Related papers: Tensor network approach to electromagnetic duality…
Let $M$ be an $n$-dimensional manifold, $V$ the space of a representation $\rho: GL(n)\longrightarrow GL(V)$. Locally, let $T(V)$ be the space of sections of the tensor bundle with fiber $V$ over a sufficiently small open set $U\subset M$,…
The goal of this paper is to exhibit a deep relation between the partition function of the Ising model on a planar trivalent graph and the generating series of the spin network evaluations on the same graph. We provide respectively a…
We consider the general free field theory such that system of equations of motion includes a subsystem with a special property. If the subsystem is considered by itself, it would be a topological field theory having no local degrees of…
We describe the doubled space of Double Field Theory as a group manifold $G$ with an arbitrary generalized metric. Local information from the latter is not relevant to our discussion and so $G$ only captures the topology of the doubled…
We investigate self-dualities in three-dimensional $\mathcal{N}=2$ supersymmetric gauge theories. The electric and magnetic theories share the same gauge group. The examples include $SU(2N)$, $SO(7)$ and $SO(8)$ with various matter…
We study classical noncommutative (NC) electromagnetic duality in both 3D and 4D space-times through the Seiberg-Witten (SW) map to all orders in theta. We evaluate the role of space-time dimensions, of the gauge coupling constant g^2…
We introduce a family of dual-unitary circuits in 1+1 dimensions which constitute a discrete analog of conformal field theories. These circuits are quantum cellular automata which are invariant under the joint action of Lorentz and scale…
String and particle braiding statistics are examined in a class of topological orders described by discrete gauge theories with a gauge group $G$ and a 4-cocycle twist $\omega_4$ of $G$'s cohomology group…
Gauge theories on graphs and networks are attracting increasing attention not only as approaches to quantum gravity but also as models for performing quantum computation. Here we propose a Dirac gauge theory for topological spinors in $3+1$…
The Hilbert space of a quantum system with internal global symmetry $G$ decomposes into sectors labelled by irreducible representations of $G$. If the system is chaotic, the energies in each sector should separately resemble ordinary random…
For any quantum system invariant under gauging a higher-form global symmetry, we construct a non-invertible topological defect by gauging in only half of spacetime. This generalizes the Kramers-Wannier duality line in 1+1 dimensions to…
We find the canonical and Belinfante energy-momentum tensors and their nonzero traces. We note that the dilatation symmetry is broken and the divergence of the dilatation current is proportional to the topological mass of the gauge field.…
It has been observed that certain localizations of the spectrum of topological modular forms are self-dual (Mahowald-Rezk, Gross-Hopkins). We provide an integral explanation of these results that is internal to the geometry of the…
We study 2-d $\phi F$ gauge theories with the objective to understand, also at the quantum level, the emergence of induced gravity. The wave functionals - representing the eigenstates of a vanishing flat potential - are obtained in the…
Bi-spinor and G-structure methods are used to classify the possible consistent truncations of type II supergravity to $d=6$ Einstein-Maxwell (gauged) supergravity, and its consistent sub-sectors. In the absence of R-symmetry gauging and a…
The algebraic structure of representation theory naturally arises from 2D fixed-point tensor network states, which conceptually formulates the pattern of long-range entanglement realized in such states. In 3D, the same underlying structure…
We prove the first nontrivial reconstruction theorem for modular tensor categories: the category associated to any twisted Drinfeld double of any finite group, can be realised as the representation category of a completely rational…
Tensor networks implementing quantum error correcting codes have recently been used to construct toy models of holographic duality explicitly realizing some of the more puzzling features of the AdS/CFT correspondence. These models reproduce…
We consider the finite generation property for cohomology of a finite tensor category C, which requires that the self-extension algebra of the unit Ext*_C(1,1) is a finitely generated algebra and that, for each object V in C, the graded…
We study lattice Hamiltonian realisations of (3+1)d Dijkgraaf-Witten theory with gapped boundaries. In addition to the bulk loop-like excitations, the Hamiltonian yields bulk dyonic string-like excitations that terminate at gapped…