Related papers: Differential and integral invariants under Mobius …

We deform two-dimensional topological gravity by making use of its gauge theory formulation. The obtained noncommutative gravity model is shown to be invariant under a class of transformations that reduce to standard diffeomorphisms once…

In modular invariant models of flavor, observables must be modular invariant. The observables discussed so far in the literature are functions of the modulus $\tau$ and its conjugate, $\bar\tau$. We point out that certain combinations of…

We consider families of geometries of D--dimensional space, described by a finite number of parameters. Starting from the De Witt metric we extract a unique integration measure which turns out to be a geometric invariant, i.e. independent…

Conformal group of transformations in the momentum space, consisting of translations $p'_{\mu}=p_{\mu}+h_{\mu}$, rotations $p'_{\mu}=\Lambda^{\nu}_{\mu}p_{\nu}$, dilatation $p'_{\mu}=\lambda p_{\mu}$ and inversion $p'_{\mu}=…

For every diffeomorphism $\varphi:M\to N$ between 3--dimensional Riemannian manifolds $M$ and $N$ there are in general locally two 2--dimensional distributions $D_{\pm}$ such that $\varphi$ is conformal on both of them. We state necessary…

In this work we derive braid group representations and Stokes matrices for Liouville conformal blocks with one irregular operator. By employing the Coulomb gas formalism, the corresponding conformal blocks can be interpreted as…

Using the example of Liouville theory, we show how the separation into left- and rightmoving degrees of freedom of a nonrational conformal field theory can be made explicit in terms of its integrable structure. The key observation is that…

Using diffeomorphism group vector fields on $\mathbb{C}$-multiplied tori and the related Lie-algebraic structures, we study multi-dimensional dispersionless integrable systems that describe conformal structure generating equations of…

It is widely believed that the celebrated 2D Ising model at criticality has a universal and conformally invariant scaling limit, which is used in deriving many of its properties. However, no mathematical proof of universality and conformal…

Classical invariant theory of a complex reflection group $W$ highlights three beautiful structures: -- the $W$-invariant polynomials constitute a polynomial algebra, over which -- the $W$-invariant differential forms with polynomial…

We investigate functionals defined on manifolds through parameterizations. If they are to be meaningful, from a geometrical viewpoint, they ought to be invariant under reparameterizations. Standard, local, integral functionals with this…

We establish the deformation theory of Lie groupoid morphisms, describe the corresponding deformation cohomology of morphisms, and show the properties of the cohomology. We prove its invariance under isomorphisms of morphisms. Additionally,…

Every locally normal representation of a local chiral conformal quantum theory is covariant with respect to global conformal transformations, if this theory is diffeomorphism covariant in its vacuum representation. The unitary, strongly…

We consider a projective transformation and establish the invariants for this transformation group up to order seven. We use the obtained invariants to construct a class of nonlinear evolution equations and identify some symmetry-integrable…

The Liouville equation is well known to be linearizable by a point transformation. It has an infinite dimensional Lie point symmetry algebra isomorphic to a direct sum of two Virasoro algebras. We show that it is not possible to discretize…

It is shown that the AdS_3 gravity action with boundary terms is non invariant under diffeomorphisms and that its Lie derivative has the form of the Weyl anomaly in two dimensions. This variation is compensated by a Weyl transformation of…

This is a brief overview of our work on the theory of group invariant solutions to differential equations. The motivations and applications of this work stem from problems in differential geometry and relativistic field theory. The key…

We investigate the problem of estimating a smooth invertible transformation f when observing independent samples X_1, ..., X_n ~ P \circ f, where P is a known measure. We focus on the two dimensional case where P and f are defined on R^2.…

Conformally-invariant and pure, scale-invariant theories of gravity are particularly interesting in four or higher dimensions. Yet, in contrast to their four-dimensional counterparts, theories in higher dimensions are significantly more…

A Hamiltonian system is completely integrable (in the sense of Liouville) if there exist as many independent integrals of motion in involution as the dimension of the configuration space. Under certain regularity conditions,…