Dilatation operator and the Super Yang-Mills duals of open strings on AdS Giant Gravitons

TL;DR

This paper investigates the one-loop anomalous dimensions of operators in N=4 SYM dual to open strings on AdS giant gravitons, deriving a Hamiltonian that reveals spectral bands and geometric interpretations.

Contribution

It introduces a bosonic lattice Hamiltonian for AdS giant operators, capturing their mixing and spectral properties, with a novel semiclassical analysis.

Findings

Hamiltonian describes mixing of excited AdS giant operators

Evidence for continuous spectral bands in the Hamiltonian

Geometrical interpretation of operator labeling

Abstract

We study the one-loop anomalous dimensions of the Super Yang-Mills dual operators to open strings ending on AdS giant gravitons. AdS giant gravitons have no upper bound for their angular momentum and we represent them by the contraction of scalar fields, carrying the appropriate R-charge, with a totally symmetric tensor. We represent the open string motion along AdS directions by appending to the giant graviton operator a product of fields including covariant derivatives. We derive a bosonic lattice Hamiltonian that describes the mixing of these excited AdS giants operators under the action of the one-loop dilatation operator of N=4 SYM. This Hamiltonian captures several intuitive differences with respect to the case of sphere giant gravitons. A semiclassical analysis of the Hamiltonian allows us to give a geometrical interpretation for the labeling used to describe the fields products appended to the AdS giant operators. It also allows us to show evidence for the existence of continuous bands in the Hamiltonian spectrum.