BPS Condensates, Matrix Models and Emergent String Theory

TL;DR

This paper introduces a matrix model approach to compute anomalous dimensions in SYM at strong coupling, linking BPS condensates to string configurations and offering a new way to test AdS/CFT without relying on integrability.

Contribution

It presents a novel matrix quantum mechanics method to analyze excitations around BPS condensates, connecting gauge theory operators to dual string states and providing a quantum description of string configurations.

Findings

Derives part of the classical string sigma model Hamiltonian.

Explains quantum effects suppression in the infinite momentum limit.

Offers an alternative to integrability-based tests of AdS/CFT.

Abstract

A prescription is given for computing anomalous dimensions of single trace operators in SYM at strong coupling and large $N$ using a reduced model of matrix quantum mechanics. The method involves treating some parts of the operators as "BPS condensates" which, in certain limit, have a dual description as null geodesics on the $S^5$. In the gauge theory, the condensate is similar to a representative of the chiral ring and it is described by a background of commuting matrices. Excitations around these condensates correspond to excitations around this background and take the form of "string bits" which are dual to the "giant magnons" of Hofman and Maldacena. In fact, the matrix model approach gives a {\it quantum} description of these string configurations and explains why the infinite momentum limit suppresses the quantum effects. This method allows, not only to derive part of the classical sigma model Hamiltonian of the dual string (in the infinite momentum limit), but also its quantum canonical structure. Therefore, it provides an alternative method of testing the AdS/CFT correspondence without the need of integrability.