Splitting spinning strings in AdS/CFT

TL;DR

The paper investigates the semiclassical decay of macroscopic spinning strings in AdS5×S5 via spontaneous splitting of a folded string. It shows that an infinite tower of local charges fixes the outgoing string data and derives functional relations between charges, including a generating functional for the higher charges. It connects to the dual N=4 SYM through non-planar dilatation operators and a spin-chain perspective, discussing the role of an effective genus parameter J^2/N and the obstacles to matching to full quantum amplitudes. The results indicate a dominant, charge-preserving channel that hints at a controlled extension of integrability beyond the planar limit.

Abstract

We study the semiclassical decay of macroscopic spinning strings in AdS_5 x S^5 through spontaneous splitting of the folded string worldsheet. Based on similar considerations in flat space this decay channel is expected to dominate the full quantum computation. The outgoing strings are uniquely specified by an infinite set of conserved (local) charges with a regular expansion in inverse powers of the initial angular momentum. We compute these charges and determine functional relations between them. Finally, a preliminary discussion of the corresponding calculation in the non-planar sector of the dual gauge theory is presented.

Figures (5)

• Figure 1: Semi-classical decay of a folded, rotating string in flat space-time, following Iengo:2003ct. The plot on the right shows snapshots at various values of $\tau$. The outgoing pieces exhibit kinks, which propagate outward along the strings. New momenta $P_x^I= -P_x^{II}$ are generated in the decay process.
• Figure 2: Sketch of the relation between the semi-classical and the full quantum calculations. The surface depicts the quantum decay amplitude over the (horizontal) plane spanned by the mass-square of the two outgoing strings, $(M_I)^2$ and $(M_{II})^2$. The amplitude reaches its maximum over the curve allowed by semi-classical decay.
• Figure 3: Plot of the relation between $\beta_{12}$ (horizontal) and $\beta^0_{34}$ (vertical) as defined in (\ref{['e:beta1234def']}). The various curves correspond to various values for the filling fraction $\alpha\in[0.05,\ldots 0.5]$.
• Figure 4: The energy ${\cal E}_0^I$ of the first outgoing string as a function of $\beta_{12}$, for various filling fractions $\alpha\in[0.05,\ldots,0.5]$. The straight line corresponds to $\alpha=0.5$.
• Figure 5: The combination of new angular charges $\Delta:= ({\cal J}_{14}^{I})^2 - ({\cal J}_{23}^{I})^2$ plotted as a function of $\beta_{12}$, again for $\alpha$ in the range $[0.05,\ldots,0.5]$. The upper curve corresponds to $\alpha=0.5$.