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A spectrum generating algebra is constructed and used to find all the physical states of the $W_3$ string with standard ghost number. These states are shown to have positive norm and their partition function is found to involve the Ising…
It has been recently claimed [arXiv:1102.3434] that quantum gravity models where the number of dimensions reduces at the ultraviolet exhibit a potentially observable cutoff in the primordial gravitational wave spectrum, and that this is a…
We discuss a novel dark matter signature relevant for directional detection of Weakly Interacting Massive Particles (WIMPs). For heavy enough WIMPs and low enough recoil energies, the maximum of the recoil rate is not in the direction of…
The properties of higher-dimensional black holes can differ significantly from those of black holes in four dimensions, since neither the uniqueness theorem, nor the staticity theorem or the topological censorship theorem generalize to…
We investigate in this work the meaning of weak values through the prism of property ascription in quantum systems. Indeed, the weak measurements framework contains only ingredients of the standard quantum formalism, and as such weak…
Recent criticism of higher-dimensional extensions of Einstein's theory is considered. This may have some justification as regards string theory, but is misguided as applied to five-dimensional theories with a large extra dimension. Such…
In this second part of the paper, dedicated to theories with extra dimensions, a new physical notion about the "tensor length scale" is introduced, based on the gravitational theories with covariant and contravariant metric tensor…
The extraordinary concept of weak value amplification has attracted considerable attention for addressing foundational questions in quantum mechanics and for metrological applications in high precision measurement of small physical…
We explain how the representation theory associated with supersymmetry in diverse dimensions is encoded within the representation theory of supersymmetry in one time-like dimension. This is enabled by algebraic criteria, derived, exhibited,…
Stable topological defects of light (pseudo)scalar fields can contribute to the Universe's dark energy and dark matter. Currently the combination of gravitational and cosmological constraints provides the best limits on such a possibility.…
By controlling synaptic and neural correlations, deep learning has achieved empirical successes in improving classification performances. How synaptic correlations affect neural correlations to produce disentangled hidden representations…
We introduce new techniques that can preserve unitarity of the system including ghost particles. Negative norms of the particles can be involved in zero-norm states by constraints of the physical space. These are useful to apply the…
Weak convergence of probability measures is one of the most important topics in the field probability and statistics. In this survey paper, we look at weak convergence of probability measures from the topological vector space point of view.…
Fermionic and bosonic ghost systems are defined each in terms of a single vertex algebra which admits a one-parameter family of conformal structures. The observation that these structures are related to each other provides a simple way to…
We show that the dimension of spacetime becomes complex-valued when its short-scale geometry is invariant under a discrete scaling symmetry. This characteristic can generically arise in quantum gravities, for instance, in those based on…
An essential aspect of cosmic voids is that these underdense regions provide complementary information about the properties of our Universe. Unlike dense regions, voids are avoided by matter and are less contaminated by baryonic processes.…
We present a comprehensive full-sky 3-dimensional analysis of the weak-lensing fields and their corresponding power spectra. Using the formalism of spin-weight spherical harmonics and spherical Bessel functions, we relate the two-point…
The existence of light rings in a spacetime is closely related to the existence of black hole horizons and observables such as the ringdown and the shadow. Black holes, compared to nonvacuum ultracompact objects, have rather unique…
In a unitary ring with involution, we prove that each element has at most one weak group inverse if and only if each idempotent element has a unique weak group inverse. Furthermore, we define the $m$-weak group inverse and show some…
Quantum correlations become formidable tools for beating classical capacities of measurement. Preserving these advantages in practical systems, where experimental imperfections are unavoidable, is a challenge of the utmost importance. Here…