On The Uniqueness of Minimal Coupling in Higher-Spin Gauge Theory

By Nicolas Boulanger, Serge Leclercq, P. Sundell. 2008

174 citations recorded by the source corpus.

We address the uniqueness of the minimal couplings between higher-spin fields and gravity. These couplings are cubic vertices built from gauge non-invariant connections that induce non-abelian deformations of the gauge algebra. We show that Fradkin-Vasiliev's cubic 2?s?s vertex, which contains up to 2s?2 derivatives dressed by a cosmological constant ?, has a limit where: (i) ????0; (ii) the spin-2 Weyl tensor scales non-uniformly with s; and (iii) all lower-derivative couplings are scaled away. For s = 3 the limit yields the unique non-abelian spin 2?3?3 vertex found recently by two of the authors, thereby proving the uniqueness of the corresponding FV vertex. We extend the analysis to s = 4 and a class of spin 1?s?s vertices. The non-universality of the flat limit high-lightens not only the problematic aspects of higher-spin interactions with ? = 0 but also the strongly coupled nature of the derivative expansion of the fully nonlinear higher-spin field equations with ??0, wherein the standard minimal couplings mediated via the Lorentz connection are subleading at energy scales (|?|)1/2??E??Mp. Finally, combining our results with those obtained by Metsaev, we give the complete list of all the manifestly covariant cubic couplings of the form 1?s?s? and 2?s?s?, in Minkowski background.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/294ba90d2204f230bfa5f414856845d67ec34fca

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

In Nuclear and High Energy Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Elements of Vasiliev theory (2014, methodology): “A lot is known about cubic interactions both in the metric-like approach of Fronsdal [6–23] and in the frame-like approach of Vasiliev and Fradkin-Vasiliev [2–4, 24–30].”
Higher spins in AdS5 at one loop: vacuum energy, boundary conformal anomalies and AdS/CFT (2014, unknown): “) coupling to the curvature [42, 43] which does not allow the application of the standard algorithm for computing the b4 Seeley coefficient used in [16].”
Unfolding mixed-symmetry fields in AdS and the BMV conjecture: I. General formalism (2008, background): “The above proposal also rhymes well with the fact that higher-spin gauge theories have local interactions that are “exotic” (see [62] for a recent discussion) in the sense that their canonical perturbative expansion is given by a derivative expansion headed by “top-vertices” covered by inverse power”
Higher spin interactions in four-dimensions: Vasiliev versus Fronsdal (2015, background): “Whenever a pseudo-local tail, called Born–Infeld tail in [22], can be resumed into a finite multiple of a primary, it is well-defined, which is not the case for the unfolded equations discussed in section 3 as we will explain now.”
Towards metric-like higher spin gauge theories in three dimensions (2012, background): “5) by adding higher-derivative contributions to the action (see also [40, 11]).”
How higher-spin gravity surpasses the spin-two barrier (2010, methodology): “As was demonstrated in [28], in a flat background the non-abelian 2-s-s vertex is unique and involves a total number of 2s−2 derivatives.”
Cubic interactions of massless higher spins in (A)dS: Metric-like approach (2011, methodology): “The 3−3−2 vertex was also obtained in [50, 51] in terms of metric-like fields.”
On the tensionless limit of string theory, off-shell higher spin interaction vertices and BCFW recursion relations (2010, unknown): “[15].”
Quartic AdS interactions in higher-spin gravity from Conformal Field Theory (2015, background): “For these vertices, what remains in the flat space limit is only the term with the highest number of derivatives [8, 15].”