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The quantum marginal problem asks whether a set of given density matrices are consistent, i.e., whether they can be the reduced density matrices of a global quantum state. Not many non-trivial analytic necessary (or sufficient) conditions…
Many extensions of the standard model predict the existence of hidden sectors that may contain unbroken abelian gauge groups. We argue that in the presence of quantum decoherence photons may convert into hidden photons on sufficiently long…
A new kind of classically stable static solitons called metastable quasi-topological defects (MQTD) and a systematic method to search for them is presented, with examples from realistic particle physics models. They are characterized by a…
The algebraic stability theorem for $\mathbb{R}$-persistence modules is a fundamental result in topological data analysis. We present a stability theorem for $n$-dimensional rectangle decomposable persistence modules up to a constant…
The conjectured equivalence of the heterotic string to a $K_3$ compactified type IIA superstring is combined with the conjectured equivalence of the latter to a compactified 11-dimensional supermembrane to derive a string membrane duality…
The ordinary quantum theory points out that general relativity is negligible for spatial distances up to the Planck scale. Consistency in the foundations of the quantum theory requires a``soft'' spacetime structure of the general relativity…
In this thesis we deal with the specific collective phenomena in condensed matter - striped-structures formation. Such structures are observed in different branches of condensed matter physics, like surface physics or physics of…
We identify configurations of intersecting branes that correspond to the meta-stable supersymmetry breaking vacua in the four-dimensional N=1 supersymmetric Yang-Mills theory coupled to massive flavors. We show how their energies, the…
In extended supergravity theories there are $p$-brane solutions preserving different numbers of supersymmetries, depending on the charges, the spacetime dimension and the number of original supersymmetries (8, 16 or 32). We find U-duality…
We study in detail the dynamics of unstable two-level quantum systems by adopting the Bloch-vector representation. We identify a novel class of critical scenarios in which the so-called energy-level and decay-width vectors, ${\bf E}$ and…
Hidden symmetries are the backbone of Integrable two-dimensional theories. They provide classical solutions of higher dimensional models as well, they seem to survive partially quantisation and their discrete remnants in M-theory called…
We review the remarkable interplay between modular symmetries and supergravity, which has led to major advances in both physics and mathematics in recent decades. Our focus will be on four-dimensional models with $\mathcal{N}=1$ and…
The absolute stability of a dark matter (DM) particle is not a binding requirement. Here we suggest a few scenarios where the DM particle is liable to decay via extremely feeble interactions. This can happen via inexplicably small Yukawa…
The effect of quantum fluctuations on a nearly flat, nonrelativistic two-dimensional membrane with extrinsic curvature stiffness and tension is investigated. The renormalization group analysis is carried out in first-order perturbative…
This paper is a pedagogical yet critical introduction to the quantum description of unstable systems, mostly at the level of a graduate quantum mechanics course. Quantum decays appear in many different fields of physics, and their…
In this thesis we investigate some aspects of the dramatic consequences of supersymmetry breaking on string vacua. In particular, we focus on the issue of vacuum stability in ten-dimensional string models with broken, or without,…
The complex physics of self-assembly in colloidal crystals on deformable interfaces and surfaces poses interesting possibilities for the designability and synthesis of next-generation metamaterials. The goal of this article is to…
We investigate models of SU(N) SQCD with adjoint matter and non trivial mesonic deformations. We apply standard methods in the dual magnetic theory and we find meta-stable supersymmetry breaking vacua with arbitrary large lifetime. We…
U-duality p-branes in toroidally compactified type II superstring theories in space-time dimensions $10 > D \ge 4$ can be constructed explicitly based on the conjectured U-duality symmetries and the corresponding known single-charge super…
We reexamine the question of quantum consistency of supergravities in eight dimensions. Theories with 16 supercharges suffer from the anomalies under the action of its discrete modular groups. In minimally supersymmetric theory coupled to…