Current Interactions from the One-Form Sector of Nonlinear Higher-Spin Equations

The form of higher-spin current interactions in the sector of one-forms is derived from the nonlinear higher-spin equations in $AdS_4$. Quadratic corrections to higher-spin equations are shown to be independent of the phase of the parameter $\eta =\exp i\varphi$ in the full nonlinear higher-spin equations. The current deformation resulting from the nonlinear higher-spin equations is represented in the canonical form with the minimal number of space-time derivatives. The non-zero spin-dependent coupling constants of the resulting currents are determined in terms of the higher-spin coupling constant $\eta\bar\eta$. Our results confirm the conjecture that (anti-)self-dual nonlinear higher-spin equations result from the full system at ($\eta=0$) $\bar \eta=0$.Comment: 38 pages, no figures; V2: 39 pages, minor corrections, to be published versio

Higher-Rank Fields and Currents

$Sp(2M)$ invariant field equations in the space ${\cal M}_M$ with symmetric matrix coordinates are classified. Analogous results are obtained for Minkowski-like subspaces of ${\cal M}_M$ which include usual $4d$ Minkowski space as a particular case. The constructed equations are associated with the tensor products of the Fock (singleton) representation of $Sp(2M)$ of any rank ${\mathbf{r }}$. The infinite set of higher-spin conserved currents multilinear in rank-one fields in ${\cal M}_M$ is found. The associated conserved charges are supported by $({\mathbf{r }} M-\frac{{\mathbf{r }} ({\mathbf{r }} -1)}{2})-$dimensional differential forms in ${\cal M}_M$, that are closed by virtue of the rank-$2{\mathbf{r }}$ field equations. The cohomology groups $H^p(\sigma^{\mathbf{r }}_-)$ with all $p$ and ${\mathbf{r }}$, which determine the form of appropriate gauge fields and their field equations, are found both for ${\cal M}_M$ and for its Minkowski-like subspace.Comment: 27 pages; V2: Significant extension of the results to computation of all $\sigma_-$ cohomologies, 43 pages; V3: Discussion of equations in generalized Minkowski space from the perspective of usual Minkowski space and reference added, typos corrected, the journal version, 44 page

Controlled Natural Language Processing as Answer Set Programming: an Experiment

Most controlled natural languages (CNLs) are processed with the help of a pipeline architecture that relies on different software components. We investigate in this paper in an experimental way how well answer set programming (ASP) is suited as a unifying framework for parsing a CNL, deriving a formal representation for the resulting syntax trees, and for reasoning with that representation. We start from a list of input tokens in ASP notation and show how this input can be transformed into a syntax tree using an ASP grammar and then into reified ASP rules in form of a set of facts. These facts are then processed by an ASP meta-interpreter that allows us to infer new knowledge

Homotopy Operators and Locality Theorems in Higher-Spin Equations

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.Comment: 22 pages, no figures; V3: Some normalizations changed to conform to 1807.00001, acknowledgement added; V4: 20 pages. Matches the published version. Clarifications and reference added. Section 7 is removed in favor of a more detailed future publicatio