相关论文: The Geometry of Supergravity Torsion Constraints
These are lectures notes for the introductory graduate courses on geometric complexity theory (GCT) in the computer science department, the university of Chicago. Part I consists of the lecture notes for the course given by the first author…
Geometric modeling by constraints, whose applications are of interest to communities from various fields such as mechanical engineering, computer aided design, symbolic computation or molecular chemistry, is now integrated into standard…
We examine how generalised geometries can be associated with a labelled Dynkin diagram built around a gravity line. We present a series of new generalised geometries based on the groups $\mathit{Spin}(d,d)\times\mathbb{R}^+$ for which the…
In this article, the quantum representation of the algebra among reduced twisted geometries (with respect to the Gauss constraint) is constructed in the gauge invariant Hilbert space of loop quantum gravity. It is shown that the reduced…
This thesis analyses gauged supergravities in various dimensions and their possible origin from compactifications of string theory. In the effective description the fluxes appear in the theory as deformation parameters generating a…
Some general features of locally supersymmetric theories (N=1 in four dimensions) involving Chern-Simons forms and antisymmetric tensors are sketched out. The relevance of the three-form multiplet both for the description of Chern-Simons…
In this expository paper we present a brief introduction to the geometrical modeling of some quantum computing problems. After a brief introduction to establish the terminology, we focus on quantum information geometry and ZX-calculus,…
This essay aims to summarize the main physical features arising from a new supersymmetric theory of gravitation. Based on preliminary discussions about classical field theory, cosmology, algebra and group theory, and taking formal results…
I give a short review of the theory of twisted symmetries of differential equations, emphasizing geometrical aspects. Some open problems are also mentioned.
The aim of this paper is to discuss a kinematical algebraic structure of a theory of gravity, that would be unitary, renormalizable and coupled in the same manner to both spinorial and tensorial matter fields. An analysis of the common…
We introduce new local gauge invariant variables for N=1 supersymmetric Yang-Mills theory, explicitly parameterizing the physical Hilbert space of the theory. We show that these gauge invariant variables have a geometrical interpretation,…
Interacting AdS_4 higher spin gauge theories with N \geq 1 supersymmetry so far have been formulated as constrained systems of differential forms living in a twistor extension of 4D spacetime. Here we formulate the minimal N=1 theory in…
We review exceptional field theories as the duality-covariant reformulation of maximal supergravity theories in ten and eleven dimensions, that make the underlying exceptional symmetries explicit. Beyond their structural role in unifying…
This paper is a survey of some of the developments in coarse extrinsic geometry since its inception in the work of Gromov. Distortion, as measured by comparing the diameter of balls relative to different metrics, can be regarded as one of…
We review the remarkable progress that has been made the last 15 years towards the classification of supersymmetric solutions with emphasis on the description of the bilinears and spinorial geometry methods. We describe in detail the…
We present the geometric foundations and derivations of equations of motion for symmetric teleparallel theories of gravity in the coincident gauge and covariant frameworks. We discuss the theoretical challenges introduced by the auxiliary…
In this work we present a gauge-invariant three-dimensional teleparallel supergravity theory using the Chern-Simons formalism. The present construction is based on a supersymmetric extension of a particular deformation of the Poincar\'e…
We review some recent applications of machine learning to algebraic geometry and physics. Since problems in algebraic geometry can typically be reformulated as mappings between tensors, this makes them particularly amenable to supervised…
We investigate the occurrence of divergences in maximal supergravity in various dimensions from the point of view of supersymmetry constraints on the U-duality invariant threshold functions defining the higher derivative couplings in the…
In this paper, we perform a detailed investigation on the various geometrical properties of trapped surfaces and the boundaries of trapped region in general relativity. This treatment extends earlier work on LRS II spacetimes to a general 4…