Derrick's theorem beyond a potential

Alberto Nicolis; Junpu Wang; Kurt Hinterbichler; Lam Hui; Solomon Endlich

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Derrick's theorem beyond a potential

Solomon Endlich, Kurt Hinterbichler, Lam Hui, Alberto Nicolis, Junpu Wang

High Energy Physics - Theory · Submitted 25 Feb 2010

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Here, we show that these galileon theories do not possess stable solitonic solutions.

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arXiv ID1002.4873 (version 1)

Pith IDA5F4CT66, Pith's permanent record of this paper and its review

CitationAlberto Nicolis, Junpu Wang, Kurt Hinterbichler, Lam Hui, Solomon Endlich. "Derrick's theorem beyond a potential." arXiv:1002.4873 (2010). https://pith.science/paper/A5F4CT66

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What the abstract itself states, as probabilities: claims first 0.08 · states limitation 0.49 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.75 · mentions code or data availability 0.02.

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Scalar field theories with derivative interactions are known to possess solitonic excitations, but such solitons are generally unsatisfactory because the effective theory fails precisely where nonlinearities responsible for the solitons are important. A new class of theories possessing (internal) galilean invariance can in principle bypass this difficulty. Here, we show that these galileon theories do not possess stable solitonic solutions. As a by-product, we show that no stable solitons exist for a different class of derivatively coupled theories, describing for instance the infrared dynamics of superfluids, fluids, solids and some k-essence models.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Scalar field theories with derivative interactions are known to possess solitonic excitations, but such solitons are generally unsatisfactory because the effective theory fails precisely where nonlinearities responsible for the solitons are important.	background 1.00	0.04	0.03	asserted 0.98
s1	A new class of theories possessing (internal) galilean invariance can in principle bypass this difficulty.	background 0.86	0.06	0.03	hedged possibility 0.99
s2	Here, we show that these galileon theories do not possess stable solitonic solutions.	result 0.99	0.95	0.93	asserted 1.00
s3	As a by-product, we show that no stable solitons exist for a different class of derivatively coupled theories, describing for instance the infrared dynamics of superfluids, fluids, solids and some k-essence models.	result 0.97	0.93	0.12	asserted 1.00

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Original abstract

Scalar field theories with derivative interactions are known to possess solitonic excitations, but such solitons are generally unsatisfactory because the effective theory fails precisely where nonlinearities responsible for the solitons are important. A new class of theories possessing (internal) galilean invariance can in principle bypass this difficulty. Here, we show that these galileon theories do not possess stable solitonic solutions. As a by-product, we show that no stable solitons exist for a different class of derivatively coupled theories, describing for instance the infrared dynamics of superfluids, fluids, solids and some k-essence models.

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References

Forward citations

Cited by 11 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

UV properties of Galileons: Spectral Densities
hep-th 2015-02 conditional novelty 7.0 of 10

Galileon theories are argued to be 'non-localizable' quantum field theories with exponentially growing spectral densities, computed explicitly for a duality-solvable model.
A no-hair theorem for the galileon
hep-th 2012-02 accept novelty 7.0 of 10

Static, spherically symmetric black holes cannot support a non-trivial galileon field profile, even with non-minimal couplings to gravity.
K-Oscillons: Oscillons with Non-Canonical Kinetic Terms
astro-ph.CO 2013-03 conditional novelty 6.0 of 10

Oscillons exist in scalar theories with non-canonical kinetic terms whenever a specific combination of kinetic and potential coefficients is positive, and they are unstable to long-wavelength perturbations in more tha...
Boundary Terms and Junction Conditions for Generalized Scalar-Tensor Theories
gr-qc 2012-06 conditional novelty 6.0 of 10

The authors compute Gibbons-Hawking-like boundary terms and Israel-like junction conditions for the full Horndeski scalar-tensor action, writing bulk and boundary equations of motion in explicitly second-order form.
Chronology Protection in Galileon Models and Massive Gravity
hep-th 2011-11 conditional novelty 6.0 of 10

Galileon and massive gravity effective theories forbid closed timelike curves because the scalar becomes infinitely strongly coupled and the background unstable exactly when a curve would close.

Show 6 more citing papers

General Embedded Brane Effective Field Theories
hep-th 2011-03 conditional novelty 6.0 of 10

The Galileon is one member of a larger family of brane-induced scalar field theories on curved space, all with second-order equations and symmetry-protected potentials.
Symmetries for Galileons and DBI scalars on curved space
hep-th 2011-03 conditional novelty 6.0 of 10

Embedding a maximally symmetric 3-brane in a maximally symmetric five-dimensional bulk produces scalar field theories on curved space that retain the full nonlinear shift-like symmetries of the flat-space Galileon.
Galilean symmetry in the effective theory of inflation: new shapes of non-Gaussianity
hep-th 2010-11 accept novelty 6.0 of 10

Imposing an approximate Galilean symmetry on the effective theory of inflation yields three independent six-derivative cubic operators, two with equilateral-like bispectra and one with a flattened (enfolded) shape.
Aspects of Galileon Non-Renormalization
hep-th 2016-06 conditional novelty 5.0 of 10

Galileon interaction operators are not renormalized by loops of heavy fields coupled in a symmetry-respecting way, unlike the leading operators of general relativity, P(X) theories, and the conformal dilaton, which are.
A formal introduction to Horndeski and Galileon theories and their generalizations
hep-th 2013-07 accept novelty 3.0 of 10

In four dimensions, Horndeski's 1974 scalar-tensor Lagrangian and the covariantized generalized Galileon Lagrangian describe exactly the same set of theories, and the review writes out the explicit dictionary between them.
Theoretical Aspects of Massive Gravity
hep-th 2011-05 accept novelty 3.0 of 10

Massive gravity can be organized as a consistent effective field theory with a raised cutoff and no Boulware-Deser ghost, though a UV completion remains unknown.

How the literature uses it

34 arXiv papers cite this in 50 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 39 sentences without a confident label

Contests it 2 papers

An extension of Derrick's theorem to the single galileon case was considered in [ref] , where they concluded that such terms cannot stabilize solitons, here we see how one can get around this conclusion.

Multi-galileons, solitons and Derrick's theorem · Derrick's theorem and examples · contest 0.76
Also, we will point out that ghost instabilities will develop for certain configurations, which has been neglected in [ref] , and clarify why the zero-mode argument of [ref] can not be naively generalized to include the light-like soliton case.

Note on the Stabilities of the Light-like Galileon Solutions · Introduction · contest 0.87

Cites it as support 1 paper

Thirdly, the real measure of the breakdown of the effective field theory is not determined by derivatives of $π_c$, but rather by requiring universally that gradients are small $∂≪Λ_c$ [ref] .

DBI and the Galileon reunited · Relevant operators and quantum corrections · 0.96

Cites it as background 6 papers

It is also an explicit example of the Vainshtein effect, whereby dressing the kinetic term for fluctuations raises the effective cutoff of the theory[For a discussion of how this works in the the simplest Galileon model see [ref] ].

Low-Energy Effective Field Theory for Chromo-Natural Inflation · Loop Corrections and Technical Naturalness · 0.80
The topological defects present in this general class of theories are often termed “$k$-defects," and some aspects of these objects have been studied in earlier works [ref] .

Doppelganger defects · Introduction · 0.96
However, less attention has been paid to their spatially varying, nonlinear dynamics (e.g. [ref] ).

K-Oscillons: Oscillons with Non-Canonical Kinetic Terms · Introduction · 0.90

What it cites · 12 sentences without a confident label

Cites as support 2 papers

The handful of galilean-invariant terms described above represent a consistent truncation of the theory in which we can self-consistently study non-linear classical solutions [ref] .

Classical and Quantum Consistency of the DGP Model · Introduction · 0.96
Here we are rescued by galilean invariance, thanks to which the $L_n$'s above do not get renormalized upon loop corrections, and terms with fewer derivatives per field are not generated quantum-mechanically [ref] .

Strong Interactions and Stability in the DGP Model · Introduction · 0.98

Cites as background 6 papers

Such a symmetry has been dubbed `galilean invariance', and $π$ the `galileon' [ref] .

The galileon as a local modification of gravity · Introduction · 0.97
It is worth mentioning that the galileon describes the sub-horizon dynamics of the scalar sector of the DGP [ref] model ($n=3$), and of more generic theories that modify general relativity in the IR [ref] .

Classical and Quantum Consistency of the DGP Model · Introduction · 0.92
It is worth mentioning that the galileon describes the sub-horizon dynamics of the scalar sector of the DGP [ref] model ($n=3$), and of more generic theories that modify general relativity in the IR [ref] .

4D Gravity on a Brane in 5D Minkowski Space · Introduction · 0.92

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