Kaluza-Klein from colour-kinematics duality for massive fields

Abstract We consider a broad class of massive four dimensional effective theories describing an infinite tower of charged massive spin 1 states, interacting with massless spin 1 and spin 0. The spectrum is chosen to be the same as that appears in the Kaluza-Klein theory reduction of 5d Yang-Mills to ensure the absence of any spurious poles in a possible double copy formulation. The effective theories are characterized by multiple different couplings between different fields which are unconstrained by symmetries and low energy criteria. Remarkably, by demanding that the scattering amplitudes preserve colour-kinematics duality for different scattering processes, required for the existence of a massive double copy, we find that our 4d Lagrangian is fixed uniquely to the Kaluza-Klein compactification of 5d Yang-Mills theory together with its known double copy consistent higher derivative operators.

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Massive gravity from double copy

Journal of High Energy Physics ◽

10.1007/jhep12(2020)030 ◽

2020 ◽

Vol 2020 (12) ◽

Cited By ~ 1

Author(s):

Arshia Momeni ◽

Justinas Rumbutis ◽

Andrew J. Tolley

Keyword(s):

Sigma Model ◽

Massive Gravity ◽

Effective Field ◽

Effective Theory ◽

Nonlinear Sigma Model ◽

Limit Theory ◽

Four Dimensions ◽

Yang Mills ◽

Massive Spin ◽

Double Copy

Abstract We consider the double copy of massive Yang-Mills theory in four dimensions, whose decoupling limit is a nonlinear sigma model. The latter may be regarded as the leading terms in the low energy effective theory of a heavy Higgs model, in which the Higgs has been integrated out. The obtained double copy effective field theory contains a massive spin-2, massive spin-1 and a massive spin-0 field, and we construct explicitly its interacting Lagrangian up to fourth order in fields. We find that up to this order, the spin-2 self interactions match those of the dRGT massive gravity theory, and that all the interactions are consistent with a Λ3 = (m2MPl)1/3 cutoff. We construct explicitly the Λ3 decoupling limit of this theory and show that it is equivalent to a bi-Galileon extension of the standard Λ3 massive gravity decoupling limit theory. Although it is known that the double copy of a nonlinear sigma model is a special Galileon, the decoupling limit of massive Yang-Mills theory is a more general Galileon theory. This demonstrates that the decoupling limit and double copy procedures do not commute and we clarify why this is the case in terms of the scaling of their kinematic factors.

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

International Journal of Modern Physics A ◽

10.1142/s0217751x06031661 ◽

2006 ◽

Vol 21 (28n29) ◽

pp. 5905-5956 ◽

Cited By ~ 28

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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GAUGE GROUP AND TOPOLOGY CHANGE

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887811005622 ◽

2011 ◽

Vol 08 (06) ◽

pp. 1225-1238 ◽

Cited By ~ 2

Author(s):

IZUMI TANAKA ◽

SEIJI NAGAMI

Keyword(s):

Group Action ◽

Transformation Group ◽

High Symmetry ◽

Topology Change ◽

Yang Mills ◽

And Topology ◽

Present Universe ◽

Klein Theory ◽

Kaluza Klein ◽

Bundle Structure

The purpose of this study is to examine the effect of topology change in the initial universe. In this study, the concept of G-cobordism is introduced to argue about the topology change of the manifold on which a transformation group acts. This G-manifold has a fiber bundle structure if the group action is free and is related to the spacetime in Kaluza–Klein theory or Einstein–Yang–Mills system. Our results revealed the fundamental processes of compactification in G-manifolds. In these processes, the initial high symmetry and multidimensional universe changes to present universe by the mechanism which lowers the dimensions and symmetries.

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The importance of quantum effects in Kaluza–Klein theory

Canadian Journal of Physics ◽

10.1139/p86-120 ◽

1986 ◽

Vol 64 (5) ◽

pp. 644-652 ◽

Cited By ~ 8

Author(s):

D. J. Toms

Keyword(s):

Effective Action ◽

Gauge Coupling ◽

Quantum Effects ◽

Induced Gravity ◽

Yang Mills ◽

Self Consistent ◽

Klein Theory ◽

Dimensional Gravity ◽

The Stability ◽

Kaluza Klein

This paper presents a discussion of the role of quantum effects in Kaluza–Klein theories. It is demonstrated why it is not possible to examine the existence of self-consistent solutions induced by quantum corrections to the classical theory if only the vacuum energy is used. The importance of the induced gravity and induced Yang–Mills terms in the effective action are emphasized. General criteria are given for the existence of self-consistent solutions in certain cases, and an expression is given for the gauge-coupling constant. Quantization of five-dimensional gravity with a cosmological constant is considered. Expressions are given for the constants that multiply the induced gravity and Yang–Mills terms in the one-loop effective action for this theory. Although the theory is one-loop finite, the necessity for performing finite renormalizations—a fact that has hitherto been overlooked—is discussed. Results of an analysis of the stability of self-consistent solutions are given, where it is shown why many of the solutions are unstable to small perturbations. A number of prospects for future work are given.

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SEMICLASSICAL DECAY OF KALUZA-KLEIN VACUUM IN HIGHER DERIVATIVE GRAVITY

Modern Physics Letters A ◽

10.1142/s0217732393001367 ◽

1993 ◽

Vol 08 (17) ◽

pp. 1621-1626

Author(s):

BIPLAB BHAWAL ◽

H.S. MANI

Keyword(s):

Physical Properties ◽

Ground State ◽

Space Time ◽

Higher Derivative ◽

Klein Theory ◽

Decay State ◽

Kaluza Klein

Semiclassical decay of the ground state of Kaluza-Klein theory has been studied in the context of higher derivative corrections to the Einstein action. Two solutions describing the decay state of the vacuum have been obtained. The first solution is asymptotic to the Witten bubble space-time, whereas the second solution is entirely new, but with the same physical properties. Properties of these solutions are discussed.

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Geodesic flows on semidirect-product Lie groups: geometry of singular measure-valued solutions

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2008.0263 ◽

2008 ◽

Vol 465 (2102) ◽

pp. 457-476 ◽

Cited By ~ 16

Author(s):

Darryl D Holm ◽

Cesare Tronci

Keyword(s):

Semidirect Product ◽

Dual Pair ◽

Geodesic Motion ◽

Yang Mills ◽

Klein Theory ◽

Continuum Description ◽

Mills Field ◽

Circulation Theorem ◽

Kaluza Klein ◽

The Continuum

The EPDiff equation (or the dispersionless Camassa–Holm equation in one dimension) is a well-known example of geodesic motion on the Diff group of smooth invertible maps (diffeomorphisms). Its recent two-component extension governs geodesic motion on the semidirect product DiffⓈ , where denotes the space of scalar functions. This paper generalizes the second construction to consider geodesic motion on DiffⓈ , where denotes the space of scalar functions that take values on a certain Lie algebra (e.g. = ⊗ (3)). Measure-valued delta-like solutions are shown to be momentum maps possessing a dual pair structure, thereby extending previous results for the EPDiff equation. The collective Hamiltonians are shown to fit into the Kaluza–Klein theory of particles in a Yang–Mills field and these formulations are shown to apply also at the continuum partial differential equation level. In the continuum description, the Kaluza–Klein approach produces the Kelvin circulation theorem.

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