Fuzzy spheres in pp wave matrix string theory

Abstract

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, g_s« 1, the behavior is determined by the combination Mg_s where M is a dimensionless parameter proportional to the strength of the Ramond-Ramond background. For Mg_s«1, 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 Mg_s»1, 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 N² 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.