Giant Gravitons - with Strings Attached (I)

TL;DR

This work develops a graphical, Young-diagram–based framework to study operators dual to excited giant gravitons with open strings in N=4 SYM, focusing on the free-field limit. By introducing restricted Schur polynomials and three graphical rules, the authors reduce two-point function computations to manipulations of diagram labels and demonstrate a factorization into open-string overlaps and Schur-polynomial factors. Applications include analyses of gravitational radiation, locality in the emergent worldvolume gauge theory, and processes like splitting and joining of strings, with evidence for a local 3+1D U(m) gauge theory on the giant-brane worldvolume. The results illuminate how geometry and locality are encoded in Young diagrams and support the broader picture of emergent spacetime and gauge dynamics from matrix degrees of freedom, while remaining within the zero-coupling limit, with future work addressing F-term corrections.

Abstract

In this article, the free field theory limit of operators dual to giant gravitons with open strings attached are studied. We introduce a graphical notation, which employs Young diagrams, for these operators. The computation of two point correlation functions is reduced to the application of three simple rules, written as graphical operations performed on the Young diagram labels of the operators. Using this technology, we have studied gravitational radiation by giant gravitons and bound states of giant gravitons, transitions between excited giant graviton states and joining of open strings attached to the giant.

Figures (8)

• Figure 1: The representations used to compute the amplitude for gravitational radiation from a bound state of $n$ sphere giants. $R$ has $p$ rows and $n$ columns where $p$ is $O(N)$ and $n$ is $O(1)$. $R'$ is obtained by removing a single box.
• Figure 2: The representations used to test locality of sphere giants.
• Figure 3: The representations used to test locality of AdS giants.
• Figure 4: Translation of a Young diagram into membrane plus string excitations. The string excitations correspond to the darkened boxes.
• Figure 5: The representations used to test the interpretation of the $F_0$ and $F_1$ contributions to the two point functions. The darkened boxes represent the position of the string. There are $p$ white boxes in each diagram shown.