Related papers: Decomposing Quantum Field Theories
It is argued that quantum gravity has an interpretation as a topological field theory provided a certain constraint from the path intergral measure is respected. The constraint forces us to couple gauge and matter fields to gravity for…
We prove a decomposition formula for the dimensional reduction of an extended topological field theory that arises as an orbifold of an equivariant topological field theory. Our decomposition formula can be expressed in terms of a…
We introduce Compositional Quantum Field Theory (CQFT) as an axiomatic model of Quantum Field Theory, based on the principles of locality and compositionality. Our model is a refinement of the axioms of General Boundary Quantum Field…
Gravitational theories with multiple scalar fields coupled to the metric and each other --- a natural extension of the well studied single-scalar-tensor theories --- are interesting phenomenological frameworks to describe deviations from…
We argue that rational conformally invariant quantum field theories in two dimensions are closely related to torsion elements of the algebraic K-theory group K_3(C). If such a theory has an integrable matrix perturbation with purely elastic…
Noncommutative (NC) quantum field theory is the subject of many analyses on formal and general aspects looking for deviations and, therefore, potential noncommutative spacetime effects. Within of this large class, we may now pay some…
This thesis is broadly split into two parts. In the first part, simple state sum models for minimally coupled fermion and scalar fields are constructed on a $1$-manifold. The models are independent of the triangulation and give the same…
In this talk I briefly review recent developments in quantum field theories on a noncommutative Euclidean space, with Heisenberg-like commutation relations between coordinates. I will be concentrated on new physics learned from this…
We construct spaces of 1-dimensional supersymmetric Euclidean field theories and show that they represent real or complex K-theory. A noteworthy feature of our bordism category is that the identity bordism of a point is connected to…
In [arXiv:0808.1677] 3 dimensional field theories are proposed to on-shell represent N=8 SUSY algebra and SO(7) or SO(4)xSO(4) subgroups of full SO(8) automorphism. They are theories of 8 scalar and 8 spinor matrix fields with Yukawa,…
This paper fires the opening salvo in the systematic construction of the lattice-continuum correspondence, a precise dictionary that describes the emergence of continuum quantum theories from finite, nonperturbatively defined models…
Supersymmetric gauge theories have played a central role in applications of quantum field theory to mathematics. Topologically twisted supersymmetric gauge theories often admit a rigorous mathematical description: for example, the Donaldson…
In these lectures we present a general introduction to topological quantum field theories. These theories are discussed in the framework of the Mathai-Quillen formalism and in the context of twisted N=2 supersymmetric theories. We discuss…
In these lecture notes, I review how to use large N techniques to solve quantum field theories in various dimensions. In particular, the case of N-dimensional quantum mechanics, non-relativistic cold and dense neutron matter, and scalar…
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…
A geometric interpretation of quantum self-interacting string field theory is given. Relations between various approaches to the second quantization of an interacting string are described in terms of the geometric quantization. An algorithm…
We present a new group field theory describing 3d Riemannian quantum gravity coupled to matter fields for any choice of spin and mass. The perturbative expansion of the partition function produces fat graphs colored with SU(2) algebraic…
Studying a quantum field theory involves a choice of space-time manifold and a choice of background for any global symmetries of the theory. We argue that many more choices are possible when specifying the background. In the context of…
We show that the equations of motion defined over a specific field space are realizable as operator conditions in the physical sector of a generalized Floer theory defined over that field space. The ghosts associated with such a…
In this paper we consider non-anticommutative field theories in $\mathcal{N} =2$ superspace formalism on three-dimensional manifolds with a boundary. We modify the original Lagrangian in such a way that it preserves half the supersymmetry…