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The canonical formalism of the (2+2) formulation of general relativity of 4 spacetime dimensions is studied under no symmetry assumptions, where the spacetime is viewed as a local product of a 2 dimensional base manifold of Lorentzian…
In the framework of supersymmetric Grand Unified Theories, the minimal Higgs sector is often extended by introducing multi-dimensional Higgs representations in order to obtain realistic models. However these constructions should remain…
Typical dualities in arbitrary dimensions are understood through a Hilbert-space extension method. By these results, we rigorously dualize the quantum ingappabilities to discrete height model in one dimension which is inaccessible by…
We reanalyze the recent computation of the amplitude of the Higgs boson decay into two photons presented by Gastmans et al.. The reasons for which this result cannot be the correct one have been discussed in some recent papers. We address…
It has long been recognized that lattice gauge theory formulations, when applied to general relativity, conflict with the invariance of the theory under diffeomorphisms. Additionally, the traditional lattice field theory approach consists…
Regularization approaches have demonstrated their effectiveness for solving ill-posed problems. However, in the context of variational restoration methods, a challenging question remains, which is how to find a good regularizer. While total…
We present a comprehensive analysis of the prescription we recently put forward for the computation of real-time correlation functions using gauge/gravity duality. The prescription is valid for any holographic supergravity background and it…
Canonical quantization of gravitational systems is obstructed by the problem of time. Due to diffeomorphism symmetry the Hamiltonian vanishes: dynamics with respect to a background time parameter appears "frozen." Two strategies towards the…
We consider 2-dimensional orientable self-shrinkers $\Sigma$ for the Mean Curvature Flow of polynomial volume growth immersed in $\mathbb R^n$. We look at closed one forms minimizing the norm $\int_\Sigma \eterm |\omega|^2$ in their…
Controlled frames and g-frames were considered recently as generalizations of frames in Hilbert spaces. In this paper we generalize some of the known results in frame theory to controlled g-frames. We obtain some new properties of…
Existing theoretical stabilization results for linear, hyperbolic multi-dimensional problems are extended to the discretized multi-dimensional problems. In contrast to existing theoretical and numerical analysis in the spatially…
In the context of (0,2) gauged linear sigma models, we explore chains of perturbatively dual heterotic string compactifications. The notion of target space duality originates in non-geometric phases and can be used to generate distinct…
We are developing a general, unified, and rigorous analytical framework for using gravitational lensing by compact objects to test different theories of gravity beyond the weak-deflection limit. In this paper we present the formalism for…
This work introduces topological regularization as a framework for handling ultraviolet divergences in quantum field theory, reinterpreting infinities as topological obstructions at spacetime boundaries. Through geometric compactification…
In the double field theory, gauge symmetries are realized as generalized diffeomorphisms in the doubled spacetime. By consistency of the theory, dependence of tensor fields on the doubled coordinates is strongly constrained. This causes…
Generalized complex geometry is an example of a powerful formalism to attempt the construction of a language adequate to string theory. With the remarkable property of unifying symplectic and complex manifolds as special cases of a broader…
This paper pursues a twofold goal. First, we introduce and study in detail a new notion of variational analysis called generalized metric subregularity, which is a far-going extension of the conventional metric subregularity conditions. Our…
Following a previous article we continue our study on non-terminating hypergeometric series with one free parameter, which aims to find arithmetical constraints for a given hypergeometric series to admit a gamma product formula. In this…
Parametric finite element discretizations of constrained geometric flows must simultaneously address high-order geometric stiffness, mesh degeneration, and nonlinear global constraints. This paper develops a stabilized dual-SAV (scalar…
A recent analysis of real general relativity based on multisymplectic techniques has shown that boundary terms may occur in the constraint equations, unless some boundary conditions are imposed. This paper studies the corresponding form of…