Gravitational dielectric effect and Myers effect

Abstract

In this paper we study the gravitational dielectric phenomena of a D2-brane in the background of Kaluza-Klein monopoles and D6-branes. In both cases the spherical D2-brane with nonzero radius becomes classical solution of the D2-brane action. We also investigate the gravitational Myers effect in the background of D6-branes. This phenomenon occurs since the tension of the D2-brane balances with the repulsive force between D0-branes and D6-branes.In the electromagnetism, oppositely charged particles under the uniform electric field separate from each other to cancel out the background flux. This is the well-known dielectric effect, and analogous phenomena can be observed in the type II superstring theories and the M-theory[1].Let us illustrate the dielectric phenomenon in the type IIA superstring theory with the case where a spherical D2-brane is located in the background of coincident NS5branes[2]. NS5-branes carry the magnetic charge of the NS-NS 2-form potential, and its 3-from flux vertically penetrates three dimensional sphere S 3 which encloses NS5branes in the transverse space. The D2-brane is assumed to be spherical in the S 3 . In case there is no magnetic flux on the D2-brane, it collapses because of its tension. On the other hand, if the magnetic flux exists on the D2-brane, the background NS-NS 3-form flux supports it against the collapse 2 . Notice that the number of the magnetic flux on the D2-brane is less than that of NS5-branes. This is the dielectric effect in the type IIA superstring theory 3 .Interestingly the dielectric phenomena in the type II superstring theories admit the dual descriptions. Namely similar dielectric effects are observed from the dynamics of D0-branes, which are identical to the magnetic flux on the D2-brane[9, 10].The dynamical variables of M coincident D0-branes are U(M) gauge field and nine adjoint scalars, and the latter represent the position of D0-branes when they are simultaneously diagonalized. In the background of NS5-branes, D0-branes form a fuzzy (noncommutative) geometry in the S 3 because of the support from the NS-NS 3-form flux [11,12,13]. In fact D0-branes compose a fuzzy sphere in the S 3 , which matches the D2-brane picture when the number of D0-branes or magnetic flux is sufficiently large. This is called the Myers effect [14].Since the essence of the dielectric effect and the Myers effect is the existence of the background flux, at first sight it seems impossible to observe these effects in purely gravitational backgrounds. Note, however, that the NS5-brane is related via T-duality to a Kaluza-Klein monopole which forms the purely gravitational geometry [15,16].Therefore it is natural to expect gravitational versions of the dielectric effect and the Myers effect in the background of Kaluza-Klein monopoles 4 .2 Here we fix the position of the D2-brane in the radial direction in the transverse space of NS5branes. When a fluctuation around the radial direction is taken into account, the spherical D2-brane falls in the throat of NS5-branes [3,4]. The final sta...

Fuzzy Rings in D6-Branes and Magnetic Field Background

“…We use the Myers T-dual nonabelin Born-Infeld action [3], which describes the M D0-branes system, to find the solutions in the background of D6-branes and Melvin magnetic tube field. In the D6-Branes background we see that, besides the fuzzy sphere solution that found by Hyakutake [11], there has also ring solutions. These solution are formed by the gravitational dielectric effect.…”

“…Since the eleven-dimensional spacetime is flat this metric is expected to be an exact solution of the M-theory including higher derivative terms. We can recast the eleven-dimensional metric in the following canonical form [8] ds 2 11 = e −2φ/3 ds 2 10 + e 4φ/3 (dx 11…”

Spherical D-brane by tachyon condensation

“…We show that the effective action of the spherical D2-brane is reproduced by inserting the tachyon profile into the effective theory of non-BPS D3-branes, together with the correct tension and the RRcoupling for a D2-D0 bound state. An analysis on the stability of the spherical D2-brane is also given by using the method developed in [9,15,16]. As shown in these papers, the size of the sphere can be stable in the constant RR-flux background but in a delicate way.…”

Quintessence and phantom dark energy from ghostD-branes

“…A concrete example of this effect is when N D3-branes blow up into a solitary D5brane via the formation of a fuzzy S 2 , more commonly referred to as the Myers effect. If the scalar fields transform under an appropriate representation of a higher dimensional gauge group, then the D3-branes can be polarized into higher dimensional branes in an analogous fashion through the extended Myers effect [22,25] 1 . For example, if the scalars transform under irreducible representations of the n-fold tensor product of SO( 5), then the 1 Although there exists a different action, proposed by Tseytlin [26], which does not admit such an effect.…”