SPONTANEOUS COMPACTIFICATION TO NONSYMMETRIC COSET SPACES

1987 ◽  
Vol 02 (01) ◽  
pp. 57-61 ◽  
Author(s):  
P. BÁNTAY
Keyword(s):  
Space Time ◽  
Coset Space ◽  
Spontaneous Compactification ◽  
Yang Mills ◽  
Coset Spaces

We investigate the conditions under which a 4+d-dimensional Einstein-Yang-Mills system has spontaneously compactifying solutions with space-time M4×G/H, where G/H is a d-dimensional nonsymmetric coset space.

KALUZA-KLEIN THEORY

1986 ◽  
Vol 01 (01) ◽  
pp. 1-37 ◽  
Author(s):  
J. STRATHDEE
Keyword(s):  
Internal Space ◽  
Coset Space ◽  
Spontaneous Compactification ◽  
Zero Modes ◽  
Coset Spaces ◽  
Klein Theory ◽  
Recent Developments ◽  
Ground State Geometry ◽  
Energy Physics ◽  
Kaluza Klein

Recent developments in Kaluza-Klein theory are reviewed. Starting with the concept of spontaneous compactification, the problem of determining the ground state geometry and its symmetry is discussed. While it is generally believed that only the zero modes can be relevant for low energy physics, it is possible in some cases to deduce the entire excitation spectrum. This is true when the internal space is a coset space. A technique is described for setting up harmonic expansions on coset spaces. Consistency in chiral Kaluza-Klein theories demands freedom from both gauge and gravitational anomalies. General features of the chiral anomalies are reviewed.

scholarly journals Flat self-dual gravity

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Kirill Krasnov ◽  
Evgeny Skvortsov
Keyword(s):  
Light Cone ◽  
Space Time ◽  
Kinetic Term ◽  
Light Cone Gauge ◽  
Yang Mills ◽  
Covariant Action ◽  
Chiral Interaction ◽  
Double Copy

Abstract We construct a new covariant action for “flat” self-dual gravity in four space-time dimensions. The action has just one term, but when expanded around an appropriate background gives rise to a kinetic term and a cubic interaction. Upon imposing the light-cone gauge, the action reproduces the expected chiral interaction of Siegel. The new action is in many ways analogous to the known covariant action for self-dual Yang-Mills theory. There is also a sense in which the new self-dual gravity action exhibits the double copy of self-dual Yang-Mills structure.

scholarly journals EXTENSION OF THE POINCARÉ GROUP AND NON-ABELIAN TENSOR GAUGE FIELDS

2010 ◽  
Vol 25 (31) ◽  
pp. 5765-5785 ◽  
Author(s):  
GEORGE SAVVIDY
Keyword(s):  
Gauge Group ◽  
Gauge Transformation ◽  
Space Time ◽  
Gauge Fields ◽  
Poincaré Group ◽  
Matrix Representations ◽  
Poincare Group ◽  
Yang Mills ◽  
The Matrix ◽  
Transversal Plane

In the recently proposed generalization of the Yang–Mills theory, the group of gauge transformation gets essentially enlarged. This enlargement involves a mixture of the internal and space–time symmetries. The resulting group is an extension of the Poincaré group with infinitely many generators which carry internal and space–time indices. The matrix representations of the extended Poincaré generators are expressible in terms of Pauli–Lubanski vector in one case and in terms of its invariant derivative in another. In the later case the generators of the gauge group are transversal to the momentum and are projecting the non-Abelian tensor gauge fields into the transversal plane, keeping only their positively definite spacelike components.

scholarly journals A MAXWELL-LIKE FORMULATION OF GRAVITATIONAL THEORY IN MINKOWSKI SPACE–TIME

2007 ◽  
Vol 16 (06) ◽  
pp. 1027-1041 ◽  
Author(s):  
EDUARDO A. NOTTE-CUELLO ◽  
WALDYR A. RODRIGUES
Keyword(s):  
Gravitational Field ◽  
Minkowski Space ◽  
Gravitational Theory ◽  
Space Time ◽  
Lorentzian Geometry ◽  
Field Equations ◽  
Yang Mills ◽  
Minkowski Space Time ◽  
Clifford Bundle ◽  
Gauge Fixing

Using the Clifford bundle formalism, a Lagrangian theory of the Yang–Mills type (with a gauge fixing term and an auto interacting term) for the gravitational field in Minkowski space–time is presented. It is shown how two simple hypotheses permit the interpretation of the formalism in terms of effective Lorentzian or teleparallel geometries. In the case of a Lorentzian geometry interpretation of the theory, the field equations are shown to be equivalent to Einstein's equations.

scholarly journals About renormalized effective action for the Yang-Mills theory in four-dimensional space-time

2018 ◽  
Vol 191 ◽  
pp. 06001
Author(s):  
A.V. Ivanov
Keyword(s):  
Infinite Series ◽  
Effective Action ◽  
Dimensional Space ◽  
Space Time ◽  
Coupling Constant ◽  
Asymptotic Approach ◽  
Yang Mills ◽  
Dimensional Space Time ◽  
Bare Coupling Constant ◽  
Renormalization Theory

This work is related to the asymptotic approach in the renormalization theory and its problems. As the main example, the Yang-Mills theory in four-dimensional space-time is considered. It has been shown earlier [16] that using the asymptotic of the bare coupling constant one can find an expression for the renormalized effective action, however, this formula has problems (divergence ln " and infinite series). This work shows the relation of these values and provides an answer for the renormalized effective action.

scholarly journals Uq(N) GAUGE THEORIES

1994 ◽  
Vol 09 (30) ◽  
pp. 2835-2847 ◽  
Author(s):  
LEONARDO CASTELLANI
Keyword(s):  
Quantum Groups ◽  
Differential Calculus ◽  
Gauge Theories ◽  
Space Time ◽  
Yang Mills ◽  
Commutation Relations ◽  
Transformation Rules ◽  
Field Strengths

Improving on an earlier proposal, we construct the gauge theories of the quantum groups U q(N). We find that these theories are also consistent with an ordinary (commuting) space-time. The bicovariance conditions of the quantum differential calculus are essential in our construction. The gauge potentials and the field strengths are q-commuting "fields," and satisfy q-commutation relations with the gauge parameters. The transformation rules of the potentials generalize the ordinary infinitesimal gauge variations. For particular deformations of U (N) ("minimal deformations"), the algebra of quantum gauge variations is shown to close, provided the gauge parameters satisfy appropriate q-commutations. The q-Lagrangian invariant under the U q(N) variations has the Yang–Mills form [Formula: see text], the "quantum metric" gij being a generalization of the Killing metric.

scholarly journals More about the instanton/soliton/kink correspondence

2016 ◽  
Vol 14 (01) ◽  
pp. 1750012 ◽  
Author(s):  
Andrea Addazi
Keyword(s):  
Soliton Solutions ◽  
Scalar Fields ◽  
Space Time ◽  
Yang Mills ◽  
Charge Formula

We demonstrate that all gauge instantons in a [Formula: see text] Yang–Mills theory, with generic topological vacuum charge [Formula: see text], correspond to soliton solutions and kink scalar fields in [Formula: see text] space-time.

scholarly journals SPIN GAUGE THEORY OF GRAVITY IN CLIFFORD SPACE: A REALIZATION OF KALUZA–KLEIN THEORY IN FOUR-DIMENSIONAL SPACE–TIME

2006 ◽  
Vol 21 (28n29) ◽  
pp. 5905-5956 ◽  
Author(s):  
MATEJ PAVŠIČ
Keyword(s):  
Dimensional Space ◽  
Space Time ◽  
Dirac Field ◽  
Spin Connection ◽  
Yang Mills ◽  
Object A ◽  
Klein Theory ◽  
Dimensional Space Time ◽  
The Right ◽  
Kaluza Klein

A theory in which four-dimensional space–time is generalized to a larger space, namely a 16-dimensional Clifford space (C-space) is investigated. Curved Clifford space can provide a realization of Kaluza–Klein. A covariant Dirac equation in curved C-space is explored. The generalized Dirac field is assumed to be a polyvector-valued object (a Clifford number) which can be written as a superposition of four independent spinors, each spanning a different left ideal of Clifford algebra. The general transformations of a polyvector can act from the left and/or from the right, and form a large gauge group which may contain the group U (1) × SU (2) × SU (3) of the standard model. The generalized spin connection in C-space has the properties of Yang–Mills gauge fields. It contains the ordinary spin connection related to gravity (with torsion), and extra parts describing additional interactions, including those described by the antisymmetric Kalb–Ramond fields.

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