Journal
JOURNAL OF HIGH ENERGY PHYSICS
Volume -, Issue 5, Pages -Publisher
SPRINGER
DOI: 10.1088/1126-6708/2009/05/123
Keywords
D-branes; Non-Commutative Geometry; M(atrix) Theories; AdS-CFT Correspondence
Categories
Funding
- STFC [ST/G000565/1]
- MEXT KAKENHI [20740128]
- STFC [ST/G000565/1] Funding Source: UKRI
- Grants-in-Aid for Scientific Research [20740128] Funding Source: KAKEN
- Science and Technology Facilities Council [ST/G000565/1] Funding Source: researchfish
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We analyse the fluctuations of the ground-state/funnel solutions proposed to describe M2-M5 systems in the level-k mass-deformed/pure Chern-Simons-matter ABJM theory of multiple membranes. We show that in the large N limit the fluctuations approach the space of functions on the 2-sphere rather than the naively expected 3-sphere. This is a novel realisation of the fuzzy 2-sphere in the context of Matrix Theories, which uses bifundamental instead of adjoint scalars. Starting from the multiple M2-brane action, a U(1) Yang-Mills theory on R-2,R-1 x S-2 is recovered at large N, which is consistent with a single D4-brane interpretation in Type IIA string theory. This is as expected at large k, where the semiclassical analysis is valid. Several aspects of the fluctuation analysis, the ground-state/funnel solutions and the mass-deformed/pure ABJM equations can be understood in terms of a discrete noncommutative realisation of the Hopf fibration. We discuss the implications for the possibility of finding an M2-brane worldvolume derivation of the classical S 3 geometry of the M2-M5 system. Using a rewriting of the equations of the SO(4)-covariant fuzzy 3-sphere construction, we also directly compare this fuzzy 3-sphere against the ABJM ground-state/funnel solutions and show them to be different.
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