Linearization stability of gravitational and gauge fields

1979 ◽  
Vol 20 (3) ◽  
pp. 443-453 ◽  
Author(s):  
Judith M. Arms
Keyword(s):  
Gauge Fields ◽  
Linearization Stability

Unification of Gauge Forces and Gravity using Tangled Vortex Knots and Entanglement Dynamics

2020 ◽  
Author(s):  
Mrittunjoy Guha Majumdar
Keyword(s):  
Field Theory ◽  
Short Range ◽  
Gauge Fields ◽  
Entanglement Dynamics ◽  
Unified Field Theory ◽  
Linear Dynamics ◽  
Unified Field ◽  
The Standard Model ◽  
Theory Of Everything ◽  
The Continuum

In this paper, the statistics of excitation-tangles in a postulated background ideal-superfluid field is studied. The structure of the Standard Model is derived in terms of tangle vortex-knots and soliton. Gravity is observed in terms of torsion and curvature in the continuum. In this way, non-linear dynamics and excitations give rise to a unified field theory as well as a Theory of Everything. As a result of this unification, spacetime and matter are shown to be fundamentally equivalent, while gauge fields arise from reorientation and excitations of the the fundamental underlying field. Finally, the equivalence of topological and quantum entanglement is explored to posit a theory of everything in terms of long- and short-range entanglement between fundamental quantum units (bits) of information.

scholarly journals Non-Abelian generalizations of the Hofstadter model: spin–orbit-coupled butterfly pairs

2020 ◽  
Vol 9 (1) ◽  
Author(s):  
Yi Yang ◽  
Bo Zhen ◽  
John D. Joannopoulos ◽  
Marin Soljačić
Keyword(s):  
Quantum Hall ◽  
Building Blocks ◽  
Real Space ◽  
Gauge Fields ◽  
Spin Orbit ◽  
Abelian Gauge ◽  
Experimental Realization ◽  
Integer Quantum Hall Effect ◽  
Integer Quantum ◽  
Necessary And Sufficient

Abstract The Hofstadter model, well known for its fractal butterfly spectrum, describes two-dimensional electrons under a perpendicular magnetic field, which gives rise to the integer quantum Hall effect. Inspired by the real-space building blocks of non-Abelian gauge fields from a recent experiment, we introduce and theoretically study two non-Abelian generalizations of the Hofstadter model. Each model describes two pairs of Hofstadter butterflies that are spin–orbit coupled. In contrast to the original Hofstadter model that can be equivalently studied in the Landau and symmetric gauges, the corresponding non-Abelian generalizations exhibit distinct spectra due to the non-commutativity of the gauge fields. We derive the genuine (necessary and sufficient) non-Abelian condition for the two models from the commutativity of their arbitrary loop operators. At zero energy, the models are gapless and host Weyl and Dirac points protected by internal and crystalline symmetries. Double (8-fold), triple (12-fold), and quadrupole (16-fold) Dirac points also emerge, especially under equal hopping phases of the non-Abelian potentials. At other fillings, the gapped phases of the models give rise to topological insulators. We conclude by discussing possible schemes for experimental realization of the models on photonic platforms.

ANTI-SELF-DUAL SOLUTIONS OF THE YANG-MILLS EQUATIONS IN 4n DIMENSIONS

1992 ◽  
Vol 07 (23) ◽  
pp. 2077-2085 ◽  
Author(s):  
A. D. POPOV
Keyword(s):  
Scalar Field ◽  
Euclidean Space ◽  
Lie Algebra ◽  
Linear Equations ◽  
Dual Solutions ◽  
Gauge Fields ◽  
System Of Equations ◽  
Semisimple Lie Algebra ◽  
Yang Mills ◽  
Self Duality

The anti-self-duality equations for gauge fields in d = 4 and a generalization of these equations to dimension d = 4n are considered. For gauge fields with values in an arbitrary semisimple Lie algebra [Formula: see text] we introduce the ansatz which reduces the anti-self-duality equations in the Euclidean space ℝ4n to a system of equations breaking up into the well known Nahm's equations and some linear equations for scalar field φ.

scholarly journals Nilpotent symmetries as a mechanism for Grand Unification

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Lars Andersson ◽  
András László ◽  
Błażej Ruba
Keyword(s):  
Gauge Field ◽  
Scalar Product ◽  
Local Symmetry ◽  
Matter Field ◽  
Gauge Fields ◽  
Spacetime Symmetries ◽  
Invariant Scalar ◽  
Spacetime Manifold ◽  
Local Symmetries ◽  
Dilatation Group

Abstract In the classic Coleman-Mandula no-go theorem which prohibits the unification of internal and spacetime symmetries, the assumption of the existence of a positive definite invariant scalar product on the Lie algebra of the internal group is essential. If one instead allows the scalar product to be positive semi-definite, this opens new possibilities for unification of gauge and spacetime symmetries. It follows from theorems on the structure of Lie algebras, that in the case of unified symmetries, the degenerate directions of the positive semi-definite invariant scalar product have to correspond to local symmetries with nilpotent generators. In this paper we construct a workable minimal toy model making use of this mechanism: it admits unified local symmetries having a compact (U(1)) component, a Lorentz (SL(2, ℂ)) component, and a nilpotent component gluing these together. The construction is such that the full unified symmetry group acts locally and faithfully on the matter field sector, whereas the gauge fields which would correspond to the nilpotent generators can be transformed out from the theory, leaving gauge fields only with compact charges. It is shown that already the ordinary Dirac equation admits an extremely simple prototype example for the above gauge field elimination mechanism: it has a local symmetry with corresponding eliminable gauge field, related to the dilatation group. The outlined symmetry unification mechanism can be used to by-pass the Coleman-Mandula and related no-go theorems in a way that is fundamentally different from supersymmetry. In particular, the mechanism avoids invocation of super-coordinates or extra dimensions for the underlying spacetime manifold.

scholarly journals Gauge × gauge = gravity on homogeneous spaces using tensor convolutions

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
L. Borsten ◽  
I. Jubb ◽  
V. Makwana ◽  
S. Nagy
Keyword(s):  
Homogeneous Spaces ◽  
Gauge Fields ◽  
Convolution Product ◽  
Tensor Fields ◽  
Einstein Universe ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Static Einstein Universe ◽  
Definition Of ◽  
Gauge Gravity

Abstract A definition of a convolution of tensor fields on group manifolds is given, which is then generalised to generic homogeneous spaces. This is applied to the product of gauge fields in the context of ‘gravity = gauge × gauge’. In particular, it is shown that the linear Becchi-Rouet-Stora-Tyutin (BRST) gauge transformations of two Yang-Mills gauge fields generate the linear BRST diffeomorphism transformations of the graviton. This facilitates the definition of the ‘gauge × gauge’ convolution product on, for example, the static Einstein universe, and more generally for ultrastatic spacetimes with compact spatial slices.

scholarly journals Anomalous transport independent of gauge fields

2020 ◽  
Vol 2 (3) ◽  
Author(s):  
Mamiya Kawaguchi ◽  
Ken Kikuchi
Keyword(s):  
Anomalous Transport ◽  
Gauge Fields

scholarly journals Bulk interactions and boundary dual of higher-spin-charged particles

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Adrian David ◽  
Yasha Neiman
Keyword(s):  
Relative Velocity ◽  
Black Hole Solution ◽  
Vector Model ◽  
Boundary Theory ◽  
Gauge Fields ◽  
Leading Order ◽  
Gravitational Forces ◽  
Penrose Transform ◽  
Higher Spin ◽  
Non Locality

Abstract We consider higher-spin gravity in (Euclidean) AdS4, dual to a free vector model on the 3d boundary. In the bulk theory, we study the linearized version of the Didenko-Vasiliev black hole solution: a particle that couples to the gauge fields of all spins through a BPS-like pattern of charges. We study the interaction between two such particles at leading order. The sum over spins cancels the UV divergences that occur when the two particles are brought close together, for (almost) any value of the relative velocity. This is a higher-spin enhancement of supergravity’s famous feature, the cancellation of the electric and gravitational forces between two BPS particles at rest. In the holographic context, we point out that these “Didenko-Vasiliev particles” are just the bulk duals of bilocal operators in the boundary theory. For this identification, we use the Penrose transform between bulk fields and twistor functions, together with its holographic dual that relates twistor functions to boundary sources. In the resulting picture, the interaction between two Didenko-Vasiliev particles is just a geodesic Witten diagram that calculates the correlator of two boundary bilocals. We speculate on implications for a possible reformulation of the bulk theory, and for its non-locality issues.

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