Towards quantum dielectric branes: curvature corrections in Abelian beta function and non-Abelian Born–Infeld action

Cornalba, Lorenzo; Schiappa, Ricardo

doi:10.1016/j.nuclphysb.2004.12.019

Cited by 12 publications

(13 citation statements)

References 79 publications

(208 reference statements)

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“…This is interesting as it appears that the energy of a collapsing fuzzy sphere in flat space is the same as an essentially static sphere in a space-time throat, and is related to the formation of a bound state of (p, q) fivebranes [2]. In the large r region we find 10) which translates into the condition that the fuzzy sphere has a maximum radius given by…”

Section: Ns5-brane Backgroundmentioning

confidence: 80%

Fuzzy sphere dynamics and non-abelian DBI in curved backgrounds

Thomas

Ward

2006

J. High Energy Phys.

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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.

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Section: Ns5-brane Backgroundmentioning

confidence: 80%

Fuzzy sphere dynamics and non-abelian DBI in curved backgrounds

Thomas

Ward

2006

J. High Energy Phys.

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“…As a second example, we consider the simplest possible leading term, the nonrelativistic kinetic term (28). Using the boost transformation rule (12,15) up to order X 4 , we find that adding the symmetrized version of terms in the abelian relativistic kinetic term suffices up to O(X 5 ) to make the action invariant, but this breaks down at O(X 6 ). Fortunately, it is possible to add terms involving commutators at this order to restore Poincaré invariance.…”

Section: Order-by-order Construction Of Invariant Actionsmentioning

confidence: 98%

Poincaré invariance in multiple D-brane actions

Brecher¹,

Koerber²,

Ling³

et al. 2006

J. High Energy Phys.

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We show that the requirement of Poincaré invariance (more specifically invariance under boosts/rotations that mix brane directions with transverse directions) places severe constraints on the form of actions describing multiple D-branes, determining an infinite series of correction terms to the currently known actions. For the case of D0-branes, we argue that up to field redefinitions, there is a unique Lorentz transformation rule for the coordinate matrices consistent with the Poincaré algebra. We characterize all independent Poincaré invariant structures by describing the leading term of each and providing an implicit construction of a Lorentz invariant completion. Our construction employs new matrix-valued Lorentz covariant objects built from the coordinate matrices, which transform simply under the (extremely complicated) Lorentz transformation rule for the matrix coordinates.1 These could be the usual D0-branes of type IIA string theory with d = 9, or any other pointlike D-branes arising from higher dimensional branes wrapped on cycles in a compactification.2 Here, all bulk fields have been set to zero.3 Indeed, to our knowledge none of the actions for multiple D-branes that have appeared previously in the literature are Poincaré invariant apart from the cases p = −1 and p = 9 which are trivial.4 Early work on understanding the structure of non-abelian D-brane actions based on general principles was initiated by Douglas [2,3]. For general reviews discussing the physics of multiple D-branes, including many additional references, see [4,5].

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“…Let us note that such a term was also obtained in Refs. [70,71] from the expansion of the Dirac-Born-Infeld action. The second and the third H-dependent terms appear as (parts of) the Chern-Simons action.…”

Section: Gauge Theory With Fluxesmentioning

confidence: 99%

Matrix theory origins of non-geometric fluxes

Chatzistavrakidis

Jonke

2013

J. High Energ. Phys.

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We explore the origins of non-geometric fluxes within the context of M theory described as a matrix model. Building upon compactifications of Matrix theory on non-commutative tori and twisted tori, we formulate the conditions which describe compactifications with non-geometric fluxes. These turn out to be related to certain deformations of tori with non-commutative and nonassociative structures on their phase space. Quantization of flux appears as a natural consequence of the framework and leads to the resolution of nonassociativity at the level of the unitary operators. The quantum-mechanical nature of the model bestows an important role on the phase space. In particular, the geometric and non-geometric fluxes exchange their properties when going from position space to momentum space thus providing a duality among the two. Moreover, the operations which connect solutions with different fluxes are described and their relation to T-duality is discussed. Finally, we provide some insights on the effective gauge theories obtained from these matrix compactifications.

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Towards quantum dielectric branes: curvature corrections in Abelian beta function and non-Abelian Born–Infeld action

Cited by 12 publications

References 79 publications

Fuzzy sphere dynamics and non-abelian DBI in curved backgrounds

Fuzzy sphere dynamics and non-abelian DBI in curved backgrounds

Poincaré invariance in multiple D-brane actions

Matrix theory origins of non-geometric fluxes

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