Fuzzy Spheres in pp Wave Matrix String Theory

TL;DR

This paper investigates the behavior of matrix string theory in a type IIA pp wave background, revealing a transition from perturbative strings to fuzzy sphere configurations at strong coupling, with detailed spectral analysis of fluctuations.

Contribution

It provides a detailed analysis of fuzzy sphere vacua in pp wave matrix string theory and characterizes the fluctuation spectrum around these vacua, highlighting new nonperturbative features.

Findings

At small g_s, the theory reduces to perturbative strings.

At large M g_s, fuzzy sphere vacua emerge with nonzero lightcone momenta.

The fluctuation spectrum around fuzzy spheres is independent of sphere radius.

Abstract

The behaviour of matrix string theory in the background of a type IIA pp wave at small string coupling, g_s << 1, is determined by the combination M g_s where M is a dimensionless parameter proportional to the strength of the Ramond-Ramond background. For M g_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 M g_s >> 1, the theory admits degenerate vacua representing fundamental strings blown up into fuzzy spheres with nonzero lightcone momenta. We determine the spectrum of small fluctuations around these vacua. Around such a vacuum all N-squared degrees of freedom are excited with comparable energies. The spectrum of masses has a spacing which is independent of the radius of the fuzzy sphere, in agreement with expected behaviour of continuum giant gravitons. Furthermore, for fuzzy spheres characterized by reducible representations of SU(2) and vanishing Wilson lines, the boundary conditions on the field are characterized by a set of continuous angles which shows that generically the blown up strings do not ``close''.