Related papers: On Fields over Fields
Assuming the existence of a field theory in D dimensions dual to (D+1)-dimensional flat space, governed by the asymptotic symmetries of flat space, we make some preliminary remarks about the properties of this field theory. We review…
The unconstrained frame-like formulation of an infinite tower of completely symmetric tensor gauge fields is reviewed and examined in the limit where the cosmological constant goes to zero. By partially fixing the gauge and solving the…
Derived geometry provides powerful tools to handle non-transverse intersections and singular moduli problems arising in geometry and theoretical physics. While derived algebraic geometry has been extensively developed, classical field…
A discrete field formalism exposes the physical meaning and origins of gauge fields, their symmetries and singularities. They represent a lack of a stricter field-source coherence.
Using techniques of algorithmic algebraic geometry, we present a new and efficient method for explicitly computing the vacuum space of N=1 gauge theories. We emphasize the importance of finding special geometric properties of these spaces…
We consider the volume of the gauge orbit space for gauge fields on four-dimensional complex projective space. The analysis uses a parametrization of gauge fields where gauge transformations act homogeneously on the fields, facilitating a…
Discretization of supersymmetric theories is an old problem in lattice field theory. It has resisted solution until quite recently when new ideas drawn from orbifold constructions and topological field theory have been brought to bear on…
The focus of the present thesis is on the analysis of gauge symmetry and its various impacts on gauge theories. In the first part of this thesis, we have studied different aspects of symmetries in connection with various field and string…
A space for gauge theories is defined, using projective limits as subsets of Cartesian products of homomorphisms from a lattice on the structure group. In this space, non-interacting and interacting measures are defined as well as functions…
In a completely systematic and geometric way, we derive maximal and half-maximal supersymmetric gauged double field theories in lower than ten dimensions. To this end, we apply a simple twisting ansatz to the $D=10$ ungauged maximal and…
The zero modes of closed strings on a torus --the torus coordinates plus dual coordinates conjugate to winding number-- parameterize a doubled torus. In closed string field theory, the string field depends on all zero-modes and so can be…
This paper focuses on polynomial dynamical systems over finite fields. These systems appear in a variety of contexts, in computer science, engineering, and computational biology, for instance as models of intracellular biochemical networks.…
We consider the supersymmetric field theories on the noncommutative $R^4$ using the superspace formalism on the commutative space. The terms depending on the parameter of the noncommutativity $\Theta$ are regarded as the interactions. In…
We study N=1 supersymmetric U(N) gauge theories coupled to an adjoint chiral field with superpotential. We consider the full supersymmetric moduli space of these theories obtained by adding all allowed chiral operators. These include…
In this note we summarize a few of the many recent developments in two-dimensional quantum field theories. We begin with a review of the current state of quantum sheaf cohomology, a heterotic analogue of quantum cohomology. We then turn to…
A new gauge theory of gravity is presented. The theory is constructed in a flat background spacetime and employs gauge fields to ensure that all relations between physical quantities are independent of the positions and orientations of the…
We study the gauge/gravity duality for theories with four dimensional ${\cal N}=2$ supersymmetries. We consider the large class of generalized quiver field theories constructed recently by one of us (D.G.). These field theories can also be…
A foundational investigation of the basic structural properties of two-dimensional anomalous gauge theories is performed. The Hilbert space is constructed as the representation of the intrinsic local field algebra generated by the…
By studying the geometric properties of correlation functions on the theory space, we are naturally led to a connection for the infinite dimensional vector bundle of composite fields over the theory space. We show how the short distance…
In this paper we study 3-form gauge fields in four-dimensional N=1 supersymmetric theories. We give the sigma model action together with its Poincare dual action for massless and massive 3-forms. The resulting target space geometries are…