1,721,003 research outputs found
Generalized connections and higher spin equations
No full textWe 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
On the relation between local and geometric Lagrangians for higher spins
No full textEquations of motion for free higher-spin gauge fields of any symmetry can be formulated in terms of linearised curvatures. On the other hand, gauge invariance alone does not fix the form of the corresponding actions which, in addition, either contain higher derivatives or involve inverse powers of the d'Alembertian operator, thus introducing possible subtleties in degrees of freedom count. We suggest a path to avoid ambiguities, starting from local, unconstrained Lagrangians previously proposed, and integrating out the auxiliary fields from the functional integral, thus generating a unique non-local theory expressed in terms of curvatures
Low-Spin Models for Higher-Spin Lagrangians
No full textHigher-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
Geometric massive higher spins and current exchanges.
No full textGeneralised 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
On the geometry of higher-spin gauge fields (TOPCITE: 144 citazioni su SPIRES HEP)
No full textWe review a recent construction of the free-field equations for totally symmetric
tensors and tensor-spinors that exhibits the corresponding linearized geometry.
These equations are not local for all spins >2, involve unconstrained fields and
gauge parameters, rest on the curvatures introduced long ago by de Wit and
Freedman and reduce to the local (Fang–)Fronsdal form upon partial gauge
fixing. We also describe how the higher-spin geometry is realized in free string
field theory, and how the gauge fixing to the light cone can be effected
Minimal local Lagrangians for higher-spin geometry (TOPCITE: 71 citazioni in INSPIRE HEP)
No full textThe Fronsdal Lagrangians for free totally symmetric rank-s tensors φμ1...μs rest on suitable trace constraints for their gauge
parameters and gauge fields. Only when these constraints are removed, however, the resulting equations reflect the expected free
higher-spin geometry.We show that geometric equations, in both their local and non-local forms, can be simply recovered from
local Lagrangians with only two additional fields, a rank-(s −3) compensator αμ1...μs−3 and a rank-(s −4) Lagrange multiplier
βμ1...μs−4 . In a similar fashion, we show that geometric equations for unconstrained rank-n totally symmetric spinor-tensors
ψμ1...μn can be simply recovered from local Lagrangians with only two additional spinor-tensors, a rank-(n − 2) compensator
ξμ1...μn−2 and a rank-(n−3) Lagrange multiplier λμ1...μn−3
Geometric Lagrangians for massive higher-spin fields
No full textAbstractLagrangians for massive, unconstrained, higher-spin bosons and fermions are proposed. The idea is to modify the geometric, gauge invariant Lagrangians describing the corresponding massless theories by the addition of suitable quadratic polynomials. These polynomials provide generalisations of the Fierz–Pauli mass term containing all possible traces of the basic field. No auxiliary fields are needed
Free geometric equations for higher spins
No full textAbstractWe show how allowing non-local terms in the field equations of symmetric tensors uncovers a neat geometry that naturally generalizes the Maxwell and Einstein cases. The end results can be related to multiple traces of the generalized Riemann curvatures Rα1⋯αs;β1⋯βs introduced by de Wit and Freedman, divided by suitable powers of the D'Alembertian operator □. The conventional local equations can be recovered by a partial gauge fixing involving the trace of the gauge parameters Λα1⋯αs−1, absent in the Fronsdal formulation. The same geometry underlies the fermionic equations, that, for all spins s+1/2, can be linked via the operator ∂̷□ to those of the spin-s bosons
Higher spin fields and duality
No full textWe review the construction of free gauge theories for gauge fields in arbitrary representations of the Lorentz group in D dimensions. We describe the multi-form calculus which gives the natural geometric framework for these theories. We also discuss duality transformations that give different field theory representations of the same physical degrees of freedom, and discuss the example of gravity in D dimensions and its dual realisations in detail
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