   +2 more sources

On the universal pairing for 2‐complexes

Bulletin of the London Mathematical Society, Volume 57, Issue 9, Page 2838-2853, September 2025.
Abstract The universal pairing for manifolds was defined and shown to lack positivity in dimension 4 in [Freedman, Kitaev, Nayak, Slingerland, Walker, and Wang, J. Geom. Topol. 9 (2005), 2303–2317]. We prove an analogous result for 2‐complexes, and show that the universal pairing does not detect the difference between simple homotopy equivalence and 3 ...
Mikhail Khovanov, Vyacheslav Krushkal, John Nicholson   +2 more
wiley   +1 more source

A Diagrammatic Temperley‐Lieb Categorification

International Journal of Mathematics and Mathematical Sciences, Volume 2010, Issue 1, 2010., 2010
The monoidal category of Soergel bimodules categorifies the Hecke algebra of a finite Weyl group. In the case of the symmetric group, morphisms in this category can be drawn as graphs in the plane. We define a quotient category, also given in terms of planar graphs, which categorifies the Temperley‐Lieb algebra.
Ben Elias, Alistair Savage
wiley   +1 more source

Relative defects in relative theories: Trapped higher-form symmetries and irregular punctures in class S

SciPost Physics, 2022
A relative theory is a boundary condition of a higher-dimensional topological quantum field theory (TQFT), and carries a non-trivial defect group formed by mutually non-local defects living in the relative theory.
Lakshya Bhardwaj, Simone Giacomelli, Max Hübner, Sakura Schäfer-Nameki
doaj   +1 more source