Related papers: The Geometry of Deformation Quantization and Self-…

We examine a generalisation of the usual self-duality equations for Yang-Mills theory when the colour space admits a non-trivial involution. This involution allows us to construct a non-trivial twist which may be combined with the Hodge…

We propose a natural Fedosov type quantization of generalized Lagrange models and gravity theories with metrics lifted on tangent bundle, or extended to higher dimension, following some stated geometric/ physical conditions (for instance,…

Infinite-dimensional algebras of hidden symmetries of the self-dual Yang-Mills equations are considered. A current-type algebra of symmetries and an affine extension of conformal symmetries introduced recently are discussed using the…

In previous work (Singh, 2011), we constructed an action in six dimensions using Yang-Mills fields and an auxiliary Abelian field. Here we first write down all the equations of motion and the constraints which arise from such an action.…

Plebanski's second heavenly equation reduces the problem of finding a self-dual Einstein metric to solving a non-linear second-order PDE for a single function. Plebanski's original equation is for self-dual metrics obtained as perturbations…

It is proven that the physical measure for the two-dimensional Yang-Mills theory is purely singular with respect to the kinematical Ashtekar-Lewandowski measure. For this, an explicit decomposition of the gauge orbit space into supports of…

We conjecture that many (maybe all) integrable equations and spin systems in 2+1 dimensions can be obtained from the (2+1)-dimensional Gauss-Mainardi-Codazzi and Gauss-Weingarten equations, respectively. We also show that the…

Integration of Kirillov form on a coadjoint orbit of Virasoro algebra yields the coupling of a background field to Polyakov's two dimensional quantum gravity. This background field is used to be called the diffeomorphism field. Einstein's…

This dissertation is an exposition of Kontsevich's proof of the formality theorem and the classification of deformation quantisation on a Poisson manifold. We begin with an account of the physical background and introduce the Weyl-Moyal…

Unimodular gravity can be formulated so that transverse diffeomorphisms and Weyl transformations are symmetries of the theory. For this formulation of unimodular gravity, we work out the two-point and three-point $h_{\mu\nu}$ contributions…

We present a description of two dimensional Yang-Mills gauge theory on the plane and on compact surfaces, examining the topological, geometric and probabilistic aspects.

The possible role of gravity in a noncommutative geometry is investigated. Due to the Moyal *-product of fields in noncommutative geometry, it is necessary to complexify the metric tensor of gravity. We first consider the possibility of a…

This paper studies the quantization of the deformation of Hessian structures on a two-dimensional vector space, in the framework of Koszul-Vinberg algebras. We analyze how Hessian structures can be deformed to obtain quantum structures…

We couple a recently-established N=1 globally supersymmetric self-dual Yang-Mills multiplet in three dimensions to supergravity. This becomes possible due to our previous result on globally supersymmetric formulation based on a compensator…

We propose that chiral two-dimensional Yang-Mills theory on a Riemann surface is dual to a deformed stationary subsector of the Gromov-Witten theory of that Riemann surface. Firstly, we argue that the algebraic structure that underlies the…

In this thesis, we derive the equations of motion of Chiral Higher Spin Gravity (HiSGRA) in terms of its underlying $L_\infty$-algebra. Chiral HiSGRA contains self-dual Yang-Mills and self-dual gravity as closed subsectors, which themselves…

A method for the deformation quantization of coadjoint orbits of semisimple Lie groups is proposed. It is based on the algebraic structure of the orbit. Its relation to geometric quantization and differentiable deformations is explored.

Spherically symmetric gravity in Ashtekar variables coupled to Yang-Mills theory in two dimensions and its relation to dilaton gravity and Poisson sigma models are discussed. After introducing its loop quantization, quantum corrections for…

We point out that the Cartan geometry known as the second-order conformal structure provides a natural differential geometric framework underlying gauge theories of conformal gravity. We are concerned by two theories: the first one will be…

We consider the four-dimensional reduced quasi-classical self-dual Yang--Mills equation and show that non-triviality of the second exotic cohomology group of its symmetry algebra implies existence of a two-component integrable…