Mixed-symmetry tensor conserved currents and AdS/CFT correspondence

We present the full list of conserved currents built of two massless spinor fields in Minkowski space and their derivatives multiplied by Clifford algebra elements. The currents have particular mixed-symmetry type described by Young diagrams with one row and one column of arbitrary lengths and heights. Along with Yukawa-like totally antisymmetric currents the complete set of constructed currents exactly matches the spectrum of AdS mixed-symmetry fields arising in the generalized Flato-Fronsdal theorem for two spinor singletons. As a by-product, we formulate and study general properties of primary fields and conserved currents of mixed-symmetry type.Comment: 17 pages; v2: typos corrected, clarifications and refs added; v3: more explanations and refs added; contribution to the J.Phys.A special volume on "Higher Spin Theories and AdS/CFT" edited by Matthias Gaberdiel and Mikhail Vasilie

Continuous spin fields of mixed-symmetry type

We propose a description of continuous spin massless fields of mixed-symmetry type in Minkowski space at the level of equations of motion. It is based on the appropriately modified version of the constrained system originally used to describe massless bosonic fields of mixed-symmetry type. The description is shown to produce generalized versions of triplet, metric-like, and light-cone formulations. In particular, for scalar continuous spin fields we reproduce the Bekaert-Mourad formulation and the Schuster-Toro formulation. Because a continuous spin system inevitably involves infinite number of fields, specification of the allowed class of field configurations becomes a part of its definition. We show that the naive choice leads to an empty system and propose a suitable class resulting in the correct degrees of freedom. We also demonstrate that the gauge symmetries present in the formulation are all Stueckelberg-like so that the continuous spin system is not a genuine gauge theory

Lagrangian Formulation for Free Mixed-Symmetry Bosonic Gauge Fields in (A)dS(d)

Covariant Lagrangian formulation for free bosonic massless fields of arbitrary mixed-symmetry type in (A)dS(d) space-time is presented. The analysis is based on the frame-like formulation of higher-spin field dynamics [1] with higher-spin fields described as p-forms taking values in appropriate modules of the (A)dS(d). The problem of finding free field action is reduced to the analysis of an appropriate differential complex, with the derivation Q associated with the variation of the action. The constructed action exhibits additional gauge symmetries in the flat limit in agreement with the general structure of gauge symmetries for mixed-symmetry fields in Minkowski and (A)dS(d) spaces.Comment: 17 pages, v2: clarifications added, misprints corrected; v3: minor changes, typos correcte

Monodromic vs geodesic computation of Virasoro classical conformal blocks

AbstractWe compute 5-point classical conformal blocks with two heavy, two light, and one superlight operator using the monodromy approach up to third order in the superlight expansion. By virtue of the AdS/CFT correspondence we show the equivalence of the resulting expressions to those obtained in the bulk computation for the corresponding geodesic configuration

One-point thermal conformal blocks from four-point conformal integrals

Abstract We develop the thermal shadow formalism to study the conformal blocks decomposition in D-dimensional conformal field theory on S β 1 × S D − 1 {\mathbbm{S}}_{\beta}^1\times {\mathbbm{S}}^{D-1} , where the temperature is T = β −1. It is demonstrated that both the 1-point thermal (T ≠ 0) conformal blocks and the 4-point plane (T = 0) conformal blocks are defined by the same 4-point conformal integral. It is shown that up to power prefactors the 1-point thermal conformal block is given by the fourth Appell function

Multipoint conformal integrals in D dimensions. Part I. Bipartite Mellin-Barnes representation and reconstruction

Abstract We propose a systematic approach to calculating n-point one-loop parametric conformal integrals in D dimensions which we call the reconstruction procedure. It relies on decomposing a conformal integral over basis functions which are generated from a set of master functions by acting with the cyclic group ℤ n . In order to identify the master functions we introduce a bipartite Mellin-Barnes representation by means of splitting a given conformal integral into two additive parts, one of which can be evaluated explicitly in terms of multivariate generalized hypergeometric series. For the box and pentagon integrals (i.e. n = 4, 5) we show that a computable part of the bipartite representation contains all master functions. In particular, this allows us to evaluate the parametric pentagon integral as a sum of ten basis functions generated from two master functions by the cyclic group ℤ5. The resulting expression can be tested in two ways. First, when one of propagator powers is set to zero, the pentagon integral is reduced to the known box integral, which is also rederived through the reconstruction procedure. Second, going to the non-parametric case, we reproduce the known expression for the pentagon integral given in terms of logarithms derived earlier within the geometric approach to calculating conformal integrals. We conclude by considering the hexagon integral (n = 6) for which we show that those basis functions which follow from the computable part of the bipartite representation are not enough and more basis functions are required. In the second part of our project we will describe a method of constructing a complete set of master/basis functions in the n-point case

Towards higher-spin AdS2_2/CFT1_1 holography

International audienceWe aim at formulating a higher-spin gravity theory around AdS$_{2}$ relevant for holography. As a first step, we investigate its kinematics by identifying the low-dimensional cousins of the standard higher-dimensional structures in higher-spin gravity such as the singleton, the higher-spin symmetry algebra, the higher-rank gauge and matter fields, etc. In particular, the higher-spin algebra is given here by [λ] and parameterized by a real parameter λ. The singleton is defined to be a Verma module of the AdS$_{2}$ isometry subalgebra so (2, 1) ⊂ [λ] with conformal weight $\Delta =\frac{1\pm \lambda }{2}.$ On the one hand, the spectrum of local modes is determined by the Flato-Fronsdal theorem for the tensor product of two such singletons. It is given by an infinite tower of massive scalar fields in AdS$_{2}$ with ascending masses expressed in terms of λ. On the other hand, the higher-spin fields arising through the gauging of [λ] algebra do not propagate local degrees of freedom. Our analysis of the spectrum suggests that AdS$_{2}$ higher-spin gravity is a theory of an infinite collection of massive scalars with fine-tuned masses, interacting with infinitely many topological gauge fields. Finally, we discuss the holographic CFT$_{1}$ duals of the kinematical structures identified in the bulk