Fuzzy spheres in pp wave matrix string theory

The nonperturbative behavior of strings in type IIA pp wave backgrounds with a compact lightlike direction is investigated using matrix string theory. At small string coupling, [Formula Presented] the behavior is determined by the combination [Formula Presented] where M is a dimensionless parameter proportional to the strength of the Ramond-Ramond background. For [Formula Presented] the matrix string theory is conventional; only the degrees of freedom in the Cartan subalgebra contribute, and the theory reduces to copies of the perturbative string. For [Formula Presented] the theory admits degenerate vacua representing fundamental strings blown up into fuzzy spheres with nonzero light-cone momenta. We determine the spectrum of small fluctuations around these vacua. Around such a vacuum all [Formula Presented] degrees of freedom are excited with comparable energies. The spectrum of masses has a spacing that is independent of the radius of the fuzzy sphere, in agreement with the expected behavior of continuum giant gravitons. For “reducible” vacua we find that the momenta of fluctuations are generically irrational multiples of the inverse radius of the compact direction, showing that these blown up strings never close.