Giant gravitons, Bogomol’nyi-Prasad-Sommerfield bounds, and noncommutativity

Abstract

It has been recently suggested that gravitons moving in AdS m × S n spacetimes along the S n blow up into spherical (n−2) branes whose radius increases with increasing angular momentum. This leads to an upper bound on the angular momentum, thus "explaining" the stringy exclusion principle. We show that this bound is present only for states which saturate a BPS-like condition involving the energy E and angular momentum J, E ≥ J/R, where R is the radius of S n . Restriction of motion to such states lead to a noncommutativity of the coordinates on S n . As an example of motions which do not obey the exclusion principle bound, we show that there are finite action instanton configurations interpolating between two possible BPS states. We suggest that this is consistent with the proposal that there is an effective description in terms of supergravity defined on noncommutative spaces and noncommutativity arises here because of imposing supersymmetry. August, 2000

Matrix dynamics of fuzzy spheres

“…Indeed, non-commutativity of space-time may be of a more basic nature, as indicated by its appearance in string field theories [32]. Fuzzy spheres have also been investigated in the context of dynamics of giant gravitons [8,10,[25][26][27][28][29][30][31].…”

Giants on deformed backgrounds Part II: the gauge field fluctuations

“…To conclude, we would like to stress that the above results accomplish the study of [8] for undeformed giant gravitons, taking into account the contributions of the worldvolume gauge fields 1 . In particular, we observe that the frequencies (3.27) coincide with the four ω (0) k in (3.26).…”

“…We see that the scalar and gauge fluctuations decouple. In particular, the scalar equations give the usual [8] …”

“…Instead of (2.8), to study the fluctuation spectrum it is convenient to use the following parametrization of the AdS 5 part of the metric [8,1] …”

“…The corresponding states are classified according to their SO(4) (the isomorphisms of the three-sphere) and U(1) ×U(1) quantum numbers (ℓ; m 2 , m 3 ) and the universal shift depends on the deformation parameters through the linear combination (γ 2 m 3 −γ 3 m 2 ) 2 . There exists a smooth limit to the undeformed case by sending γ i → 0 and this also gives us the behavior of the gauge field fluctuations of giant gravitons not included in the scalar analysis of [8]. The effect of the deformation is to break SO(4) down to U(1) × U(1) and a Zeeman-like effect occurs.…”