Null branes in string theory backgrounds

We construct gauge theory of interacting symmetric traceless tensors of all ranks s = 0, 1, 2, 3, ... which generalizes Weyl-invariant dilaton gravity to the higher spin case, in any dimension d > 2. The action is given by the trace of the projector to the subspace with positive eigenvalues of an arbitrary hermitian differential operatorĤ, and the symmetric tensors emerge after expansion of the latter in power series in derivatives. After decomposition in perturbative series around conformally flat pointĤ = 2 with Euclidean metric, the action functional describes conformal higher spin theory. Namely, the linear in fluctuation term cancels, while the one quadratic in fluctuation breaks up as a sum of conformal higher spin theories, the latter being free gauge theories of symmetric traceless tensors of rank s with with the algebra of observables of the quantized point particle. Each global symmetry produces a Noether current constructed out of ψ according to general formula we present in the paper. In the caseĤ = 2 the algebra of observables is an extension of the conformal algebra decomposed w.r.t. its adjoint action as a direct sum of finite-dimensional representations characterized by traceless rectangular two-row Young tableaux. This infinite-dimensional algebra coincides, in d = 3, 4, 6 with conformal higher spin algebras constructed before in terms of even spinor oscillators, which origin is due to twistor reformulation of the dynamics of the massless particle. The construction of the paper may be a starting point for diverse conjectures. First, we discuss the extension of the geometry "quantized point particle + conformal higher spin fields in d dimensions" to the one "tensionless d − 1 brane + higher spin massless fields in d + 1 dimensions", where the phase of ψ appear to describe transverse motion of the brane inside d + 1-bulk. This picture arises in the semiclassical approximation to the quantized particle dynamics, the latter approximation provides d-dimensional generalization of W -geometry elaborated on by Hull in d = 1, 2 case. Next, we propose a candidate on the role of Higgs-like higher spin compensator able to spontaneously break higher spin symmetries. At last, we make the conjecture that, in even dimensions d, the action of conformal higher spin theory equals the logarithmically divergent term of the action of massless higher spin fields on AdS d+1 evaluated on the solutions of Dirichlet-like problem, where conformal higher spin fields are boundary values of massless higher spin fields on AdS d+1 , the latter conjecture conforms with recent proposal (for d = 4) by Tseytlin and provides information on the full higher spin action in AdS d+1 .

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“…Really, consider a tensionless D − 2-brane in a gravity background in D-dimensional space (see e.g. [40]), with the world volume action…”

Section: Acknowledgementsmentioning

confidence: 99%

Conformal higher spin theory

2003

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“…They are nontrivial when one uses the most general ansatz (3.6). 7 In the case when the background fields depend on more than one coordinate, and we fix all brane coordinates X a except one, the exact solutions are given by the same expressions as in the case just considered, if the metric G ab is a diagonal one. In this way, we have realized the possibility to obtain probe brane solutions as functions of every single one coordinate, on which the background depends.…”

Section: Summary and Discussionmentioning

confidence: 99%

Probe branes dynamics: exact solutions in general backgrounds

Bozhilov

2003

Nuclear Physics B

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“…The equations of motion for the Lagrange multipliers λ 0 and λ j which follow from (3) give the constraints :…”

Section: Null Branes 21 Lagrangian Formulationmentioning

confidence: 99%

“…Different methods have been applied to solve them approximately or, if possible, exactly in a fixed background. On the other hand, quite general exact solutions can be found by using an appropriate ansatz, which exploits the symmetries of the underlying curved space-time [1,2,3]. We will use namely this approach.…”

Section: Solving the Equations Of Motionmentioning

confidence: 99%

Exact Brane Solutions in Curved Backgrounds

Bozhilov¹

2012

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We consider the classical null p-brane dynamics in D-dimensional curved backgrounds and apply the Batalin-Fradkin-Vilkovisky approach for BRST quantization of general gauge theories. Then we develop a method for solving the tensionless p-brane equations of motion and constraints. This is possible whenever there exists at least one Killing vector for the background metric. It is shown that the same method can be also applied for the tensile 1-branes. Finally, we give two examples of explicit exact solutions in four dimensions.

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Null branes in string theory backgrounds

Abstract: We consider null bosonic p-branes moving in curved space-times and develop a method for solving their equations of motion and constraints, which is suitable for string theory backgrounds. As an application, we give an exact solution for such a background in ten dimensions.

Cited by 7 publications

References 21 publications

Conformal higher spin theory

Conformal higher spin theory

Probe branes dynamics: exact solutions in general backgrounds

Exact Brane Solutions in Curved Backgrounds

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