Holonomy
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Submanifolds and Holonomy Open
Basics of Submanifold Theory in Space Forms The fundamental equations for submanifolds of space forms Models of space forms Principal curvatures Totally geodesic submanifolds of space forms Reduction of the codimension Totally umbilical su…
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Gravitational spin-orbit coupling in binary systems, post-Minkowskian approximation, and effective one-body theory Open
A novel approach for extracting gauge-invariant information about spin-orbit coupling in gravitationally interacting binary systems is introduced. This approach is based on the "scattering holonomy", i.e. the integration (from the infinite…
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Nonsingular spherically symmetric black-hole model with holonomy corrections Open
We present a covariant model of a spherically symmetric black hole with corrections motivated by loop quantum gravity. The effective modifications, parametrized by a positive constant $\lambda$, are implemented through a canonical transfor…
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Floquet semimetal with Floquet-band holonomy Open
Exotic topological states of matter, such as a Floquet topological insulator or Floquet-Weyl semimetal, can be induced by periodic driving. This work proposes a Floquet semimetal with Floquet-band holonomy. That is, the system is gapless, …
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A one parameter family of Calabi-Yau manifolds with attractor points of rank two Open
In the process of studying the ζ-function for one parameter families of Calabi-Yau manifolds we have been led to a manifold, first studied by Verrill, for which the quartic numerator of the ζ-function factorises into two quadrics remarkabl…
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Signature change in two-dimensional black-hole models of loop quantum gravity Open
Signature change has been identified as a generic consequence of holonomy modifications in spherically symmetric models of loop quantum gravity with real connections, which includes modified Schwarzschild solutions. Here, this result is ex…
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Spherically symmetric sector of self-dual Ashtekar gravity coupled to matter: Anomaly-free algebra of constraints with holonomy corrections Open
Using self dual Ashtekar variables, we investigate (at the effective level)\nthe spherically symmetry reduced model of loop quantum gravity, both in vacuum\nand when coupled to a scalar field. Within the real Ashtekar-Barbero\nformulation,…
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Resolution of strong singularities and geodesic completeness in loop quantum Bianchi-II spacetimes Open
Generic resolution of singularities and geodesic completeness in the loop\nquantization of Bianchi-II spacetimes with arbitrary minimally coupled matter\nis investigated. Using the effective Hamiltonian approach, we examine two\navailable …
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Signature change in loop quantum gravity: Two-dimensional midisuperspace models and dilaton gravity Open
Models of loop quantum gravity based on real connections have a deformed\nnotion of general covariance, which leads to the phenomenon of signature\nchange. This result is confirmed here in a general analysis of all\nmidisuperspace models w…
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Mirror symmetry for G 2-manifolds: twisted connected sums and dual tops Open
Recently, at least 50 million of novel examples of compact $G_2$ holonomy\nmanifolds have been constructed as twisted connected sums of asymptotically\ncylindrical Calabi-Yau threefolds. The purpose of this paper is to study mirror\nsymmet…
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Compact, singular G2-holonomy manifolds and M/heterotic/F-theory duality Open
A bstract We study the duality between M-theory on compact holonomy G 2 -manifolds and the heterotic string on Calabi-Yau three-folds. The duality is studied for K3-fibered G 2 -manifolds, called twisted connected sums, which lend themselv…
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Canonical metrics on holomorphic Courant algebroids Open
The solution of the Calabi Conjecture by Yau implies that every Kähler Calabi–Yau manifold (Formula presented.) admits a metric with holonomy contained in (Formula presented.), and that these metrics are parameterized by the positive cone …
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The Standard Model, The Exceptional Jordan Algebra, and Triality Open
Jordan, Wigner and von Neumann classified the possible algebras of quantum mechanical observables, and found they fell into 4 "ordinary" families, plus one remarkable outlier: the exceptional Jordan algebra. We point out an intriguing rela…
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3d TQFTs from Argyres–Douglas theories Open
We construct a new class of three-dimensional topological quantum field theories (3d TQFTs) by considering generalized Argyres–Douglas theories on S¹ × M₃ with a non-trivial holonomy of a discrete global symmetry along the S¹. For the mini…
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A new construction of compact torsion-free $G_2$-manifolds by gluing families of Eguchi–Hanson spaces Open
We give a new construction of compact Riemannian 7-manifolds with holonomy\n$G_2$. Let $M$ be a torsion-free $G_2$-manifold (which can have holonomy a\nproper subgroup of $G_2$) such that $M$ admits an involution $\\iota$ preserving\nthe $…
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Calabi‐Yau Threefolds with Small Hodge Numbers Open
A list of Calabi‐Yau threefolds is presented with holonomy groups that are precisely , rather than a subgroup, with small Hodge numbers, which are understood to be those manifolds with height . With the completion of a project to compute t…
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Integer homology 3-spheres admit irreducible representations in SL(2,C) Open
We prove that the fundamental group of any integer homology $3$ -sphere different from the $3$ -sphere admits irreducible representations of its fundamental group in $\\operatorname{SL}(2,\\mathbb{C})$ . For hyperbolic integer homology sph…
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Torsion in quantum field theory through time-loops on Dirac materials Open
Assuming dislocations could be meaningfully described by torsion, we propose\nhere a scenario based on the role of time in the low-energy regime of\ntwo-dimensional Dirac materials, for which coupling of the fully antisymmetric\ncomponent …
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How quickly can anyons be braided? Or: How I learned to stop worrying about diabatic errors and love the anyon Open
Topological phases of matter are a potential platform for the storage and processing of quantum information with intrinsic error rates that decrease exponentially with inverse temperature and with the length scales of the system, such as t…
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Covariance in self-dual inhomogeneous models of effective quantum geometry: Spherical symmetry and Gowdy systems Open
When applying the techniques of Loop Quantum Gravity (LQG) to symmetry-reduced gravitational systems, one first regularizes the scalar constraint using holonomy corrections, prior to quantization. In inhomogeneous system, where a residual …
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Three-dimensional non-Abelian quantum holonomy Open
When a quantum system undergoes slow changes, the evolution of its state depends only on the corresponding trajectory in Hilbert space. This phenomenon, known as quantum holonomy, brings to light the geometric aspects of quantum theory. De…
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Emergent dimensions and branes from large- confinement Open
$\\mathcal{N}=1$ $SU(N)$ super-Yang-Mills theory on $\\mathbb{R}^3\\times S^1$\nis believed to have a smooth dependence on the circle size $L$. Making $L$\nsmall leads to calculable non-perturbative color confinement, mass gap, and\nstring…
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Supersymmetric backgrounds, the Killing superalgebra, and generalised special holonomy Open
We prove that, for M theory or type II, generic Minkowski flux backgrounds preserving $\mathcal{N}$ supersymmetries in dimensions $D\geq4$ correspond precisely to integrable generalised $G_{\mathcal{N}}$ structures, where $G_{\mathcal{N}}$…
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Quark number holonomy and confinement-deconfinement transition Open
We propose a new quantity which describes the confinement-deconfinement\ntransition based on topological properties of QCD. The quantity which we call\nthe quark number holonomy is defined as the integral of the quark number\nsusceptibilit…
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Infinite loop spaces and positive scalar curvature in the presence of a fundamental group Open
This is a continuation of our previous work with Botvinnik on the nontriviality of the secondary index invariant on spaces of metrics of positive scalar curvature, in which we take the fundamental group of the manifolds into account. We sh…
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Semiclassical dynamics, Berry curvature, and spiral holonomy in optical quasicrystals Open
We describe the theory of the dynamics of atoms in two-dimensional quasicrystalline optical lattices. We focus on a regime of shallow lattice depths under which the applied force can cause Landau-Zener tunneling past a dense hierarchy of g…
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Loop quantum cosmology-corrected Gauss–Bonnet singular cosmology Open
In this work we investigate which Loop Quantum Cosmology (LQC)-corrected Gauss–Bonnet [Formula: see text] gravity can realize two singular cosmological scenarios, the intermediate inflation and the singular bounce scenarios. The intermedia…
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The Universal Lie $\infty$-Algebroid of a Singular Foliation Open
We consider singular foliations \mathcal{F} as locally finitely generated \mathscr{O} -submodules of \mathscr{O} -derivations closed under the Lie bracket, where \mathscr{O} is the ring of smooth, holomorphic, or real analytic functions on…
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Twisted geometries coherent states for loop quantum gravity Open
We introduce a new family of coherent states for loop quantum gravity, inspired by the twisted geometry parametrization. We compute their peakedness properties and compare them with the heat-kernel coherent states. They show similar featur…
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Topological tameness of Margulis Spacetimes Open
We show that Margulis spacetimes without parabolic holonomy elements are topologically tame. A Margulis spacetime is the quotient of the $3$-dimensional Minkowski space by a free proper isometric action of the free group of rank $\geq 2$. …