BPS Condensates, Matrix Models and Emergent String Theory

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.

36 pages, 1 figure, 2 appendices, v2: references added

References in corpus (11)

• Giant Magnons
• Magnon Bound States and the AdS/CFT Correspondence
• Dyonic Giant Magnons
• Infinite spin limit of semiclassical string states
• Spiky strings and giant magnons on S5
• Dressing the Giant Magnon
• A study of open strings ending on giant gravitons, spin chains and integrability
• Multispin Giant Magnons
• Quantum Mechanical Sectors in Thermal N=4 Super Yang-Mills on RxS^3
• A description of 1/4 BPS configurations in minimal type IIB SUGRA
• Aspects of emergent geometry in the AdS/CFT context

Cited by in corpus (8)

• Single spike solutions for strings on S2 and S3
• Finite-Size Effects for Dyonic Giant Magnons
• Large Winding Sector of AdS/CFT
• BPS states in type IIB SUGRA with $SO(4)\times SO(2)_{gauged} symmetry
• Scattering of single spikes
• Giant magnon bound states from strongly coupled N=4 SYM
• Emergent Classical Strings from Matrix Model
• Black Hole Production from High Energy Scattering in AdS/CFT