Anatomy of bubbling solutions

Abstract

We present a comprehensive analysis of holography for the bubbling solutions of Lin-Lunin-Maldacena. These solutions are uniquely determined by a coloring of a 2-plane, which was argued to correspond to the phase space of free fermions. We show that in general this phase space distribution does not determine fully the 1/2 BPS state of N=4 SYM that the gravitational solution is dual to, but it does determine it enough so that vevs of all single trace 1/2 BPS operators in that state are uniquely determined to leading order in the large N limit. These are precisely the vevs encoded in the asymptotics of the LLM solutions. We extract these vevs for operators up to dimension 4 using holographic renormalization and KK holography and show exact agreement with the field theory expressions.

67 pages, 6 figures; v2: typos corrected, refs added; v3: expanded explanations, more typos corrected

References in corpus (6)

• AdS/CFT correspondence and Geometry
• Fuzzball solutions for black holes and D1-brane--D5-brane microstates
• Bubbling AdS and droplet descriptions of BPS geometries in IIB supergravity
• Quantum geometry and gravitational entropy
• Particle transfer in braneworld collisions
• Quantum Mechanics of Lowest Landau Level Derived from N=4 SYM with Chemical Potential

Cited by in corpus (10)

• Diagonal multi-matrix correlators and BPS operators in N=4 SYM
• Wilson loop correlators at strong coupling: from matrices to bubbling geometries
• Matching of correlators in AdS_3/CFT_2
• Quantum geometry and gravitational entropy
• Holography of BPS surface operators
• 1/4-BPS M-theory bubbles with SO(3) x SO(4) symmetry
• Correlators Of Operators with a Large R-charge
• Half BPS states in AdS_5 x Y^{p,q}
• States of Negative Energy and $Ad{S}_5\times S_5/Z_k$
• Matrix Model Maps and Reconstruction of AdS SUGRA Interactions