Central Charges for the Double Coset

Abstract

The state space of excited giant graviton brane systems is given by the Gauss graph operators. After restricting to the su(2|3) sector of the theory, we consider this state space. Our main result is the decomposition of this state space into irreducible representations of the su(2|2) R global symmetry. Excitations of the giant graviton branes are charged under a central extension of the global symmetry. The central extension generates gauge transformations so that the action of the central extension vanishes on physical states. Indeed, we explicitly demonstrate that the central charge is set to zero by the Gauss Law of the brane world volume gauge theory.

Emergent Yang-Mills theory

“…An important conclusion of [29] is that this open string central charge is a limit of the central charge extension of [46,47]. The question was reconsidered in [35] using the language of the Gauss graph operators. In the Gauss graph language, the magnons are the edges in the Gauss graph.…”

“…In the Gauss graph language, the magnons are the edges in the Gauss graph. The conclusion of [35] is that edges stretched between nodes of the Gauss graph do carry the central charge, while edges living at a node are not charged. The central extension again generates gauge transformations so that it again vanishes when acting on physical states which are gauge invariant.…”

“…. This relation between the two implies that the transformation to Gauss graph basis is exactly the same for the fermions and bosons [35] C(s i )…”

“…Fermi statistics forbids two or more parallel edges (i.e. edges with the same orientation and endpoints) of the same fermion species [35]. We refined N Â to produce a vector N Â.…”

Scrambling in Yang-Mills

“…Vertices can be dressed by closed edges with ends attached to the same vertex or by edges between two distinct vertices. Fermi statistics forbids two or more parallel edges (edges with the same orientation and endpoints) of the same fermion species [86]. We refined N A to produce a vector N A .…”