Brane Partons and Singleton Strings

TL;DR

The paper investigates p-branes in AdS in two tension regimes—cusp-dominated rotating branes and tensionless singleton-parton configurations on the Dirac hypercone—and shows a smooth transition between these pictures. It builds a cohesive framework where discretized brane partons yield an $rak{sp}(2N)$-gauged phase-space sigma model, whose continuum limit connects to a 2d chiral $rak{sp}(2)$-gauged theory at $D=7$ and to Bars–Vasiliev higher-spin constructions, including WZW cosets with singleton chiral rings. A central theme is the open-string reformulation of singleton dynamics, via Cattaneo–Felder–Kontsevich-like phase-space quantization and BRST/GKO-type projections, to produce Vasiliev’s master-field equations with vector oscillators and weak $rak{sp}(2)$ projection. The work culminates in a detailed open-string/doubling program, where unfolding and bi-local observables encode the higher-spin interactions and a generalized Chan-Paton structure, while highlighting profound questions about quantum completion, holography, and the role of singular CFTs at brane boundaries.

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 partons on the Dirac hypercone. Evidence for a smooth transition from cusps to partons is found. First, each cusp yields D-2 normal-coordinate bound states with protected frequencies (for p>2 there are additional bound states); and can moreover be related to a short open p-brane whose tension diverges at the AdS boundary leading to a decoupled singular CFT at the ``brane at the end-of-the-universe''. Second, discretizing the closed p-brane and keeping the number N of discrete partons finite yields an sp(2N)-gauged phase-space sigma model giving rise to symmetrized N-tupletons of the minimal higher-spin algebra ho_0(D-1,2)\supset so(D-1,2). The continuum limit leads to a 2d chiral sp(2)-gauged sigma model which is critical in D=7; equivalent a la Bars-Vasiliev to an su(2)-gauged spinor string; and furthermore dual to a WZW model in turn containing a topological \hat{so}(6,2)_{-2}/(\hat{so}(6)\oplus \hat\so(2))_{-2} coset model with a chiral ring generated by singleton-valued weight-0 spin fields. Moreover, the two-parton truncation can be linked via a reformulation a la Cattaneo-Felder-Kontsevich to a topological open string on the phase space of the D-dimensional Dirac hypercone. We present evidence that a suitable deformation of the open string leads to the Vasiliev equations based on vector oscillators and weak sp(2)-projection. Geometrically, the bi-locality reflects broken boundary-singleton worldlines, while Vasiliev's intertwiner kappa can be seen to relate T and R-ordered deformations of the boundary and the bulk of the worldsheet, respectively.

Figures (4)

• Figure 1: The Pöschl-Teller potential: The $\sigma$-dependent mass-term on the rotating string has height $\sim 1/L$ a small "well" of width $\sim L$ which fits precisely one even bound state.
• Figure 2: Long-string interactions: Two long strings with cusps at their ends interact. Two cusps annihilate while emitting waves that later recombine into a new pair of cusps.
• Figure 3: Parity and time-reversal in ambient spacetime: The parity transformation $v_Ax^A_i\rightarrow -v_Ax^A_i$ reverses the orientation of the worldline of a singleton rotating in ambient space.
• Figure 4: Amputation and Role of Intertwiner: An external two-singleton composite $|\Psi\rangle_{12}=|\alpha\rangle_1|\beta\rangle_2+|\widetilde{\alpha}\rangle_1|\widetilde{\beta}\rangle_2$, is mapped to a twisted-adjoint vertex operator $\Phi=|\alpha\rangle\langle\beta|+|\widetilde{\alpha}\rangle\langle\widetilde{\beta}|$ inserted into an $R$-ordered disc correlator, or, equivalently, to a massless vertex operator ${\cal V} =\Phi\star\kappa=|\alpha\rangle\langle\widetilde{\beta}|+|\widetilde{\alpha}\rangle\langle\beta|$ inserted into a $T$-ordered boundary correlator. The arrows indicate the orientations of the corresponding worldlines, and the amputation amounts to replacing $\Phi=C\star M$ by $C\star\Delta$ where $M$ and $\Delta$ are the singular and normalizable $\mathfrak{sp}(2)$ projectors.