Related papers: A Moyal Quantization of the Continuous Toda Field
We describe a compactification of the six-dimensional (2,0) theory on a four-sphere which gives rise to a two-dimensional Toda theory at long distances. This construction realizes chiral Toda fields as edge modes trapped near the poles of…
We construct a set of non-rational conformal field theories that consist of deformations of Toda field theory for sl(n). Besides conformal invariance, the theories still enjoy a remnant infinite-dimensional affine symmetry. The case n=3 is…
We present some methods of determining explicit solutions for self-dual supermembranes in 4+1 and 8+1 dimensions with spherical or toroidal topology. For configurations of axial symmetry, the continuous SU(\infty) Toda equation turns out to…
A geometric formulation of the Moyal deformation for the Self-dual Yang-Mills theory and the Chiral Model approach to Self-dual gravity is given. We find in Fedosov's geometrical construction of deformation quantization the natural…
In this paper we study the quantum cosmology of homogeneous and isotropic cosmology, via the Weyl-Wigner-Groenewold-Moyal formalism of phase space quantization, with perfect fluid as a matter source. The corresponding quantum cosmology is…
We discuss geometrical aspects of Toda Fields generalizing the links between Liouville gravity and uniformization of Riemann surfaces of genus greater than one. The framework is the interplay between the hermitian and the holomorphic…
The self-duality equations of Chern-Simons Higgs theory in a background curved spacetime are studied by making use of the U(1) gauge potential decomposition theory and $\phi$-mapping method. The special form of the gauge potential…
The double copy relates scattering amplitudes and classical solutions in Yang-Mills theory, gravity, and related field theories. Previous work has shown that this has an explicit realisation in self-dual YM theory, where the equation of…
We present a simple, systematic and practical method to construct conformally invariant equations in arbitrary Riemann spaces. This method that we call "Weyl-to-Riemann" is based on two features of Weyl geometry. i) A Weyl space is defined…
Gauge theories on a space-time that is deformed by the Moyal-Weyl product are constructed by twisting the coproduct for gauge transformations. This way a deformed Leibniz rule is obtained, which is used to construct gauge invariant…
A. Weinstein has conjectured a nice looking formula for a deformed product of functions on a hermitian symmetric space of non-compact type. We derive such a formula for symmetric symplectic spaces using ideas from geometric quantization and…
We construct a family of constant curvature metrics on the Moyal plane and compute the Gauss-Bonnet term for each of them. They arise from the conformal rescaling of the metric in the orthonormal frame approach. We find a particular…
Four-dimensional quaternion-Kaehler metrics with an isometry are determined by solutions to the SU($\infty$) Toda equation. We set up a perturbation theory to construct approximate solutions to the latter which can be interpreted as…
We prove that the self-interacting scalar field on the four-dimensional degenerate Moyal plane is renormalisable to all orders when adding a suitable counterterm to the Lagrangean. Despite the apparent simplicity of the model, it raises…
The Bohr-Sommerfeld approximation to the eigenvalues of a one-dimensional quantum Hamiltonian is derived through order $\hbar^2$ (i.e., including the first correction term beyond the usual result) by means of the Moyal star product. The…
We study the Jones and Tod correspondence between selfdual conformal 4-manifolds with a conformal vector field and abelian monopoles on Einstein-Weyl 3-manifolds, and prove that invariant complex structures correspond to shear-free geodesic…
Developing on the ideas of R. Stora and coworkers, a formulation of two dimensional field theory endowed with extended conformal symmetry is given, which is based on deformation theory of holomorphic and Hermitian spaces. The geometric…
Liouville and Toda gravity theories with non-vanishing interaction potentials have spectra obtained by dividing the free-field spectra for these cases by the Weyl group of the corresponding $A_1$ or $A_2$ Lie algebra. We study the canonical…
Based on the work of Guillarmou, Kupiainen, and Rhodes, we construct compactified imaginary Toda theory on closed Riemann surfaces, extending the rank-one construction to the higher-rank setting. This theory is expected to describe critical…
I show that solutions of the SU(infinity) Toda field equation generating a fixed Einstein-Weyl space are governed by a linear equation on the Einstein-Weyl space. From this, obstructions to the existence of Toda solutions generating a given…