Related papers: Scale-invariant phase space and the conformal grou…
We construct a four-dimensional supersymmetric QCD in conformal window with a marginally relevant deformation which triggers the spontaneous breaking of (approximate) scale invariance and the subsequent confinement, generating a mass gap,…
We study the breakdown of conformal symmetry in a conformally invariant gravitational model. The symmetry breaking is introduced by defining a preferred conformal frame in terms of the large scale characteristics of the universe. In this…
This article discusses and explains the Hamiltonian formulation for a class of simple gauge invariant mechanical systems consisting of point masses and idealized rods. The study of these models may be helpful to advanced undergraduate or…
We explore various aspects of 2-form topological gauge theories in (3+1)d. These theories can be constructed as sigma models with target space the second classifying space $B^2G$ of the symmetry group $G$, and they are classified by…
An important unanswered question in quantum field theory is to understand precisely under which conditions scale invariance implies invariance under the full conformal group. While the general answer in two dimensions has been known for…
Recall that the moduli space of smooth (that is, stable) cubic curves is isomorphic to the quotient of the upper half plane by the group of fractional linear transformations with integer coefficients. We establish a similar result for…
We show that the dimer model on a bipartite graph on a torus gives rise to a quantum integrable system of special type - a cluster integrable system. The phase space of the classical system contains, as an open dense subset, the moduli…
We embed second class constrained systems by a formalism that combines concepts of the BFFT method and the unfixing gauge formalism. As a result, we obtain a gauge-invariant system where the introduction of the Wess-Zumino (WZ) field is…
In this article we study the structure of $\Gamma$-invariant spaces of $L^2(\bf R)$. Here $\bf R$ is a second countable LCA group. The invariance is with respect to the action of $\Gamma$, a non commutative group in the form of a semidirect…
The Hamiltonian formulation of lattice gauge theories plays a central role in quantum simulations of gauge theories, and understanding their spectrum and other properties is expected to become crucial in the upcoming years. The relevant…
Based on projective representations of smooth Deligne cohomology groups, we introduce an analogue of the space of conformal blocks to compact oriented (4k+2)-dimensional Riemannian manifolds with boundary. For the standard…
We formulate the necessary conditions for the integrability of a certain family of Hamiltonian systems defined in the constant curvature two-dimensional spaces. Proposed form of potential can be considered as a counterpart of a homogeneous…
We reformulate Fourier-space crystallography in the language of cohomology of groups. Once the problem is understood as a classification of linear functions on the lattice, restricted by a particular group relation, and identified by gauge…
We consider the conformal group of a space of dim n=p+q, with SO(p,q) metric. The quotient of this group by its homogeneous Weyl subgroup gives a principal fiber bundle with 2n-dim base manifold and Weyl fibers. The Cartan generalization to…
Conformal self-dual fields in flat space-time of even dimension greater than or equal to four are studied. Ordinary-derivative formulation of such fields is developed. Gauge invariant Lagrangian with conventional kinetic terms and…
I show how the isomorphism between the Lie groups of types $B_2$ and $C_2$ leads to a faithful action of the Clifford algebra $\mathcal C\ell(3,2)$ on the phase space of 2-dimensional dynamics, and hence to a mapping from Dirac spinors…
We introduce the natural lift of spacetime diffeomorphisms for conformal gravity and discuss the physical equivalence between the natural and gauge natural structure of the theory. Accordingly, we argue that conformal transformations must…
The nongeneric six- and eightdimensional orbits of SO(4,2) are described in explicitly covariant way. The relevant Hamiltonian dynamical systems are constructed and canonically quantized. It is shown that the resulting unitary…
We discuss the dynamics of a particular two-dimensional (2D) physical system in the four dimensional (4D) (non-)commutative phase space by exploiting the consistent Hamiltonian and Lagrangian formalisms based on the symplectic structures…
We show that there exist infinite-dimensional quasi-flats in the compactly supported Hamiltonian diffeomorphism group of the Liouville domain, with respect to the spectral norm, if and only if the symplectic cohomology of this Liouville…