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On the Conformal Symmetry of Exceptional Scalar Theories

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Kara Farnsworth, Kurt Hinterbichler, Ondrej Hulik

High Energy Physics - Theory · Submitted 24 Feb 2021

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

The authors' main claim The DBI and special galileon theories exhibit a conformal symmetry at unphysical values of the spacetime dimension.

how it is stated · asserted 1.00 read the record →

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arXiv ID2102.12479 (version 1)
Pith IDFEESGI52, Pith's permanent record of this paper and its review
CitationKara Farnsworth, Kurt Hinterbichler, Ondrej Hulik. "On the Conformal Symmetry of Exceptional Scalar Theories." arXiv:2102.12479 (2021). https://pith.science/paper/FEESGI52
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,580 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.68 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.07 · compares with prior results 0.13 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

The DBI and special galileon theories exhibit a conformal symmetry at unphysical values of the spacetime dimension. We find the Lagrangian form of this symmetry. The special conformal transformations are non-linearly realized on the fields, even though conformal symmetry is unbroken. Commuting the conformal transformations with the extended shift symmetries, we find new symmetries, which when taken together with the conformal and shift symmetries close into a larger algebra. For DBI this larger algebra is the conformal algebra of the higher dimensional bulk in the brane embedding view of DBI. For the special galileon it is a real form of the special linear algebra. We also find the Weyl transformations corresponding to the conformal symmetries, as well as the necessary improvement terms to make the theories Weyl invariant, to second order in the coupling in the DBI case and to lowest order in the coupling in the special galileon case.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 The DBI and special galileon theories exhibit a conformal symmetry at unphysical values of the spacetime dimension. result 0.90 0.27 0.47 asserted 1.00
s1 We find the Lagrangian form of this symmetry. contribution 0.56 0.96 0.10 asserted 1.00
s2 The special conformal transformations are non-linearly realized on the fields, even though conformal symmetry is unbroken. result 0.99 0.57 0.14 asserted 1.00
s3 Commuting the conformal transformations with the extended shift symmetries, we find new symmetries, which when taken together with the conformal and shift symmetries close into a larger algebra. result 0.64 0.95 0.25 asserted 1.00
s4 For DBI this larger algebra is the conformal algebra of the higher dimensional bulk in the brane embedding view of DBI. interpretation 0.52 0.77 0.15 asserted 1.00
s5 For the special galileon it is a real form of the special linear algebra. result 0.96 0.85 0.13 asserted 1.00
s6 We also find the Weyl transformations corresponding to the conformal symmetries, as well as the necessary improvement terms to make the theories Weyl invariant, to second order in the coupling in the DBI case and to lowest order in the coupling in the special galileon case. result 0.79 0.95 0.12 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

The DBI and special galileon theories exhibit a conformal symmetry at unphysical values of the spacetime dimension. We find the Lagrangian form of this symmetry. The special conformal transformations are non-linearly realized on the fields, even though conformal symmetry is unbroken. Commuting the conformal transformations with the extended shift symmetries, we find new symmetries, which when taken together with the conformal and shift symmetries close into a larger algebra. For DBI this larger algebra is the conformal algebra of the higher dimensional bulk in the brane embedding view of DBI. For the special galileon it is a real form of the special linear algebra. We also find the Weyl transformations corresponding to the conformal symmetries, as well as the necessary improvement terms to make the theories Weyl invariant, to second order in the coupling in the DBI case and to lowest order in the coupling in the special galileon case.

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References
How the literature uses it

2 arXiv papers cite this in 2 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

What it cites · 51 sentences without a confident label

Compares with 2 papers
  • In the third line there are additional terms linear in the curvature that do not appear in [ref] , but these can be removed by field re-definitions that vanish in flat space with $σ= 2b·x$, at the expense of making the Weyl transformation [ref] more complicated.

    Hidden Conformal Invariance of Scalar Effective Field Theories · Special Galileon · 0.85

  • The breaking pattern is to the $d$ dimensional conformal algebra, since the shifts $S^AB$ are the only ones that do not preserve the vacuum $ϕ=0$, sl(d+2,ℝ)→so(2,d) , α>0.In fact, this is the same symmetry breaking pattern as the AdS special galileon theory in $d+1$ dimensions (the $k=2$ non-abelian AdS scalar shift theory of [ref] ).

    Shift Symmetries in (Anti) de Sitter Space · Including shift symmetries · 0.91

Cites as support 1 paper
  • In [ref] it is shown that these theories also have full conformal invariance in addition to scale invariance, and that the conformal invariance is non-trivial and fixes the structure of the Lagrangian to be that of DBI/special galileon.

    Hidden Conformal Invariance of Scalar Effective Field Theories · Introduction · 0.96

Cites as background 12 papers
  • These two theories, among others [ref] , have a privileged place among scalar effective field theories; they naturally appear in the Cachazo-Yuan-He (CHY) representation [ref] and act as nodes in a web of theories related by the double copy and other procedures [ref] (see [ref] for a nice visual representation of this web).

    Scattering of Massless Particles in Arbitrary Dimension · Introduction · 0.92

  • These two theories, among others [ref] , have a privileged place among scalar effective field theories; they naturally appear in the Cachazo-Yuan-He (CHY) representation [ref] and act as nodes in a web of theories related by the double copy and other procedures [ref] (see [ref] for a nice visual representation of this web).

    Scattering Equations and Matrices: From Einstein To Yang-Mills, DBI and NLSM · Introduction · 0.92

  • These two theories, among others [ref] , have a privileged place among scalar effective field theories; they naturally appear in the Cachazo-Yuan-He (CHY) representation [ref] and act as nodes in a web of theories related by the double copy and other procedures [ref] (see [ref] for a nice visual representation of this web).

    Extensions of Theories from Soft Limits · Introduction · 0.92

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