Related papers: Infinite Dimensional Topological-Holomorphic Symme…
A new topological conformal field theory in four Euclidean dimensions is constructed from N=4 super Yang-Mills theory by twisting the whole of the conformal group with the whole of the R-symmetry group, resulting in a theory that is…
A quantization of (2+1)-dimensional gravity with negative cosmological constant is presented and quantum aspects of the (2+1)-dimensional black holes are studied thereby. The quantization consists of two procedures. One is related with…
In many cases the symmetry structure of quantum field theories can be neatly encoded into their associated symmetry topological field theory (SymTFT), a topological field theory in one dimension higher. For geometrically engineered QFTs in…
In this note, based on a conference talk, we show how a 3 dimensional topological field theory leads to an algebraic gadget roughly equivalent to a quantum group. This is an expository version of some material in hep-th/9212115 (where we…
Conformal algebra on R x S^3 derived from quantized gravitational fields is examined. The model we study is a renormalizable quantum theory of gravity in four dimensions described by a combined system of the Weyl action for the traceless…
The space M_n of all isomorphism classes of n-dimensional Lie algebras over a field k has a natural non-Hausdorff topology, induced from the Segal topology by the action of GL(n). One way of studying this complicated space is by topological…
We propose an exactly solvable Hamiltonian for topological phases in $3+1$ dimensions utilising ideas from higher lattice gauge theory, where the gauge symmetry is given by a finite 2-group. We explicitly show that the model is a…
In this work, we study the simplest example of the landscape of conformal field theories: one-dimensional CFTs with finite-dimensional state space. Following the definition of quantum field theory given by G. Segal, we formulate the…
Symmetry topological field theory (SymTFT) is a convenient tool for studying finite generalized symmetries of a given quantum field theory (QFT). In particular, SymTFTs encode all the symmetry structures and properties, including anomalies.…
We initiate the study of non- and ultra-relativistic higher spin theories. For sake of simplicity we focus on the spin-3 case in three dimensions. We classify all kinematical algebras that can be obtained by all possible In\"on\"u--Wigner…
We develop an algebraic structure modeling local operators in a three-dimensional quantum field theory which is partially holomorphic and partially topological. The geometric space organizing our algebraic structure is called the raviolo…
Looking for a quantum field theory model of Archimedean algebraic geometry a class of infinite-dimensional integral representations of classical special functions was introduced. Precisely the special functions such as Whittaker functions…
The quantum symmetry of a rational quantum field theory is a finite- dimensional multi-matrix algebra. Its representation category, which determines the fusion rules and braid group representations of superselection sectors, is a braided…
The concept of conformal field theory provides a general classification of statistical systems on two-dimensional geometries at the point of a continuous phase transition. Considering the finite-size scaling of certain special observables,…
These three topics are an attempt to explicate some curiosities of the inverse problem of representation theory (i.e. having a set of operators to describe the "correct" algebraic object, which is represented by them) on simple examples…
The simplest supersymmetry algebra and superspace in three dimensional Euclidean (3dE) space is examined. Representations of the algebra are considered and the implications of restricting the space of states to states with positive definite…
The present manuscript discusses a remarkable phenomenon concerning non-linear and non-integrable field theories in $(3+1)$-dimensions, living at finite density and possessing non-trivial topological charges and non-Abelian internal…
This is a nontechnical introduction to recent work on quantum gravity using ideas from higher-dimensional algebra. We argue that reconciling general relativity with the Standard Model requires a `background-free quantum theory with local…
Boundary conditions and defects of any codimension are natural parts of any quantum field theory. Surface defects in three-dimensional topological field theories of Turaev-Reshetikhin type have applications to two-dimensional conformal…
First steps are taken in a project to construct a general class of conformal and perhaps, eventually, non-conformal quantum field theories of (n-1)-dimensional extended objects in a d=2n dimensional conformal space-time manifold M. The…