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Longitudinal 5-branes as 4-spheres in Matrix theory
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We present a construction in Matrix theory of longitudinal 5-branes whose geometry in transverse space corresponds to a 4-sphere. We describe these branes through an explicit construction in terms of N*N matrices for a particular infinite series of values of N. The matrices used in the construction have a number of properties which can be interpreted in terms of the 4-sphere geometry, in analogy with similar properties of the SU(2) generators used in the construction of a spherical membrane. The physical properties of these systems correspond with those expected from M-theory; in particular, these objects have an energy and a leading long-distance interaction with gravitons which agrees with 11D supergravity at leading order in N.
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Quantum spacetime and quantum fluctuations in the IKKT model at weak coupling
In the IKKT matrix model, quantum fluctuations are negligible compared to noncommutativity scales at weak coupling for Moyal-Weyl and covariant quantum spacetime backgrounds, justifying semi-classical emergent geometry.
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