Related papers: Area-dependent quantum field theory with defects
The interpretation of D-branes in terms of open strings has lead to much interest in boundary conditions of two-dimensional conformal field theories (CFTs). These studies have deepened our understanding of CFT and allowed us to develop new…
Neural network field theory formulates field theory as a statistical ensemble of fields defined by a network architecture and a density on its parameters. We extend the construction to topological settings via the inclusion of discrete…
N=2 supersymmetric Yang--Mills theories coupled to matter are considered in the Wess--Zumino gauge. The supersymmetries are realized nonlinearly and the anticommutator between two susy charges gives, in addition to translations, gauge…
We give two presentations for bordisms of $S^2$ in the 3-dimensional oriented bordism category $\operatorname{Cob}(3) $, encoding the algebraic structures on $S^2$. After passing through topological field theories, we define two kinds of…
The general boundary formulation of quantum field theory is applied to a massive scalar field in two dimensional Rindler space. The field is quantized according to both the Schr\"odinger-Feynman quantization prescription and the holomorphic…
The four-dimensional topological Yang-Mills theory with two anticommuting charges is naturally formulated on K\"ahler manifolds. By using a superspace approach we clarify the structure of the Faddeev-Popov sector and determine the total…
We introduce a "web-based formalism" for describing the category of half-supersymmetric boundary conditions in $1+1$ dimensional massive field theories with ${\cal N}=(2,2)$ supersymmetry and unbroken $U(1)_R$ symmetry. We show that the…
A great part of the mathematical foundations of topological quantum computation is given by the theory of modular categories which provides a description of the topological phases of matter such as anyon systems. In the near future the…
We present a family of nonrelativistic Yang-Mills gauge theories in D+1 dimensions whose free-field limit exhibits quantum critical behavior with gapless excitations and dynamical critical exponent z=2. The ground state wavefunction is…
This note is intended as an introduction to the functorial formulation of quantum field theories with defects. After some remarks about models in general dimension, we restrict ourselves to two dimensions - the lowest dimension in which…
The 3+1 dimensional Yang-Mills theory with the Pontryagin term included is studied on manifolds with a boundary. Based on the geometry of the universal bundle for Yang-Mills theory, the symplectic structure of this model is exhibited. The…
In [1] (hep-th/0211069), the author has discussed the quantum parameter space of the N=1 super Yang-Mills theory with one adjoint Higgs field Phi, tree-level superpotential W_tree = m (Phi^2)/2 + g (Phi^3)/3$, and gauge group U(Nc). In…
Over the past five years, there has been significant progress on the problem of quantization of diffeomorphism covariant field theories with {\it local} degrees of freedom. The absence of a background space-time metric in these theories…
Gauge theories possess nonlocal features that, in the presence of boundaries, inevitably lead to subtleties. We employ geometric methods rooted in the functional geometry of the phase space of Yang-Mills theories to: (1) characterize a…
We extend quantum field theory by including purely virtual "cloud" sectors, to define physical off-shell correlation functions of gauge invariant quark and gluon fields, without affecting the $S$ matrix amplitudes. The extension is made of…
We describe a class of six-dimensional conformal field theories that have some properties in common with and possibly are related to a subsector of the tensionless string theories. The latter theories can for example give rise to…
It is commonly understood that the Yang-Mills non-Abelian gauge fields is the natural generalization of the well known Abelian gauge group symmetry $U(1)$ in the electrodynamics. Taking into account that the problems of the localization and…
We construct some extension ({\it Stable Field Theory}) of Cohomological Field Theory. The Stable Field Theory is a system of homomorphisms to some vector spaces generated by spheres and disks with punctures. It is described by a formal…
We study the structure of topological defects for finite Abelian symmetries in quantum field theories, and argue on physical grounds that they satisfy the definition of a higher fusion category proposed by Johnson-Freyd. Our primary focus…
We present a construction of cellular BF theory (in both abelian and non-abelian variants) on cobordisms equipped with cellular decompositions. Partition functions of this theory are invariant under subdivisions, satisfy a version of the…