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A generic method for combinatorial constructions of intrinsic geometrical spaces is presented. It is based on the well known inverse sequences of finite graphs that determine (in the limit) topological spaces. If a pattern of the…
We argue that the non gauge invariant coupling between torsion and the Maxwell or Yang-Mills fields in Einstein-Cartan theory can not be ignored. Arguments based in the existence of normal frames in neighbourhoods, and an approximation to a…
In this paper we discuss generalizations of discrete torsion to noninvertible symmetries in 2d QFTs. One point of this paper is to explain that there are two complementary generalizations. Both generalizations are counted by $H^2(G,U(1))$…
Einstein-Cartan theory is an extension of the standard formulation of General Relativity where torsion (the antisymmetric part of the affine connection) is non-vanishing. Just as the space-time metric is sourced by the stress-energy tensor…
The present paper continues the work of the authors [arXiv:1306.6887 [gr-qc]]. Here, we study generally covariant metric-torsion theories of gravity presented more concretely, setting that their Lagrangians are \emph{manifestly} generally…
The gravitational fields of vacuumless global and gauge strings have been investigated in the context of Einstein Cartan theory under the weak field assumption of the field equations. It has been shown that global string and gauge string…
In this paper we continue our investigation of the global categorical symmetries that arise when gauging finite higher groups and their higher subgroups with discrete torsion. The motivation is to provide a common perspective on the…
A basic problem of classical field theory, which has attracted growing attention over the past decade, is to find and classify all nonlinear deformations of linear abelian gauge theories. The first part of this paper summarizes and…
We study properties of Newton-Cartan gravity under transformations into all noninertial, nonrelativistic reference frames. The set of these transformations has the structure of an infinite dimensional Lie group, called the Galilean line…
Intrinsic and extrinsic geometric properties of string world sheets in curved space-time background are explored. In our formulation, the only dynamical degrees of freedom of the string are its immersion coordinates. Classical equation of…
Generalised contact structures are studied from the point of view of reduced generalised complex structures, naturally incorporating non-coorientable structures as non-trivial fibering. The infinitesimal symmetries are described in detail,…
On the affine space containing the space $\mathcal{S}$ of quantum states of finite-dimensional systems there are contravariant tensor fields by means of which it is possible to define Hamiltonian and gradient vector fields encoding relevant…
There is an interesting dichotomy between a space-time metric considered as external field in a flat background and the same considered as an intrinsic part of the geometry of space-time. We shall describe and compare two other external…
Effective geometries arising from a hypothetical discrete structure of space-time can play an important role in the understanding of the gravitational physics beyond General Relativity. To discuss this question, we make use of lessons from…
The metric-affine and generalized geometries, respectively, are arguably the appropriate mathematical frameworks for Einstein's theory of gravity and the low-energy effective massless oriented closed bosonic string field theory. In fact,…
In a geometric unified theory there is an energy momentum equation, apart from the field equations and equations of motion. The general relativity Einstein equation with cosmological constant follows from this energy momentum equation for…
We study a deformation of a $2$-graded Poisson algebra where the functions of the phase space variables are complemented by linear functions of parity odd velocities. The deformation is carried by a $2$-form $B$-field and a bivector $\Pi$,…
String geometry theory is one of the candidates of the non-perturbative formulation of string theory. In this paper, in the bosonic closed sector of string geometry theory, we completely identify the perturbative vacua, which include…
This paper explores the application of Newton-Cartan geometry to the kinetic theory of gases that includes non-relativistic gravitational effects and the principle of general covariance. Starting with an introduction to the basics of…
A geometric construction for obtaining a prolongation of a connection to a connection of a bundle of connections is presented. This determines a natural extension of the notion of canonical energy-tensor which suits gauge and gravitational…