Fuzzy sphere dynamics and non-abelian DBI in curved backgrounds

Abstract

We consider the non-Abelian action for the dynamics of NDp ′ -branes in the background of MDp-branes, which parameterises a fuzzy sphere using the SU(2) algebra. We find that the curved background leads to collapsing solutions for the fuzzy sphere except when we have D0 branes in the D6 background, which is a realisation of the gravitational Myers effect. Furthermore we find the equations of motion in the Abelian and non-Abelian theories are identical in the large N limit. By picking a specific ansatz we find that we can incorporate angular momentum into the action, although this imposes restriction upon the dimensionality of the background solutions. We also consider the case of non-Abelian non-BPS branes, and examine the resultant dynamics using world-volume symmetry transformations. We find that the fuzzy sphere always collapses but the solutions are sensitive to the combination of the two conserved charges and we can find expanding solutions with turning points. We go on to consider the coincident NS5-brane background, and again construct the non-Abelian theory for both BPS and non-BPS branes. In the latter case we must use symmetry arguments to find additional conserved charges on the world-volumes to solve the equations of motion. We find that in the Non-BPS case there is a turning solution for specific regions of the tachyon and radion fields. Finally we investigate the more general dynamics of fuzzy S 2k in the Dp-brane background, and find collapsing solutions in all cases.

On Time-Dependent Collapsing Branes and Fuzzy Odd-Dimensional Spheres

“…This could provide a stabilisation mechanism for fuzzy odd-spheres in the absence of the right RR fluxes, which provide a simple stabilisation mechanism for fuzzy even-spheres. The study of finite-N effects and the embedding of these systems in more general backgrounds [36,37] provide other possible avenues for future research. Finally it would be interesting to get a better understanding of the relation between the fuzzy-odd sphere constructions in this paper and those of [38,39] Here we include part of the calculation that led to the commutator decomposition for the fuzzy-S 3 , using two possible ways of evaluating [X i , X j ] 2 .…”

Non-abelian (p,q) strings in the warped deformed conifold

“…Using the Myers action in curved space [14,18] we should aim to reproduce the tension spectrum for the (p, q)-string initially in the large q limit in order to compare with [12], but we can also find the most general expression for the tension…”

Electrified fuzzy spheres and funnels in curved backgrounds

“…It can easily be seen that R ′ = 2R 2 √ H anḋ R = BḞ R 2 , where H is the usual harmonic function for the NS5-brane solution. If we substitute these two equations into the energy density equation for the fuzzy funnel we obtain 19) which must be conserved in time. This requires that theḞ term must vanish from the expression.…”