Related papers: Quantum Wilson surfaces and topological interactio…
The N=2* Super-Yang-Mills theory (SYM*) undergoes an infinite sequence of large-N quantum phase transitions. We compute expectation values of Wilson loops in k-symmetric and antisymmetric representations of the SU(N) gauge group in this…
The space of states and operators for a large class of background independent theories of quantum spacetime dynamics is defined. The SU(2) spin networks of quantum general relativity are replaced by labelled compact two-dimensional…
In the context of two-dimensional large-$N$ lattice Yang--Mills theory, we perform a refined study of the surface sums defined in the companion work [BCSK24]. In this setting, the surface sums are a priori expected to exhibit significant…
The analysis of the large-$N$ limit of $U(N)$ Yang-Mills theory on a surface proceeds in two stages: the analysis of the Wilson loop functional for a simple closed curve and the reduction of more general loops to a simple closed curve. In…
A rigorous analysis is presented for the entanglement spectrum of quantum many-body states possessing a higher-form group-representation symmetry generated by topological Wilson loops, which is generally non-invertible. A general framework…
After the work of Seiberg and Witten, it has been seen that the dynamics of N=2 Yang-Mills theory is governed by a Riemann surface $\Sigma$. In particular, the integral of a special differential $\lambda_{SW}$ over (a subset of) the periods…
We construct nearly topological Yang-Mills theories on eight dimensional manifolds with a special holonomy group. These manifolds are the Joyce manifold with $Spin(7)$ holonomy and the Calabi-Yau manifold with SU(4) holonomy. An invariant…
We present a summary of the progress made in the last few years on topological quantum field theory in four dimensions. In particular, we describe the role played by duality in the developments which led to the Seiberg-Witten invariants and…
In these lecture notes we explain a connection between Yang-Mills theory on arbitrary Riemann surfaces and two types of topological field theory, the so called $BF$ and cohomological theories. The quantum Yang-Mills theory is solved exactly…
We consider generic properties of the moduli space of vacua in $N=2$ supersymmetric Yang--Mills theory recently studied by Seiberg and Witten. We find, on general grounds, Picard--Fuchs type of differential equations expressing the…
Large $N$ two-dimensional QCD on a cylinder and on a vertex manifold (a sphere with three holes) is investigated. The relation between the saddle-point description and the collective field theory of QCD$_2$ is established. Using this…
It is shown that two$(1 + 1)$-dimensional (2D) free Abelian- and self-interacting non-Abelian gauge theories (without any interaction with matter fields) belong to a new class of topological field theories. These new theories capture…
We propose a Lorentz-covariant Yang-Mills ``spin-gauge'' theory, where the function valued Pauli matrices play the role of a non-scalar Higgs-field. As symmetry group we choose $SU(2) \times U(1)$ of the 2-spinors describing…
We study a model of quantum Yang-Mills theory with a finite number of gauge invariant degrees of freedom. The gauge field has only a finite number of degrees of freedom since we assume that space-time is a two dimensional cylinder. We…
We investigate states on the surface of strong and weak topological insulators and superconductors that have been gapped by a symmetry breaking term. The surface of a strong 3D topological insulator gapped by a magnetic material is well…
We consider 5d $\mathcal{N}=1$ SU(2) super Yang-Mills theory on $X\times S^1$, with $X$ a closed smooth four-manifold. A partial topological twisting along $X$ renders the theory formally independent of the metric on $X$. The theory depends…
The goal of these lectures is to give an introduction to the study of the fundamental group of a Klein surface. We start by reviewing the topological classification of Klein surfaces and by explaining the relation with real algebraic…
Gauging a finite group 0-form symmetry $G$ of a quantum field theory (QFT) results in a QFT with a Rep$(G)$ symmetry implemented by Wilson lines. The group $G$ determines the fusion of Wilson lines. However, in general, the fusion rules of…
Dijkgraaf-Witten theories are extended three-dimensional topological field theories of Turaev-Viro type. They can be constructed geometrically from categories of bundles via linearization. Boundaries and surface defects or interfaces in…
We study entanglement in two-dimensional Yang-Mills theory, viewed as a quasi-topological model of emergent space. The most familiar class of states in this theory are states defined by Euclidean path integrals over Riemann surfaces.…