No Arabic abstract
Higher-spin theory contains a complex coupling parameter $eta$. Different higher-spin vertices are associated with different powers of $eta$ and its complex conjugate $bar eta$. Using $Z$-dominance Lemma, that controls spin-locality of the higher-spin equations, we show that the third-order contribution to the zero-form $B(Z;Y;K)$ admits a $Z$-dominated form that leads to spin-local vertices in the $eta^2$ and $bar eta^2$ sectors of the higher-spin equations. These vertices include, in particular, the $eta^2$ and $bar eta^2$ parts of the $phi^4$ scalar field vertex.
Higher-spin vertices containing up to quintic interactions at the Lagrangian level are explicitly calculated in the one-form sector of the non-linear unfolded higher-spin equations using a $betato-infty$--shifted contracting homotopy introduced in the paper. The problem is solved in a background independent way and for any value of the complex parameter $eta$ in the HS equations. All obtained vertices are shown to be spin-local containing a finite number of derivatives in the spinor space for any given set of spins. The vertices proportional to $eta^2$ and $bar eta^2$ are in addition ultra-local, i.e. zero-forms that enter into the vertex in question are free from the dependence on at least one of the spinor variables $y$ or $bar y$. Also the $eta^2$ and $bar eta^2$ vertices are shown to vanish on any purely gravitational background hence not contributing to the higher-spin current interactions on $AdS_4$. This implies in particular that the gravitational constant in front of the stress tensor is positive being proportional to $etabar eta$. It is shown that the $beta$-shifted homotopy technique developed in this paper can be reinterpreted as the conventional one but in the $beta$-dependent deformed star product.
A new class of shifted homotopy operators in higher-spin gauge theory is introduced. A sufficient condition for locality of dynamical equations is formulated and Pfaffian Locality Theorem identifying a subclass of shifted homotopies that decrease the degree of non-locality in higher orders of the perturbative expansion is proven.
Two-dimensional BF theory with infinitely many higher spin fields is proposed. It is interpreted as the AdS(2) higher spin gravity model describing a consistent interaction between local fields in AdS(2) space including gravitational field, higher spin partially-massless fields, and dilaton fields. We carry out analysis of the frame-like and the metric-like formulation of the theory. Infinite-dimensional higher spin global algebras and their finite-dimensional truncations are realized in terms of o(2,1) - sp(2) Howe dual auxiliary variables.
New homotopy approach to the analysis of nonlinear higher-spin equations is developed. It is shown to directly reproduce the previously obtained local vertices. Simplest cubic (quartic in Lagrangian nomenclature) higher-spin interaction vertices in four dimensional theory are examined from locality perspective by the new approach and shown to be local. The results are obtained in a background independent fashion.
We consider the holographic duality between 4d type-A higher-spin gravity and a 3d free vector model. It is known that the Feynman diagrams for boundary correlators can be encapsulated in an HS-algebraic twistorial expression. This expression can be evaluated not just on separate boundary insertions, but on entire finite source distributions. We do so for the first time, and find that the result Z_HS disagrees with the usual CFT partition function. While such disagreement was expected due to contact corrections, it persists even in their absence. We ascribe it to a confusion between on-shell and off-shell boundary calculations. In Lorentzian boundary signature, this manifests via wrong relative signs for Feynman diagrams with different permutations of the source points. In Euclidean, the signs are instead ambiguous, spoiling would-be linear superpositions. Framing the situation as a conflict between boundary locality and HS symmetry, we sacrifice locality and choose to take Z_HS seriously. We are rewarded by the dissolution of a long-standing pathology in higher-spin dS/CFT. Though we lose the connection to the local CFT, the precise form of Z_HS can be recovered from first principles, by demanding a spin-local boundary action.