Gravity on Noncommutative D-Branes

Ardalan, F.; Arfaei, H.; Garousi, Mohammad R.; Ghodsi, Ahmad

doi:10.1142/s0217751x03010991

Cited by 30 publications

(46 citation statements)

References 13 publications

(26 reference statements)

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“…Taking into account the previous discussion, the corresponding term in the effective action induced by the part of the amplitude represented by (2.9) can be computed from 13) leading to the following induced term in the Lagrangian (2.14) This term can be obtained from the Einstein-Hilbert term L EH = 1 2κ 2 √ −gR in the weak field expansion near Minkowski space-time, g µν = η µν + 2κh µν .…”

Section: Brane Induced Gravity From String Theorymentioning

confidence: 99%

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Comments on noncommutative gravity

2006

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We study the possibility of obtaining noncommutative gravity dynamics from string theory in the Seiberg-Witten limit. We find that the resulting low-energy theory contains more interaction terms than those proposed in noncommutative deformations of gravity. The rôle of twisted diffeomorphisms in string theory is studied and it is found that they are not standard physical symmetries. It is argued that this might be the reason why twisted diffeomorphisms are not preserved by string theory in the low energy limit. Twisted gauge transformations are also discussed.

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Section: Brane Induced Gravity From String Theorymentioning

confidence: 99%

“…As in Section 2 we restrict our attention to the case of the bosonic string on a D25-brane. Graviton interactions on lower-dimensional branes have been considered in [13]. Applications of the Seiberg-Witten map to the study of induced gravity on noncommutative spaces have been studied in [23].…”

Section: Witten Limitmentioning

confidence: 99%

Comments on noncommutative gravity

2006

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“…Coordinates onF are denoted y = y (1) ,y (2) ,p (3) We define the higher-order vector (resp., covector) bundles, in brief, hv-bundles (resp., in brief, hcv-bundles), if the typical fibre is a dv-space (resp., a dcv-space) as particular cases of the hvc-bundles.…”

Section: 2mentioning

confidence: 99%

“…where we use the index s = 0, 1, 2,...,z in order to enumerate the shells, whenẼ 0 = M. Local coordinates onẼ s are denoted (1) ,y (2) ,p (3) …”

Section: 2mentioning

confidence: 99%

“…Introduction. Nowadays, interest has been established in non-Riemannian geometries derived in the low-energy string theory [18,64,65], noncommutative geometry [1,3,8,12,15,22,32,34,53,55,67,109,111,112], and quantum groups [33,35,36,37]. Various types of Finsler-like structures can be parametrized by generic off-diagonal metrics, which cannot be diagonalized by coordinate transforms but only by anholonomic maps with associated nonlinear connection (in brief, N-connection).…”

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confidence: 99%

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Nonlinear connections and spinor geometry

Vacaru¹,

Vicol

2000

International Journal of Mathematics and Mathematical Sciences

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We present an introduction to the geometry of higher-order vector and covector bundles (including higher-order generalizations of the Finsler geometry and Kaluza-Klein gravity) and review the basic results on Clifford and spinor structures on spaces with generic local anisotropy modeled by anholonomic frames with associated nonlinear connection structures. We emphasize strong arguments for application of Finsler-like geometries in modern string and gravity theory, noncommutative geometry and noncommutative field theory, and gravity.2000 Mathematics Subject Classification: 15A66, 58B20, 53C60, 83C60, 83E15.1. Introduction. Nowadays, interest has been established in non-Riemannian geometries derived in the low-energy string theory [18,64,65], noncommutative geometry [1,3,8,12,15,22,32,34,53,55,67,109,111,112], and quantum groups [33,35,36,37]. Various types of Finsler-like structures can be parametrized by generic off-diagonal metrics, which cannot be diagonalized by coordinate transforms but only by anholonomic maps with associated nonlinear connection (in brief, N-connection). Such structures may be defined as exact solutions of gravitational field equations in the Einstein gravity and its generalizations [75,79,80,94,95,96,97,98,99,100,102,103,104,105,109,110,111], for instance, in the metric-affine [19,23,56] Riemann-Cartan gravity [24,25]. Finsler-like configurations are considered in locally anisotropic thermodynamics, kinetics, related stochastic processes [85,96,107,108], and (super-) string theory [84,87,90,91,92].The following natural step in these lines is to elucidate the theory of spinors in effectively derived Finsler geometries and to relate this formalism of Clifford structures to noncommutative Finsler geometry. It should be noted that the rigorous definition of spinors for Finsler spaces and generalizations was not a trivial task because (on such spaces) there are no defined even local groups of automorphisms. The problem was solved in [82,83,88,89,93] by adapting the geometric constructions with respect to anholonomic frames with associated N-connection structure. The aim of this work is to outline the geometry of generalized Finsler spinors in a form more oriented to applications in modern mathematical physics.We start with some historical remarks: the spinors studied by mathematicians and physicists are connected with the general theory of Clifford spaces introduced in 1876 [14]. The theory of spinors and Clifford algebras play a major role in contemporary physics and mathematics. The spinors were discovered by Èlie Cartan in 1913 in 1190 S. I. VACARU AND N. A. VICOL mathematical form in his researches on representation group theory [10,11]; he showed that spinors furnish a linear representation of the groups of rotations of a space of arbitrary dimensions. The physicists Pauli [60] and Dirac [20] (in 1927, resp., for the three-dimensional and four-dimensional space-times) introduced spinors for the representation of the wave functions. In general relativity theory spinors and the Dirac equat...

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T-duality of D-brane versus O-plane actions

Hosseini

Garousi

2023

J. High Energ. Phys.

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It is known that, in the static gauge, the world-volume and the transverse Kaluza-Klein (KK) reductions of the O-plane effective actions on a circle satisfy the T-duality constraint for arbitrary base space background. In this paper we show that due to the presence of the second fundamental form in the D-brane couplings at order α′ and higher, the T-duality is satisfied only for a subclass of the couplings for arbitrary base space background. They are m = 0 couplings where m is the number of $$ \overset{\sim }{B} $$ B ~ -field (without derivative on it). For m > 0 couplings, the base space metric must be block-diagonal and the momentum U(1) vector field in the transverse reduction must be zero. However, the derivatives of the metric and the vector field are arbitrary.Using the assumption that the effective actions at the critical dimension are background independent, we then show that the T-duality constraint for the couplings at order α′ and for m = 0, fixes completely both bulk and boundary actions. These couplings indicate that the propagators of the massless open string fields receive α′-correction. We have also imposed the T-duality constraint on m = 1, 2, 3, 4 couplings. Because of the above restriction on the base space background in these cases, however, the T-duality can only partially fix the couplings for m > 0. This study shows that the Dirac-Born-Infeld (DBI) factor appears in both bulk and boundary actions at order α′.

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Gravity on Noncommutative D-Branes

Abstract: The effective action for the low energy scattering of two gravitons with a D-brane in the presence of a constant antisymmetric B field in bosonic string theory is calculated and the modification to the standard D-brane action to first order in α ′ is obtained.

Cited by 30 publications

References 13 publications

Comments on noncommutative gravity

Comments on noncommutative gravity

Nonlinear connections and spinor geometry

T-duality of D-brane versus O-plane actions

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