68 research outputs found
Weyl Action of Two-Column Mixed-Symmetry Field and Its Factorization Around (A)dS Space
We investigate the four-derivative free Weyl action for two-column
mixed-symmetry field that makes use of maximal gauge symmetries. In flat space,
the action can be uniquely determined from gauge and Weyl (trace shift)
symmetry requirements. We show that there is a smooth and unique deformation of
the flat action to (A)dS which keeps the same amount of gauge symmetries. This
action admits a factorization into two distinct two-derivative actions having
gauge parameters of different Young diagrams. Hence, this factorization pattern
naturally extends that of the Weyl actions of symmetric higher spin fields to
mixed-symmetry cases. The mass-deformation for these actions can be realized
preserving one of the gauge symmetries. Although generically non-unitary, in
special dimensions, unitarity is achieved selecting different mass deformations
for dS and AdS. We consider particular examples of our construction such as New
Massive Gravity in three dimensions, linearized bigravity in four dimensions
and their arbitrary dimensional generalizations.Comment: 25 pages, minor corrections, references added, version published in
JHE
Partially-massless higher-spin algebras and their finite-dimensional truncations
The global symmetry algebras of partially-massless (PM) higher-spin (HS)
fields in (A)dS are studied. The algebras involving PM generators up to
depth are defined as the maximal symmetries of free conformal
scalar field with order wave equation in dimensions. We review
the construction of these algebras by quotienting certain ideals in the
universal enveloping algebra of isometries. We discuss another
description in terms of Howe duality and derive the formula for computing trace
in these algebras. This enables us to explicitly calculate the bilinear form
for this one-parameter family of algebras. In particular, the bilinear form
shows the appearance of additional ideal for any non-negative integer values of
, which coincides with the annihilator of the one-row -box
Young diagram representation of . Hence, the
corresponding finite-dimensional coset algebra spanned by massless and PM
generators is equivalent to the symmetries of this representation.Comment: 22 pages, references added, revised version, accepted to JHE
A note on higher-derivative actions for free higher-spin fields
Higher-derivative theories of free higher-spin fields are investigated
focusing on their symmetries. Generalizing familiar two-derivative constrained
formulations, we first construct less-constrained Einstein-like and
Maxwell-like higher-derivative actions. Then, we construct Weyl-like actions -
the actions admitting constrained Weyl symmetries - with different numbers of
derivatives. They are presented in a factorized form making use of
Einstein-like and Maxwell-like tensors. The last (highest-derivative) member of
the hierarchy of the Weyl-like actions coincides with the Fradkin-Tseytlin
conformal higher-spin action in four dimensions.Comment: Version to appear in JHEP, 22 page
Higher-derivative massive actions from dimensional reduction
A procedure to obtain higher-derivative free massive actions is proposed. It
consists in dimensional reduction of conventional two-derivative massless
actions, where solutions to constraints bring in higher derivatives. We apply
this procedure to derive the arbitrary dimensional generalizations of
(linearized) New Massive Gravity and New Topologically Massive Gravity.Comment: 18 page
Notes on higher-spin algebras: minimal representations and structure constants
The higher-spin (HS) algebras so far known can be interpreted as the
symmetries of the minimal representation of the isometry algebra. After
discussing this connection briefly, we generalize this concept to any classical
Lie algebras and consider the corresponding HS algebras. For sp(2N) and so(N),
the minimal representations are unique so we get unique HS algebras. For sl(N),
the minimal representation has one-parameter family, so does the corresponding
HS algebra. The so(N) HS algebra is what underlies the Vasiliev theory while
the sl(2) one coincides with the 3D HS algebra hs[lambda]. Finally, we derive
the explicit expression of the structure constant of these algebras --- more
precisely, their bilinear and trilinear forms. Several consistency checks are
carried out for our results.Comment: minor corrections, references adde
Looking for partially-massless gravity
We study the possibility for a unitary theory of partially-massless (PM)
spin-two field interacting with Gravity in arbitrary dimensions. We show that
the gauge and parity invariant interaction of PM spin two particles requires
the inclusion of specific massive spin-two fields and leads to a reconstruction
of Conformal Gravity, or multiple copies of the latter in even dimensions. By
relaxing the parity invariance, we find a possibility of a unitary theory in
four dimensions, but this theory cannot be constructed in the standard
formulation, due to the absence of the parity-odd cubic vertex therein.
Finally, by relaxing the general covariance, we show that a `non-geometric'
coupling between massless and PM spin-two fields may lead to an alternative
possibility of a unitary theory. We also clarify some aspects of interactions
between massless, partially-massless and massive fields, and resolve
disagreements in the literature.Comment: 47 pages, journal version with minor correction
No-Go Theorems for Unitary and Interacting Partially Massless Spin-Two Fields
We examine the generic theory of a partially massless (PM) spin-two field
interacting with gravity in four dimensions from a bottom-up perspective. By
analyzing the most general form of the Lagrangian, we first show that if such a
theory exists, its de Sitter background must admit either so(1, 5) or so(2, 4)
global symmetry depending on the relative sign of the kinetic terms: the former
for a positive sign the latter for a negative sign. Further analysis reveals
that the coupling constant of the PM cubic self-interaction must be fixed with
a purely imaginary number in the case of a positive sign. We conclude that
there cannot exist a unitary theory of a PM spin-two field coupled to Einstein
gravity with a perturbatively local Lagrangian. In the case of a negative sign
we recover conformal gravity. As a special case of our analysis, it is shown
that the PM limit of massive gravity also lacks the PM gauge symmetry.Comment: 20 pages, LaTex, v2: references added, typos corrected; discussion
added about the pure PM theory without massless spin-2 field; extended
version of the letter accepted in PR
Exploring Free Matrix CFT Holographies at One-Loop
We extend our recent study on the duality between stringy higher spin
theories and free CFTs in the adjoint representation to other matrix
models namely the free and adjoint models as well as the free
bi-fundamental and bi-vector models. After
determining the spectrum of the theories in the planar limit by Polya counting,
we compute the one loop vacuum energy and Casimir energy for their respective
bulk duals by means of the CIRZ method that we have introduced recently. We
also elaborate on possible ambiguities in the application of this method.Comment: 37 pages, 7 figure
A Calculus for Higher Spin Interactions
Higher spin theories can be efficiently described in terms of auxiliary
St\"uckelberg or projective space field multiplets. By considering how higher
spin models couple to scale, these approaches can be unified in a conformal
geometry/tractor calculus framework. We review these methods and apply them to
higher spin vertices to obtain a generating function for massless, massive and
partially massless three-point interactions.Comment: 24 pages, 3 figures, LaTex. References added, typos corrected. Final
version to appear in JHE
Generating functions of (partially-)massless higher-spin cubic interactions
Generating functions encoding cubic interactions of (partially-)massless
higher-spin fields are provided within the ambient-space formalism. They
satisfy a system of higher-order partial differential equations that can be
explicitly solved due to their factorized form. We find that the number of
consistent couplings increases whenever the squares of the field masses take
some integer values (in units of the cosmological constant) and satisfy certain
conditions. Moreover, it is shown that only the supplemental solutions can give
rise to non-Abelian deformations of the gauge symmetries. The presence of these
conditions on the masses is a distinctive feature of (A)dS interactions that
has in general no direct counterpart in flat space.Comment: 29 pages, 2 figures. References adde
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