Open membranes in a constant <i>C</i>-field background and noncommutative boundary strings

Kawamoto, Shoichi; Sasakura, Naoki

doi:10.1088/1126-6708/2000/07/014

Cited by 63 publications

(87 citation statements)

References 15 publications

(28 reference statements)

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“…where the dimensionless tensor multiplet "coupling" h 3 p is non-vanishing provided the decoupling limit (38) has been taken with λ = 3. For λ < 3 the limit results in a linear tensor multiplet.…”

Section: Canonical Analysismentioning

confidence: 99%

A noncommutative M-theory five-brane

Bergshoeff¹,

Berman²,

Schaar³

et al. 2000

Nuclear Physics B

108

161

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We investigate, in a certain decoupling limit, the effect of having a constant C-field on the M-theory five-brane using an open membrane probe. We define an open membrane metric for the five-brane that remains non-degenerate in the limit. The canonical quantisation of the open membrane boundary leads to a noncommutative loop space which is a functional analogue of the noncommutative geometry that occurs for D-branes.

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Section: Canonical Analysismentioning

confidence: 99%

A noncommutative M-theory five-brane

Bergshoeff¹,

Berman²,

Schaar³

et al. 2000

Nuclear Physics B

108

161

View full text Add to dashboard Cite

show abstract

“…The presence of the M5-brane requires self-duality for the parallel C-field. Recently the authors of [3,73,11,43,34] showed that there is suitable decoupling limit such that the bulk theory becomes topological and only the modes in the brane are left. The resulting theory is now called OM theory, which is related to other decoupled theories by a web of dualities [34].…”

Section: Introductionmentioning

confidence: 99%

TOPOLOGICAL OPEN P-BRANES

Park

2001

Symplectic Geometry and Mirror Symmetry

157

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By exploiting the BV quantization of topological bosonic open membrane, we argue that flat 3-form C-field leads to deformations of the algebras of multi-vectors on the Dirichlet-brane world-volume as 2-algebras. This would shed some new light on geometry of M-theory 5-brane and associated decoupled theories. We show that, in general, topological open p-brane has a structure of (p + 1)-algebra in the bulk, while a structure of p-algebra in the boundary. The bulk/boundary correspondences are exactly as of the generalized Deligne conjecture (a theorem of Kontsevich) in the algebraic world of p-algebras. It also imply that the algebras of quantum observables of (p − 1)-brane are "close to" the algebras of its classical observables as p-algebras. We interpret above as deformation quantization of (p − 1)-brane, generalizing the p = 1 case. We argue that there is such quantization based on the direct relation between BV master equation and Ward identity of the bulk topological theory. The path integral of the theory will lead to the explicit formula. We also discuss some applications to topological strings and conjecture that the homological mirror symmetry has further generalizations to the categories of p-algebras.

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“…In the temporal gauge b 0i = 0 however, the theory based on the action (13) supplemented by the Gauss constraint (15) is perfectly consistent, and yields a non-Abelian deformation of the dynamics of a two-form in 3+1 dimensions, based on the group of volume preserving diffeomorphisms [44]. It would be interesting to see if the algebraic structure of (10), (11), (12) can be abstracted, and the group of vpd replaced by other groups such as finite Lie groups. It is also important to generalize it to 5+1 dimensions, if one is to make contact with the five-brane.…”

mentioning

confidence: 99%

Remarks on the topological open membrane

Pioline

2002

Phys. Rev. D

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Just as non-commutative gauge theories arise from quantising open strings in a large magnetic field, non-Abelian two-form gauge theories may conceivably be constructed by quantising open membranes in a large three-form magnetic background. We make some observations that arise in following this strategy, with an emphasis on the relation to the quantisation of volume-preserving diffeomorphisms (vpd). In particular, we construct consistent non-Abelian interactions of a two-form in 3+1 dimensions, based on gauge invariance under vpd.PACS numbers: 11.10. Kk, 11.10.Lm, 47.37.+q Keywords: Non-commutative geometry, Nambu bracket, Non-Abelian tensor, Superfluid HeliumOf the many mysteries surrounding the theory formerly known as string theory, the dynamics of the five-brane is perhaps the most intriguing. While a single type IIA or M5 brane supports a free self-dual two-form gauge field on its world-volume, together with five transverse scalar degrees of freedom and their fermionic partners [1], the case of N five-branes at small separation is much less understood. Analogy with the case of coinciding D-branes and duality with ALE singularities in type IIB string theory suggest that the chiral multiplet now transforms in the adjoint representation of a spontaneously broken U (N ), with the open membranes stretched between two five-branes playing the rôle of stringy W bosons on the five-brane worldvolume [2]. This picture is at best suggestive however, since the quantization of the membrane, if at all sensible, is still beyond reach (see [4] for a review of recent attempts however). Disregarding the fundamental origin of these low-energy degrees of freedom, no consistent local theory of interacting non-Abelian selfdual two-forms has been found to date, in line with no go theorems [5]. The nature of the U (N ) non-Abelian symmetry itself is unclear, since anomaly and entropy considerations hint at N 3 degrees of freedom rather than N 2 as expected on a naive perturbative basis [6] -an admittedly unwarranted expectation due to the absence of a tunable coupling.On the other hand, recent progress in the understanding of D-branes in background fields has taught us that non-Abelian dynamics arise even at N = 1, in the presence of a strong background magnetic or electric field [7]. Indeed, the effects of the higher-derivative Born-Infeld couplings can be resummed by going to a non-commutative description, where the U (1) gauge invariance δa µ = ∂ µ λ is replaced by a transformation δa µ = ∂ µ λ + a µ * λ − λ * a µ formally identical to the usual Yang-Mills gauge invariance [8]. The Moyal deformation of the ordinary commutative product can in fact be derived without detailed knowledge of the dynamics of open strings in a magnetic background B = dA: in the limit of large B, one may retain only the topological coupling Σ B from the action of the string with worldsheet Σ (we omit the pull-back from target space). This in turn reduces to a coupling γ A on the boundary, hence to a topological quantum mechanical model. For constant back...

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Open membranes in a constant C-field background and noncommutative boundary strings

Cited by 63 publications

References 15 publications

A noncommutative M-theory five-brane

A noncommutative M-theory five-brane

TOPOLOGICAL OPEN P-BRANES

Remarks on the topological open membrane

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