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# Higher-spin holography and cubic interactions

### Euihun Joung (Pisa)

#### 15.11.2012 at 16:15

Some issues of higher-spin (HS) gauge theory (in d+1>3), mainly related to its holography, are discussed. After providing a very brief overview on the topic, we begin with the boundary side: the HS symmetry, the effective action and the HS Weyl anomaly of scalar CFT are discussed with comments on the generic 3pt functions of HS currents. Moving to the bulk side, we focus on the metric-like description of HS gauge theory, whose interacting action is not yet known. For the quadratic action, we show, through a holographic renormalization, that the both sides match being free from the HS Weyl anomaly (for d+1>3). For the cubic interaction, using the ambient- space formulation, we construct all gauge consistent vertices whose number matches that of 3pt functions. Only one of those vertices correspond to the free scalar CFT on the boundary, hence the metric-like version of the vertex encoded in Vasiliev's equation. The construction of vertices can be generalized to dS---where we also have partially-massless HS fields---showing much richer structure of cubic interactions. We conclude with some remarks on the conformal HS action which arises from the effective action of free scalar field: its spectrum and its possible link to the unknown action of interacting HS fields.

Arnold Sommerfeld Center

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