Massless Higher Spin Gauge Fields Research Articles

Stringy AdS3 from the worldsheet

We investigate the behaviour of the bosonic string on AdS3 with H-flux at stringy scales, looking in particular for a ‘tensionless’ limit in which there are massless higher spin gauge fields. We do this by revisiting the physical spectrum of the mathfrak{s}mathfrak{l}{left(2, mathbb{R}right)}_k WZW model and considering the limit in which k becomes small. At k = 3 we find that there is an infinite stringy tower of massless higher spin fields which are part of a continuum of light states. This can be viewed as a novel tensionless limit, which appears to be distinct from that inferred from the symmetric orbifold description of superstring AdS3 vacua.

Higher spins at the quintic order: Localization effect and simplifications

We investigate the special case of quintic interactions for massless higher spin gauge fields using the string-theoretic vertex operator construction for higher spin gauge fields in Vasiliev's frame-like formalism. We compute explicitly the related 5-point interaction vertex in the low energy limit of string theory and find that: the structure of the quintic $s_1-s_2-s_3-s_4-s_5$ higher spin interaction gets drastically simplified and localized if a) the spin values satisfy the constraint $s_1+s_2+s_3=s_4+s_5+2$ (and, more generally, if the sum of three spin values roughly equals the sum of the remaining two b) One of the spin values, $s_4$ or $s_5$ is sufficiently small. In this paper, the explicit computation is done for the case $s_4=4$

Notes on conformal invariance of gauge fields

In Lagrangian gauge systems, the vector space of global reducibility parameters forms a module under the Lie algebra of symmetries of the action. Since the classification of global reducibility parameters is generically easier than the classification of symmetries of the action, this fact can be used to constrain the latter when knowing the former. We apply this strategy and its generalization for the non-Lagrangian setting to the problem of conformal symmetry of various free higher spin gauge fields. This scheme allows one to show that, in terms of potentials, massless higher spin gauge fields in Minkowski space and partially massless (PM) fields in (A)dS space are not conformal for spin strictly greater than one, while in terms of curvatures, maximal-depth PM fields in four dimensions are also not conformal, unlike the closely related, but less constrained, maximal-depth Fradkin–Tseytlin fields.

String theory and emergent AdS geometry in higher spin field theories

We analyze the Weyl invariance constraints on higher spin vertex operators in open superstring theory describing massless higher spin gauge field excitations in $d$-dimensional space-time. We show that these constraints lead to low-energy equations of motion for higher spin fields in AdS space, with the leading-order $\ensuremath{\beta}$ function for the higher spin fields producing Fronsdal's operator in ${\mathrm{AdS}}_{d+1}$, despite that the higher spin vertex operators are originally defined in flat background. The correspondence between the $\ensuremath{\beta}$ function in string theory and ${\mathrm{AdS}}_{d+1}$ Fronsdal operators in space-time is found to be exact for $d=4$, while for other space-time dimensions, it requires modifications of manifest expressions for the higher spin vertex operators. We argue that the correspondence considered in this paper is the leading order of a more general isomorphism between Vasiliev's equations and equations of motion of extended open string field theory, generalized to include the higher spin operators.

One loop tests of higher spin AdS/CFT

Vasiliev’s type A higher spin theories in AdS4 have been conjectured to be dual to the U(N) or O(N) singlet sectors in 3-d conformal field theories with N-component scalar fields. We compare the $ \mathcal{O} $ (N 0) correction to the 3-sphere free energy F in the CFTs with corresponding calculations in the higher spin theories. This requires evaluating a regularized sum over one loop vacuum energies of an infinite set of massless higher spin gauge fields in Euclidean AdS4. For the Vasiliev theory including fields of all integer spin and a scalar with Δ = 1 boundary condition, we show that the regularized sum vanishes. This is in perfect agreement with the vanishing of subleading corrections to F in the U(N) singlet sector of the theory of N free complex scalar fields. For the minimal Vasiliev theory including fields of only even spin, the regularized sum remarkably equals the value of F for one free real scalar field. This result may agree with the O(N) singlet sector of the theory of N real scalar fields, provided the coupling constant in the Vasiliev theory is identified as G N ~ 1/(N − 1). Similarly, consideration of the USp(N) singlet sector for N complex scalar fields, which we conjecture to be dual to the husp(2; 0|4) Vasiliev theory, requires G N ~ 1/(N + 1). We also test the higher spin AdS3 /CFT2 conjectures by calculating the regularized sum over one loop vacuum energies of higher spin fields in AdS3. We match the esult with the $ \mathcal{O} $ (N 0) term in the central charge of the W N minimal models; this requires a certain truncation of the CFT operator spectrum so that the bulk theory contains two real scalar fields with the same boundary conditions.

On generating functions of higher-spin cubic interactions

We present off-shell generating functions for all cubic interactions of totally symmetric massless Higher Spin gauge fields and discuss their properties.

Duality and integrability: Electromagnetism, linearized gravity, and massless higher spin gauge fields as bi-Hamiltonian systems

In the reduced phase space of electromagnetism, the generator of duality rotations in the usual Poisson bracket is shown to generate Maxwell’s equations in a second, much simpler Poisson bracket. This gives rise to a hierarchy of bi-Hamiltonian evolution equations in the standard way. The result can be extended to linearized Yang–Mills theory, linearized gravity, and massless higher spin gauge fields.

Superfield formulation of 4D, Script N = 1 massless higher spin gauge field theory and supermatrix model

We study the relation between a supermatrix model and the free 4D, = 1 supersymmetric field theory of a massless supermultiplet with spins (3, 5/2). In order to do this, we construct a superfield formulation of the theory. We show that solutions of the equations of motion for the supermultiplet (3, 5/2) satisfy the equations of motion of a supermatrix model.

Bosonic massless higher spin fields from matrix model

We study matrix models as a new approach to formulate massless higher spin gauge field theory. As a first step in this direction, we show that the free equation of motion of bosonic massless higher spin gauge fields can be derived from that of a matrix model.

Surface charges and dynamical Killing tensors for higher spin gauge fields in constant curvature spaces

In the context of massless higher spin gauge fields in constant curvature spaces, we compute the surface charges which generalize the electric charge for spin one, the color charges in Yang-Mills theories and the energy-momentum and angular momentum for asymptotically flat gravitational fields. We show that there is a one-to-one map from surface charges onto divergence free Killing tensors. These Killing tensors are computed by relating them to a cohomology group of the first quantized BRST model underlying the Fronsdal action.