59 research outputs found
Generalised connections and higher-spin equations
We consider high-derivative equations obtained setting to zero the divergence
of the higher-spin curvatures in metric-like form, showing their equivalence to
the second-order equations emerging from the tensionless limit of open string
field theory, which propagate reducible spectra of particles with different
spins. This result can be viewed as complementary to the possibility of setting
to zero a single trace of the higher-spin field strengths, which yields an
equation known to imply Fronsdal's equation in the compensator form. Higher
traces and divergences of the curvatures produce a whole pattern of
high-derivative equations whose systematics is also presented.Comment: 12 pages, minor change
Low-spin models for higher-spin Lagrangians
Higher-spin theories are most commonly modelled on the example of spin 2.
While this is appropriate for the description of free irreducible spin-s
particles, alternative options could be equally interesting. In particular
Maxwell's equations provide the effective model for maximally reducible
theories of higher spins inspired by the tensionless limit of the open string.
For both options, as well as for their fermionic counterparts, one can extend
the analogy beyond the equations for the gauge potentials, formulating the
corresponding Lagrangians in terms of higher-spin curvatures. The associated
non-localities are effectively due to the elimination of auxiliary fields and
do not modify the spectrum. Massive deformations of these theories are also
possible, and in particular in this contribution we propose a generalisation of
the Proca Lagrangian for the Maxwell-inspired geometric theories.Comment: 12 pages, PTPTeX. Contribution to the proceedings of the 3rd
International Conference on String Field Theory and Related Aspects (SFT
2010), Kyoto, Japan, 18-22 Oct 201
Mixed-symmetry multiplets and higher-spin curvatures
We study the higher-derivative equations for gauge potentials of arbitrary
mixed-symmetry type obtained by setting to zero the divergences of the
corresponding curvature tensors. We show that they propagate the same reducible
multiplets as the Maxwell-like second-order equations for gauge fields subject
to constrained gauge transformations. As an additional output of our analysis,
we provide a streamlined presentation of the Ricci-like case, where the traces
of the same curvature tensors are set to zero, and we present a simple
algebraic evaluation of the particle content associated with the Labastida and
with the Maxwell-like second-order equations.Comment: 24 page
On higher-spin supertranslations and superrotations
We study the large gauge transformations of massless higher-spin fields in
four-dimensional Minkowski space. Upon imposing suitable fall-off conditions,
providing higher-spin counterparts of the Bondi gauge, we observe the existence
of an infinite-dimensional asymptotic symmetry algebra. The corresponding Ward
identities can be held responsible for Weinberg's factorization theorem for
amplitudes involving soft particles of spin greater than two.Comment: Motivations and clarifications added. Matches published versio
Geometric massive higher spins and current exchanges
Generalised Fierz-Pauli mass terms allow to describe massive higher-spin
fields on flat background by means of simple quadratic deformations of the
corresponding geometric, massless Lagrangians. In this framework there is no
need for auxiliary fields. We briefly review the construction in the bosonic
case and study the interaction of these massive fields with external sources,
computing the corresponding propagators. In the same fashion as for the massive
graviton, but differently from theories where auxiliary fields are present, the
structure of the current exchange is completely determined by the form of the
mass term itself.Comment: 8 pages, LaTeX. Contribution to the proceedings of the 3rd RTN
Workshop ``Constituents, Fundamental Forces and Symmetries of the Universe''
(Valencia 1-5 October 2007
Cubic interactions of Maxwell-like higher spins
We study the cubic vertices for Maxwell-like higher-spins in flat and (A)dS
background spaces of any dimension. Reducibility of their free spectra implies
that a single cubic vertex involving any three fields subsumes a number of
couplings among different particles of various spins. The resulting vertices do
not involve traces of the fields and in this sense are simpler than their
Fronsdal counterparts. We propose an extension of both the free theory and of
its cubic deformation to a more general class of partially reducible systems,
that one can obtain from the original theory upon imposing trace constraints of
various orders. The key to our results is a version of the Noether procedure
allowing to systematically account for the deformations of the transversality
conditions to be imposed on the gauge parameters at the free level.Comment: 57 pages; added Section 7 including (A)dS off-shell cubic vertices
and corresponding generating function. Outlook extended with comments on
Maxwell-like spectra and higher-spin algebra
On the Lagrangian formulation of the double copy to cubic order
We investigate the Lagrangian formulation of the double-copy correspondence
between gauge theories and gravity, up to the cubic order. Building on the
definition of the double-copy field as a convolution of two vectors, we obtain
free gravitational Lagrangians as products of two Yang-Mills Lagrangians, in a
form amenable to be easily extended to the massive case. We discuss the origin
of these results from tensionless strings and show the existence of gauge
fixings that mix the two spin-one sectors and lead to an alternative,
especially simple, version of the free Lagrangian. We then construct cubic
vertices for the full double-copy multiplet, comprising a graviton, a two-form
and a scalar particle, by means of the Noether procedure. Both at the free and
at the cubic level the result gets uniquely fixed only upon imposing, on top of
gauge invariance, a left-right Lorentz symmetry ruling contraction of indices
among double-copy fields. Whereas the outcome nicely matches the cubic
interactions of supergravity, including the gauge-invariant
coupling between the scalar particle and the two-form, such a twofold Lorentz
symmetry seems to conflict with the perturbative reconstruction of space-time
geometry.Comment: 28 pages. minor editing, matches published versio
Exact renormalization group equation in presence of rescaling anomaly II - The local potential approximation
Exact renormalization group techniques are applied to mass deformed N=4
supersymmetric Yang-Mills theory, viewed as a regularised N=2 model. The
solution of the flow equation, in the local potential approximation, reproduces
the one-loop (perturbatively exact) expression for the effective action of N=2
supersymmetric Yang-Mills theory, when the regularising mass, M, reaches the
value of the dynamical cutoff. One speculates about the way in which further
non-perturbative contributions (instanton effects) may be accounted for.Comment: 13 pages, no figures, uses JHEP3.cl
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