Extended string field theory for massless higher-spin fields

We propose a new gauge field theory which is an extension of ordinary string field theory by assembling multiple state spaces of the bosonic string. The theory includes higher-spin fields in its massless spectrum together with the infinite tower of massive fields. From the theory, we can easily extract the minimal gauge-invariant quadratic action for tensor fields with any symmetry. As examples, we explicitly derive the gauge-invariant actions for some simple mixed symmetric tensor fields. We also construct covariantly gauge-fixed action by extending the method developed for string field theory.     

On the theoretical problems in constructing interactions involving higher-spin massless particles

It is shown that a gauge theory of self-interacting massless spin-3 particles which is analogous to Yang-Mills or the theory of gravity does not exist. A way out may be the existence of an interacting infinite family of massless particles of various spins. The first-order interactions which are possible between such particles show a remarkable structure. This is established by explicit construction. Detailed results are obtained for the possible algebraic structures which one may obtain for gauge theories which are induced from the gauge invariance of free lagrangians.     

On the nuclearity condition for massless fields

It is shown that quantum field theories of free massless particles satisfy a recently proposed nuclearity condition restricting the admissible number of local degrees of freedom of a theory. This result is based on an improved bound for the nuclearity index of certain specific sets of vectors in Fock space.     

On the propagation of massless fields

An inequality is discussed expressing the idea that a physical quantity associated with massless fields should propagate at the speed of light. It is shown that the inequality holds for the energy of massless bosons of spin zero and one.     

Partially massless higher-spin theory II: one-loop effective actions

We continue our study of a generalization of the D-dimensional linearized Vasiliev higher-spin equations to include a tower of partially massless (PM) fields. We compute one-loop effective actions by evaluating zeta functions for both the “minimal” and “non-minimal” parity-even versions of the theory. Specifically, we compute the log-divergent part of the effective action in odd-dimensional Euclidean AdS spaces for D = 7 through 19 (dual to the a-type conformal anomaly of the dual boundary theory), and the finite part of the effective action in even-dimensional Euclidean AdS spaces for D = 4 through 8 (dual to the free energy on a sphere of the dual boundary theory). We pay special attention to the case D = 4, where module mixings occur in the dual field theory and subtlety arises in the one-loop computation. The results provide evidence that the theory is UV complete and one-loop exact, and we conjecture and provide evidence for a map between the inverse Newton’s constant of the partially massless higher-spin theory and the number of colors in the dual CFT.     

Light-cone quantization for massless fields

When the light-cone quantization procedure is applied to massless fields care must be taken or the resulting theory will not be isomorphic to the equivalent theory quantized at equal times. The special considerations necessary for massless fields are described here and their application to recently presented calculations in 1+1 dimensions are discussed.     

Boundary terms for massless fermionic fields

Local supersymmetry leads to boundary conditions for fermionic fields in one-loop quantum cosmology involving the Euclidean normal _e n _A/A to the boundary and a pair of independent spinor fields ^A and . This paper studies the corresponding classical properties, i.e., the classical boundary-value problem and boundary terms in the variational problem. If is set to zero on a 3-sphere bounding flat Euclidean 4-space, the modes of the massless spin–1/2 field multiplying harmonics having positive eigenvalues for the intrinsic 3-dimensional Dirac operator onS ³ should vanish onS ³. Remarkably, this coincides with the property of the classical boundary-value problem when spectral boundary conditions are imposed onS ³ in the massless case. Moreover, the boundary term in the action functional is proportional to the integral on the boundary of ^A _e n _AA ^A .     

On partition function and Weyl anomaly of conformal higher-spin fields

We study 4-dimensional higher-derivative conformal higher-spin (CHS) fields generalizing Weyl graviton and conformal gravitino. They appear, in particular, as “induced” theories in the AdS/CFT context. We consider their partition function on curved Einstein-space backgrounds like (A)dS or sphere and Ricci-flat spaces. Remarkably, the bosonic (integer spin s) CHS partition function appears to be given by a product of partition functions of the standard 2nd-derivative “partially massless” spin s   fields, generalizing the previously known expression for the 1-loop Weyl graviton (s=2$s=2$) partition function. We compute the corresponding spin s   Weyl anomaly coefficients _as${\mathrm{a}}_s$ and _cs${\mathrm{c}}_s$. Our result for _as${\mathrm{a}}_s$ reproduces the expression found recently in arXiv:1306.5242 by an indirect method implied by AdS/CFT (which relates the partition function of a CHS field on S⁴$S^4$ to a ratio of known partition functions of massless higher-spin field in AdS₅ with alternate boundary conditions). We also obtain similar results for the fermionic CHS fields. In the half-integer s case the CHS partition function on (A)dS background is given by the product of squares of “partially massless” spin s partition functions and one extra factor corresponding to a special massive conformally invariant spin s field. It was noticed in arXiv:1306.5242 that the sum of the bosonic _as${\mathrm{a}}_s$ coefficients over all s is zero when computed using the ζ-function regularization, and we observe that the same property is true also in the fermionic case.     

Frame-like action and unfolded formulation for massive higher-spin fields

Unfolded equations of motion for symmetric massive bosonic fields of any spin in Minkowski and (A)dS$(A)\mathit{dS}$ spaces are presented. Manifestly gauge invariant action for a spin s?2$s?2$ massive field in any dimension is constructed in terms of gauge invariant curvatures.     

A generalized consistency condition for massless fields

Using a generalized consistency condition (gcc), we construct couplings between massless scalar fields and the spin 2 gravitational field. Specifically, we consider all possible third-order interaction terms for scalar fields and a and use the gcc to single out one. We also find three generalized current identities associated with the massless gauge fields.     

Twistor diagrams for spinning massless free fields

A set of simple identities is utilized to build up new projective twistor diagrams for massless free fields of arbitrary spin in real Minkowski space. It is effectively shown that the inner structure of the configurations which arise out of implementing the relevant techniques has characteristics that are different from those of the conventional diagrams associated with the Kirchoff-D'Adhemar-Penrose integral expressions. A nonhomogeneous version of the configurations is also provided.     

New exact Einstein-Maxwell fields for a massless charge

New solutions of the Einstein-Maxwell equations are presented. The solutions describe the gravitational fields of a massless charge.     

Frame-like actions for massless mixed-symmetry fields in Minkowski space

A frame-like action for arbitrary mixed-symmetry bosonic massless fields in Minkowski space is constructed. The action is given in a simple form and consists of two terms for a field of any spin. The fields and gauge parameters are certain tensor-valued differential forms. The formulation is based on the unfolded form of equations for mixed-symmetry fields.