Brane partons and singleton strings

Abstract

We examine p-branes in AdS D in two limits where they exhibit partonic behavior: rotating branes with energy concentrated to cusp-like solitons; tensionless branes with energy distributed over singletonic bits on the Dirac hypercone. Evidence for a smooth transition from cusps to bits are found. First, each cusp yields D − 2 normal-coordinate bound states with protected frequencies; and is dual to a short open p-brane becoming massless on the giant-vacuum brane at the end-of-the-universe. Second, the N bit -sector is an sp ( 2 N bit ) -gauged phase-space sigma model giving rise to symmetrized N bit -pletons of the minimal higher-spin algebra ho 0 ( D − 1 , 2 ) ⊃ so ( D − 1 , 2 ) . The continuum limit leads to a 2d chiral sp ( 2 ) -gauged sigma model which is critical in D = 7 ; equivalent à la Bars–Vasiliev to an su ( 2 ) -gauged spinor string; and furthermore dual to WZW model in turn containing a topological so ˆ ( 6 , 2 ) −2 / ( so ˆ ( 6 ) ⊕ so ˆ ( 2 ) ) −2 coset model giving rise to a chiral ring generated by singleton-valued weight-0 spin fields. Moreover, the two-bit truncation leads via a reformulation à la Cattaneo–Felder–Kontsevich to a topological open string on the phase space of the D-dimensional Dirac hypercone giving rise to the Vasiliev equations based on vector oscillators and weak sp ( 2 ) -projection. Geometrically, the bi-locality reflects broken boundary-singleton worldlines, and the intertwiner κ relates T- and R-ordered deformations of the boundary and the bulk of the worldsheet, respectively.