Notes on the construction of the D2-brane from multiple D0-branes

Hyakutake, Yoshifumi

doi:10.1016/j.nuclphysb.2003.09.056

Cited by 7 publications

(9 citation statements)

References 16 publications

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“…Now we trace the similar calculations as in ref. [25]. Setting X 1 = · · · = X 6 = 0, which are parallel to D6-branes, the Lagrangian for D0-branes evaluated in the background of D6-branes becomes as…”

Section: The Dielectric Effect In the Background Of D6-branesmentioning

confidence: 99%

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Gravitational dielectric effect and Myers effect

Hyakutake¹

2005

Phys. Rev. D

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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...

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Section: The Dielectric Effect In the Background Of D6-branesmentioning

confidence: 99%

“…The linear term on δ represents the instability of the configuration (25). If δ is a fluctuation around the original configuration (14), the linear term vanishes after imposing the magnetic flux conservation.…”

Section: Fluctuations Around the Spherical D2-d0 Bound Statementioning

confidence: 99%

Gravitational dielectric effect and Myers effect

Hyakutake¹

2005

Phys. Rev. D

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“…where m, n ∈ N. These matrices represent the fuzzy surface with axial symmetry around the x 3 (= z) direction [6,7]. Since what we want is a static configuration, each component does not depend on the time t. After some calculations, the equations (9) are transformed into the forms,…”

Section: The Fuzzy Bionmentioning

confidence: 99%

“…[11,12,13]. In the background of the flat space-time, when we set X 4 = · · · = X 9 = 0, this action is transformed into the form [7]…”

Section: The Effective Action For the Fuzzy Bionmentioning

confidence: 99%

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Fuzzy BIon

Hyakutake

2003

Phys. Rev. D

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We construct a solution of the BFSS matrix theory, which is a counterpart of the BIon solution representing a fundamental string ending on a bound state of a D2-brane and D0-branes. We call this solution the `fuzzy BIon' and show that this configuration preserves 1/4 supersymmetry of type IIA superstring theory. We also construct an effective action for the fuzzy BIon by analyzing the nonabelian Born-Infeld action for D0-branes. When we take the continuous limit, with some conditions, this action coincides with the effective action for the BIon configuration.Comment: 11 pages, 1 figure, reference and note adde

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On membrane interactions and a three-dimensional analog of Riemann surfaces

Kovacs

Sato

Shimada

2016

J. High Energ. Phys.

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Membranes in M-theory are expected to interact via splitting and joining processes. We study these effects in the pp-wave matrix model, in which they are associated with transitions between states in sectors built on vacua with different numbers of membranes. Transition amplitudes between such states receive contributions from BPS instanton configurations interpolating between the different vacua. Various properties of the moduli space of BPS instantons are known, but there are very few known examples of explicit solutions. We present a new approach to the construction of instanton solutions interpolating between states containing arbitrary numbers of membranes, based on a continuum approximation valid for matrices of large size. The proposed scheme uses functions on a two-dimensional space to approximate matrices and it relies on the same ideas behind the matrix regularisation of membrane degrees of freedom in M-theory. We show that the BPS instanton equations have a continuum counterpart which can be mapped to the three-dimensional Laplace equation through a sequence of changes of variables. A description of configurations corresponding to membrane splitting/joining processes can be given in terms of solutions to the Laplace equation in a three-dimensional analog of a Riemann surface, consisting of multiple copies of R 3 connected via a generalisation of branch cuts.We discuss various general features of our proposal and we also present explicit analytic solutions.

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Notes on the construction of the D2-brane from multiple D0-branes

Cited by 7 publications

References 16 publications

Gravitational dielectric effect and Myers effect

Gravitational dielectric effect and Myers effect

Fuzzy BIon

On membrane interactions and a three-dimensional analog of Riemann surfaces

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