Induced Action for Conformal Higher Spins from Worldline Path Integrals

Conformal higher spin (CHS) fields, despite being non unitary, provide a remarkable example of a consistent interacting higher spin theory in flat space background, that is local to all orders. The non-linear action is defined as the logarithmically UV divergent part of a one-loop scalar effective action. In this paper we take a particle model, that describes the interaction of a scalar particle to the CHS background, and compute its path integral on the circle. We thus provide a worldline representation for the CHS action, and rederive its quadratic part. We plan to come back to the subject, to compute cubic and higher vertices, in a future work.Comment: 24 pages, references added, minor typos correcte

Leibniz Gauge Theories and Infinity Structures

We formulate gauge theories based on Leibniz(-Loday) algebras and uncover their underlying mathematical structure. Various special cases have been developed in the context of gauged supergravity and exceptional field theory. These are based on `tensor hierarchies', which describe towers of $p$-form gauge fields transforming under non-abelian gauge symmetries and which have been constructed up to low levels. Here we define `infinity-enhanced Leibniz algebras' that guarantee the existence of consistent tensor hierarchies to arbitrary level. We contrast these algebras with strongly homotopy Lie algebras ($L_{\infty}$ algebras), which can be used to define topological field theories for which all curvatures vanish. Any infinity-enhanced Leibniz algebra carries an associated $L_{\infty}$ algebra, which we discuss.Comment: 50 pages, v2: refs added, new subsection 3.2, version to appear in Comm. Math. Phy

Frobenius-Chern-Simons gauge theory

Given a set of differential forms on an odd-dimensional noncommutative manifold valued in an internal associative algebra H, we show that the most general cubic covariant Hamiltonian action, without mass terms, is controlled by an Z_2-graded associative algebra F with a graded symmetric nondegenerate bilinear form. The resulting class of models provide a natural generalization of the Frobenius-Chern-Simons model (FCS) that was proposed in arXiv:1505.04957 as an off-shell formulation of the minimal bosonic four-dimensional higher spin gravity theory. If F is unital and the Z_2-grading is induced from a Klein operator that is outer to a proper Frobenius subalgebra, then the action can be written on a form akin to topological open string field theory in terms of a superconnection valued in the direct product of H and F. We give a new model of this type based on a twisting of C[Z_2 x Z_4], which leads to self-dual complexified gauge fields on AdS_4. If F is 3-graded, the FCS model can be truncated consistently as to zero-form constraints on-shell. Two examples thereof are a twisting of C[(Z_2)^3] that yields the original model, and the Clifford algebra Cl_2n which provides an FCS formulation of the bosonic Konstein--Vasiliev model with gauge algebra hu(4^{n-1},0).Comment: 44 page

Massive and massless higher spinning particles in odd dimensions

We study actions for massive bosonic particles of higher spins by dimensionally reducing an action for massless particles. For the latter we take a model with a SO(N) extended local supersymmetry on the worldline, that is known to describe massless (conformal) particles of higher spins in flat spacetimes of even dimensions. Dimensional reduction produces an action for massive spinning particles in odd dimensions. The field equations that emerge in a quantization a la Dirac are shown to be equivalent to the Fierz-Pauli ones. The massless limit generates a multiplet of massless states with higher spins, whose first quantized field equations have a geometric form with fields belonging to various types of Young tableaux. These geometric equations can be partially integrated to show their equivalence with the standard Fronsdal-Labastida equations. We covariantize our model to check whether an extension to curved spacetimes can be achieved. Restricting to (A)dS spaces, we find that the worldline gauge algebra becomes nonlinear, but remains first class. This guarantees consistency on such backgrounds. A light cone analysis confirms the presence of the expected propagating degrees of freedom. A covariant analysis is worked out explicitly for the massive case, which is seen to give rise to the Fierz-Pauli equations extended to (A)dS spaces. It is worth noting that in D=3 the massless limit of our model when N goes to infinity has the same field content of the Vasiliev's theory that accommodates each spin exactly once.Comment: 31 page

Noncommutative Wilson lines in higher-spin theory and correlation functions of conserved currents for free conformal fields

We first prove that, in Vasiliev's theory, the zero-form charges studied in 1103.2360 and 1208.3880 are twisted open Wilson lines in the noncommutative $Z$ space. This is shown by mapping Vasiliev's higher-spin model on noncommutative Yang--Mills theory. We then prove that, prior to Bose-symmetrising, the cyclically-symmetric higher-spin invariants given by the leading order of these $n$-point zero-form charges are equal to corresponding cyclically-invariant building blocks of $n$-point correlation functions of bilinear operators in free conformal field theories (CFT) in three dimensions. On the higher spin gravity side, our computation reproduces the results of 1210.7963 using an alternative method amenable to the computation of subleading corrections obtained by perturbation theory in normal order. On the free CFT side, our proof involves the explicit computation of the separate cyclic building blocks of the correlation functions of $n$ conserved currents in arbitrary dimension $d>2$, using polarization vectors, which is an original result. It is shown to agree, for $d=3$, with the results obtained in 1301.3123 in various dimensions and where polarization spinors were used.Comment: 1+42 pages, no figur

Particles with non abelian charges

Efficient methods for describing non abelian charges in worldline approaches to QFT are useful to simplify calculations and address structural properties, as for example color/kinematics relations. Here we analyze in detail a method for treating arbitrary non abelian charges. We use Grassmann variables to take into account color degrees of freedom, which however are known to produce reducible representations of the color group. Then we couple them to a U(1) gauge field defined on the worldline, together with a Chern-Simons term, to achieve projection on an irreducible representation. Upon gauge fixing there remains a modulus, an angle parametrizing the U(1) Wilson loop, whose dependence is taken into account exactly in the propagator of the Grassmann variables. We test the method in simple examples, the scalar and spin 1/2 contribution to the gluon self energy, and suggest that it might simplify the analysis of more involved amplitudes.Comment: 14 page