Related papers: String Holonomy and Extrinsic Geometry in Four-dim…
We consider BF-type topological field theory coupled to non-dynamical particle and string sources on spacetime manifolds of the form $\IR^1\times\MT$, where $\MT$ is a 3-manifold without boundary. Canonical quantization of the theory is…
Canonical quantization of abelian BF-type topological field theory coupled to extended sources on generic d-dimensional manifolds and with curved line bundles is studied. Sheaf cohomology is used to construct the appropriate topological…
Recently, a topological field theory of membrane-matter coupled to BF theory in arbitrary spacetime dimensions was proposed [1]. In this paper, we discuss various aspects of the four-dimensional theory. Firstly, we study classical solutions…
Non-relativistic charged particles and strings coupled with abelian gauge fields are quantized in a geometric representation that generalizes the Loop Representation. We consider three models: the string in self-interaction through a…
This review explores recent advances in the theory of $T\bar{T}$ deformation, an irrelevant yet solvable deformation of quantum field theories defined via the quadratic form of the energy-momentum tensor. It addresses classical and quantum…
Deformations of topological open string theories are described, with an emphasis on their algebraic structure. They are encoded in the mixed bulk-boundary correlators. They constitute the Hochschild complex of the open string algebra -- the…
One of the most intriguing aspects of Chern-Simons-type topological models is the fractional statistics of point particles which has been shown essential for our understanding of the fractional quantum Hall effects. Furthermore these ideas…
Graphs are topological spaces that include broader objects than discretized manifolds, making them interesting playgrounds for the study of quantum phases not realized by symmetry breaking. In particular they are known to support anyons of…
Nonrelativistic string theory is a self-contained corner of string theory, with its string spectrum enjoying a Galilean-invariant dispersion relation. This theory is unitary and ultraviolet complete, and can be studied from first…
We construct invertible field theories generalizing abelian prequantum spin Chern-Simons theory to manifolds of dimension 4k+3 endowed with a Wu structure of degree 2k+2. After analysing the anomalies of a certain discrete symmetry, we…
The standard, gapped entanglement boundary condition in Chern Simons theory breaks the topological invariance of the theory by introducing a complex structure on the entangling surface. This produces an infinite dimensional subregion…
It is shown that the topological invariants associated with the two-dimensional world-surface in string theory have nontrivial fluctuations around their nonexistent classical dynamics. Additionally it is proved that the underlying…
As of today there exist consistent, gauge-invariant string field theories describing all string theories: bosonic open and closed strings, open superstrings, heterotic strings and type II strings. The construction of these theories require…
It is shown that the canonical formulation of the abelian BF theory in D = 3 allows to obtain topological invariants associated to curves and points in the plane. The method consists on finding the Hamiltonian on-shell of the theory coupled…
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…
We construct deformation invariants of $2|1$-dimensional Euclidean field theories valued in a cohomology theory approximating topological modular forms. This implies several results anticipated by Stolz and Teichner and gives the first…
The field content of the two dimensional string theory consists of the dynamical tachyon field and some nonpropagating fields which consist in the topological sector of this theory. We propose in this paper to study this topological sector…
We study the differential geometry of principal G-bundles whose base space is the space of free paths (loops) on a manifold M. In particular we consider connections defined in terms of pairs (A,B), where A is a connection for a fixed…
The nonrelativistic bosonic string theory in a curved manifold is formulated here using gauging of symmetry approach ( Galilean Gauge theory ) . The corresponding model in flat space has some global symmetries . By localizing these…
We investigate the physics of the E-string theory and its compactifications as well as their applications to four-dimensional topology. In particular, we compute the partition function of the topologically twisted theory on $M_4\times T^2$,…