Related papers: From 2-d Polyakov Action to the 4-d Pseudo-Conform…
The correspondence between the semiclassical limit of the DOZZ quantum Liouville theory and the Nekrasov-Shatashvili limit of the N = 2 (Omega-deformed) U(2) super-Yang-Mills theories is used to calculate the unknown accessory parameter of…
We review and reformulate old and prove new results about the triad $ {\rm PPSL}_2({\mathbb Z})\subseteq{\rm PPSL}_2({\mathbb R})\circlearrowright ppsl_2({\mathbb R}) $, which provides a universal generalization of the classical automorphic…
Contact Riemannian manifolds, with not necessarily integrable complex structures, are the generalization of pseudohermitian manifolds in CR geometry. The Tanaka-Webster-Tanno connection on such a manifold plays the role of Tanaka-Webster…
The multicritical generalizations of the Lee-Yang universality class arise as renormalization-group fixed points of scalar field theories with complex $i\varphi^{2n+1}$ interaction, $n\in\mathbb{N}$, just below their upper critical…
The four dimensional Lorentz-breaking finite and determined Chern-Simons like action is generated as a one loop perturbative correction via an appropriate Lorentz-breaking coupling of the gauge field with the spinor field. Unlike the known…
We study the construction of the so-called intrinsic action for PDEs equipped with compatible presymplectic structures. In particular, we explicitly demonstrate that the intrinsic action for the standard Einstein-Hilbert gravity is the…
It is frequently useful to construct dual descriptions of theories containing antisymmetric tensor fields by introducing a new potential whose curl gives the dual field strength, thereby interchanging field equations with Bianchi…
Conformal perturbation theory is a powerful tool to describe the behavior of statistical-mechanics models and quantum field theories in the vicinity of a critical point. In the past few years, it has been extensively used to describe…
In this paper, we prove the following two results: First, we study a class of conformally invariant operators $P$ and their related conformally invariant curvatures $Q$ on even-dimensional Riemannian manifolds. When the manifold is locally…
An explicit AdS/CFT correspondence is shown for the Lie group $SO(4,2)$. The Lie symmetry structures allow for the construction of two physical theories through the tools of Cartan geometry. One is a gravitational theory that has anti-de…
We investigate a Lorentz invariant action which is quadratic in two rank-2 symmetric tensor fields in Minkowski spacetime. We apply a scalar-vector-tensor decomposition to two tensor fields by virtue of 3-dimensional rotation-invariance of…
The formation of a confining string (or a p-brane) in a Poincare' invariant theory breaks spontaneously this symmetry which is thereby realized non-linearly in the effective action of these extended objects. As a consequence the form of the…
We show that conformal manifolds in $d\geq 3$ conformal field theories with at least 4 supercharges are K\"ahler-Hodge, thus extending to 3d ${\cal N}=2$ and 4d ${\cal N}=1$ similar results previously derived for 4d ${\cal N}=2$ and ${\cal…
Chiral EFT yields singular potentials that require regularization and renormalization when implemented in a dynamical equation such as the Lippmann--Schwinger equation. We employ two different approaches, renormalization with contact terms…
The main result of this paper is the construction of a conformally covariant operator in two dimensions acting on scalar fields and containing fourth order derivatives. In this way it is possible to derive a class of Lagrangians invariant…
For any $N\ts N$ monodromy matrix we define the Lyapunov function, which is analytic on an associated N-sheeted Riemann surface. On each sheet the Lyapunov function has the standard properties of the Lyapunov function for the Hill operator.…
We give a geometric description of supersymmetric gravity/(non-)abelian $p$-form hierarchies in superspaces with 4D, $N = 1$ super-Poincare invariance. These hierarchies give rise to Chern-Simons-like invariants, such as those of the 5D, $N…
We develop a four-dimensional gauge-gravity unification based on the $% SL(2N,C)$ gauge theory taken in a universal Yang--Mills type setting. The accompanying tetrads are promoted to dynamical fields whose length, when projected onto the…
We present in the article the formulation of a version of Lorentz covariant quantum mechanics based on a group theoretical construction from a Heisenberg-Weyl symmetry with position and momentum operators transforming as Minkowski…
We show that 4--dimensional conformal field theory is most naturally formulated on Kulkarni 4--folds, i. e. real 4--folds endowed with an integrable quaternionic structure. This leads to a formalism that parallels very closely that of…