A covariant simultaneous action for branes in an arbitrary curved background spacetime is considered. The action depends on a pair of independent field variables, the brane embedding functions, through the canonical momentum of a reparametrization invariant geometric model for the brane, and an auxiliary vector field. The form of the action is analogous to a symplectic potential. Extremization of the simultaneous action produces at once the equations of motion and the Jacobi equations for the brane geometric model, and it also provides a convenient shortcut towards its second variation. In this note, we consider geometric models depending only on the intrinsic geometry of the brane worldvolume, and discuss briefly the generalization to extrinsic geometry dependent models. The approach is illustrated for Dirac-NambuGoto [DNG] branes. For a relativistic particle, a simultaneous action was introduced by Bazanski, that served as an inspiration for the present work.
Dilaton gravity with general brane localized interactions is investigated. Models with corrections up to arbitrary order in field derivatives are considered. Effective gravitational equations of motion at the brane are derived in the covariant approach. Dependence of such brane equations on the bulk quantities is discussed. It is shown that the number of the bulk independent brane equations of motion depends strongly on the symmetries assumed for the model and for the background. Examples with two and four derivatives of the fields are presented in more detail.
We present the covariant gravitational equations to describe a four-dimensional brane world in the case with the Gauss-Bonnet term in a bulk spacetime, assuming that gravity is confined on the $Z_2$ symmetric brane. It contains some components of five-dimensional Weyl curvature ($E_{μν}$) which describes all effects from the bulk spacetime just as in the case of the Randall-Sundrum second model. Applying this formalism to cosmology, we derive the generalized Friedmann equation and calculate the Weyl curvature term, which is directly obtained from a black hole solution.
In this paper we have considered the structure of the non-projectable Horava-Melby-Thompson (HMT) gravity to find braneworld scenarios. A relativistic scalar field is considered in the matter sector and we have shown how to reduce the equations of motion to first-order differential equations. In particular, we have studied thick brane solutions of both the dilatonic and Randall-Sundrum types.
In this short note we formulate Covariant Hamiltonian formalism for strings, p-branes and Non-BPS Dp-branes. We also analyse the vacuum tachyon condensation in case of unstable D1-brane.
We investigate the geometry of lightsheets comprised of null geodesics near a brane. Null geodesics which begin parallel to a brane a distance d away are typically gravitationally bound to the brane, so that the maximum distance from the geodesic to the brane never exceeds d. The geometry of resulting lightsheets is similar to that of the brane if one coarse grains over distances of order d. We discuss the implications for the covariant entropy bound applied to brane worlds.
We have found that kappa-symmetry allows a covariant quantization provided the ground state of the theory is strictly massive. For D-p-branes a Hamiltonian analysis is performed to explain the existence of a manifestly supersymmetric and Lorentz covariant description of the BPS states of the theory. The covariant quantization of the D-0-brane is presented as an example.
We discuss the covariant formulation of local field theories described by the Companion Lagrangian associated with p-branes. The covariantisation is shown to be useful for clarifying the geometrical meaning of the field equations and also their relation to the Hamilton-Jacobi formulation of the standard Dirac-Born-Infeld theory.
In this paper we derive the generalisations of Gauss-Codazzi, Raychaudhuri and area change equations for classical relativistic branes and multidimensional fluids in arbitrary background manifolds with metricity and torsion. The kinematical description we develop is fully covariant and based on the use of projection tensors tilted with respect to the brane worldsheets.
We develop a formalism that allows us to write actions for multiple D-branes with manifest general covariance. While the matrix coordinates of the D-branes have a complicated transformation law under coordinate transformations, we find that these may be promoted to (redundant) matrix fields on the transverse space with a simple covariant transformation law. Using these fields, we define a covariant distribution function (a matrix generalization of the delta function which describes the location of a single brane). The final actions take the form of an integral over the curved space of a scalar…
We construct the full effective action including DBI and WZ terms for solitonic 5-branes covariant under T-duality. The result is a completion of results known in the literature to a full T-duality covariant expression. The covariant WZ action includes previously omitted R-R terms. The obtained full covariant effective action reproduces the one obtained by S-duality from the D5-brane upon the correct choice of the covariant charge.
The component form of the equations of motion for the 5-brane in eleven-dimensions is derived from the superspace equations. These equations are fully covariant in six-dimensions. It is shown that double-dimensional reduction of the bosonic equations gives the equations of motion for a 4-brane in ten dimensions governed by the Born-Infeld action.
We discuss an open supermembrane theory on the maximally supersymmetric pp-wave background in eleven dimensions. The boundary surfaces of an open supermembrane are studied by using the covariant supermembrane theory. In particular, we find the configurations of M5-branes and 9-branes preserving a half of supersymmetries at the origin.
We reformulate boundary conditions for axisymmetric codimension-2 braneworlds in a way which is applicable to linear perturbation with various gauge conditions. Our interest is in the thin brane limit and thus this scheme assumes that the perturbations are also axisymmetric and that the surface energy-momentum tensor of the brane is proportional to its induced metric. An advantage of our scheme is that it allows much more freedom for convenient coordinate choices than the other methods. This is because in our scheme, the coordinate system in the bulk and that on the brane are completely disent…
We construct a manifestly diffeomorphic M5-brane action in dual formulation coupled to an eleven-dimensional supergravity target space. The covariantisation is carried out by using (generalised) PST technique with 5 auxiliary scalar fields, which are obtained by using a geometrical consideration as a reduction of an auxiliary 4-form of Maznytsia-Preitschopf-Sorokin. As is typical in PST-covariantised theory, our construction possesses as usual the two local PST symmetries. By using one of the local PST symmetries, the action can be reduced to the non-manifestly covariant M5-brane action in dua…
We develop a covariant scheme to describe the dynamics of small perturbations on Lovelock type extended objects propagating in a flat Minkowski spacetime. The higher-dimensional analogue of the Jacobi equation in this theory becomes a wave type equation for a scalar field $Φ$. Whithin this framework, we analyse the stability of membranes with a de Sitter geometry where we find that the Jacobi equation specializes to a Klein-Gordon (KG) equation for $Φ$ possessing a tachyonic mass. This shows that, to some extent, these type of extended objects share the symmetries of the Dirac-Nambu-Goto (DNG)…
We consider a supersymmetric extension of the SL(2;Z)-covariant D3-brane action proposed by Nurmagambetov, and prove its kappa-symmetry in an on-shell type-IIB supergravity background.
We determine a manifestly SL(2,Z)-covariant kappa-symmetric action for the type IIB (p,q) five-branes as a perturbative expansion in the world-volume field strengths within the framework where the brane tension is generated by a world-volume field. In this formulation the Lagrangian is expected to be polynomial; we construct the kappa-invariant action to fourth order in the world-volume field strengths.
We consider the open superstring action in the AdS$_4 \times \mathbf{CP}^3$ background and investigate the suitable boundary conditions for the open superstring describing the 1/2-BPS D-branes by imposing the $κ$-symmetry of the action. This results in the classification of 1/2-BPS D-branes from covariant open superstring. It is shown that the 1/2-BPS D-brane configurations are restricted considerably by the Kähler structure on $\mathbf{CP}^3$. We just consider D-branes without worldvolume fluxes.
We develop a 3+1+1 covariant formalism with cosmological and astrophysical applications. First we give the evolution and constraint equations both on the brane and off-brane in terms of 3-space covariant kinematical, gravito-electro-magnetic (Weyl) and matter variables. We discuss the junction conditions across the brane in terms of the new variables. Then we establish a closure condition for the equations on the brane. We also establish the connection of this formalism with isotropic and anisotropic cosmological brane-worlds. Finally we derive a new brane solution in the framework of our form…
We consider D-branes of open superstrings in the AdS_5 x S^5 background. The possible configurations of D-branes preserving half of supersymmetries are classified by analyzing the kappa-invariance of an open superstring in a covariant manner. We also revisit the classification of D-branes in the pp-wave background. It is shown that Penrose limits of the possible D-branes in the AdS_5 x S^5 give all of the D-branes in the pp-wave. In addition, 1/4 supersymmetric D-string, which is related to the D-string preserving 8 dynamical supersymmetries in the pp-wave, is presented. We also discuss the re…
A superspace formulation of IIB supergravity which includes the field strengths of the duals of the usual physical one, three and five-form field strengths as well as the eleven-form field strength is given. The superembedding formalism is used to construct kappa-symmetric SL(2,R) covariant D-brane actions in an arbitrary supergravity background.
We derive boundary conditions for the covariant open string corresponding to D-branes in an Hpp-wave, by requiring kappa symmetry of its bulk action. Both half-supersymmetric and quarter-supersymmetric branes are seen to arise in this way, and the analysis furthermore agrees fully with the existing probe brane and supergravity computations. We elaborate on the origin of dynamical and kinematical supersymmetries from the covariant point of view. In particular we focus on the D-string which only preserves half of the dynamical supersymmetries and none of the kinematical ones. We discuss its orig…
We briefly review a covariant analysis of D-branes of type IIB superstring on the AdS_5xS^5 background from the κ-invariance of the Green-Schwarz string action. The possible configurations of D-branes preserving half of supersymmetries are classified in both cases of AdS_5xS^5 and the pp-wave background.
Using a fully covariant formalism given by Carter for the deformation dynamics of p-branes governed by the Dirac-Nambu-Goto action in a curved background, it is proved that the corresponding Witten's phase space is endowed with a covariant symplectic structure, which can serve as a starting point for a phase space quantization of such objects. Some open questions for further research are outlined.
We explore noncommutative D-branes in the AdS_5xS^5 background from the viewpoint of κ-invariance of a covariant open string action in the Green-Schwarz formulation. Boundary conditions to ensure the κ-invariance of the action lead to possible configurations of noncommutative D-branes. With this covariant method, we derive configurations of 1/4 BPS noncommutative D-branes. The resulting D-branes other than D-string are 1/4 BPS at any places, and the D-string is exceptional and it is 1/2 BPS at the origin and 1/4 BPS outside the origin. All of them are reduced to possible 1/4 BPS or 1/2 BPS AdS…
We discuss an open supermembrane theory in the AdS_4 x S^7 and AdS_7 x S^4 backgrounds. The possible Dirichlet branes of an open supermembrane are classified by analyzing the covariant Wess-Zumino term. All of the allowed configurations are related to those on the pp-wave background via the Penrose limit.
Canonical forms are given for the nilpotent BRS operator $\d$ and the covariant `loop space' derivative ${\cal D}_{\m}$ for the p-brane fields for all odd p. The defining characteristic of ${\cal D}_{\m}$ is that it is a functional derivative operator which generalizes the ordinary functional derivative and also commutes with $\d$. Methods of construction for the canonical forms are discussed.
We give an explicit form of the PST-type SL(2;R)-covariant super D3-brane action for the flat Minkowski background. To this end, we follow the prescription developed by Hatsuda and Kamimura. As an application of the action, we obtain the supercharge of the action by using the standard Noether's method and calculate the Poisson bracket algebra of the supercharge. The central charge of the supersymmetry algebra is given in a manifestly SL(2;R)-covariant way.
We construct Spin(p+1,p+1) covariant Dp-brane bound states by using that the potentials in the RR sector of toroidically compactified type II supergravity transform as a chiral spinor of the T-duality group. As an application, we show the invariance of the zero-force condition for a probe D-brane under noncommutative deformations of the background, which gives a holographic proof of the stability of the corresponding field theory ground state under noncommutative deformations. We also identify the Spin(p+1,p+1) transformation laws by examining the covariance of the D-brane Lagrangians.
We work out boundary conditions for the covariant open string in the type IIA plane wave background, which corresponds to the D-branes in the type IIA theory. We use the kappa symmetric string action and see what kind of boundary conditions should be imposed to retain kappa symmetry. We find half BPS as well as quarter BPS branes and the analysis agrees with the previous work in the light cone gauge if the result is available. Finally we find that D0-brane is non-supersymmetric.
We study covariant open bosonic string field theories on multiple $Dp$-branes by using the deformed cubic string field theory which is equivalent to the string field theory in the proper-time gauge. Constructing the Fock space representations of the three-string vertex and the four-string vertex on multiple $Dp$-branes, we obtain the field theoretical effective action in the zero-slope limit. On the multiple $D0$-branes, the effective action reduces to the Banks-Fishler-Shenker-Susskind (BFSS) matrix model. We also discuss the relation between the open string field theory on multiple $D$-insta…
Exact holography for cosmological branes in an AdS-Schwarzschild bulk was first introduced in hep-th/0204218. We extend this notion to include all co-dimension one branes moving in non-trivial bulk spacetimes. We use a covariant approach, and show that the bulk Weyl tensor projected on to the brane can always be traded in for "holographic" energy-momentum on the brane. More precisely, a brane moving in a non-maximally symmetric bulk has exactly the same geometry as a brane moving in a maximally symmetric bulk, so long as we include the holographic fields on the brane. This correspondence is ex…
We discuss an open supermembrane in the presence of a constant three-form. The boundary conditions to ensure the kappa-invariance of the action lead to possible Dirichlet branes. It is shown that a noncommutative (NC) M5-brane is possible as a boundary and the self-duality condition that the flux on the world-volume satisfies is derived from the requirement of the kappa-symmetry. We also find that the open supermembrane can attach to each of infinitely many M2-branes on an M5-brane, namely a strong flux limit of the NC M5-brane.
For the kappa-symmetric super IIA D-brane action by the canonical approach we construct an equivalent effective action which is characterized by an auxiliary scalar field. By analyzing the canonical equations of motion for the kappa-symmetry-gauge-fixed action we find a suitable conformal-like covariant gauge fixing of reparametrization symmetry to obtain a simplified effective action where the non-linear square root structure is removed. We discuss how the two effective actions are connected.
We briefly review how to discuss noncommutative (NC) M5-branes and intersecting NC M5-branes from kappa-invariance of an open supermembrane action with constant three-form fluxes. The kappa-invariance gives rise to possible Dirichlet brane configurations. We shortly summarize a construction of projection operators for NC M5-branes and some intersecting configurations of NC M5-branes. A strong flux limit of them is also discussed.
We study the construction of covariant nonlinear duality-symmetric actions in dual formulation. Essentially, the construction is the PST-covariantisation and nonlinearisation of Zwanziger action. The covariantisation made use of three auxiliary scalar fields. Apart from these, the construction proceed in a similar way to that of the standard formulation. For example, the theories can be extended to include interactions with external fields, and that the theories possess two local PST symmetries. We then explicitly demonstrate the construction of covariant nonlinear duality-symmetric actions in…
We study intersecting noncommutative (NC) M5-branes from κ-invariance of an open supermembrane action with constant three-form fluxes. The $κ$-invariance gives rise to possible D-brane configurations for which projection operators can be determined. We construct projection operators for two types of 1/4 BPS intersecting NC M5-branes. The one is an intersection of two NC M5-branes: NC M5\bot NC M5 (3). The other is that of a NC M5-brane and a commutative (C) M5-brane: NC M5\bot C M5 (1). A NC M5-brane can be viewed as a bound state of M5 and M2, and the configurations M2\bot M5 (1) and M2\bot M…
The new first order, rheonomic, kappa-supersymmetric formalism recently introduced by us for the world-volume action of the D3-brane is extended to the case of D5-branes. This extension requires the dual formulation of the Free Differential Algebra of type IIB supergravity in terms of 6-form gauge potentials which was so far missing and is given here. Furthermore relying on our new approach we are able to write the D5-world volume action in a manifestly SL(2,R) covariant form. This is important in order to solve the outstanding problem of finding the appropriate boundary actions of D3-branes o…
The standard cosmological model, based on general relativity with an inflationary era, is very effective in accounting for a broad range of observed features of the universe. However, the ongoing puzzles about the nature of dark matter and dark energy, together with the problem of a fundamental theoretical framework for inflation, indicate that cosmology may be probing the limits of validity of general relativity. The early universe provides a testing ground for theories of gravity, since gravitational dynamics can lead to characteristic imprints on the CMB and other cosmological observations.…
We propose a method of determining masses in brane scenarios which is independent of coordinate transformations. We apply our method to the scenario of Randall and Sundrum (RS) with two branes, which provides a solution to the hierarchy problem. The core of our proposal is the use of covariant equations and expressing all coordinate quantities in terms of invariant distances. In the RS model we find that massive brane fields propagate proper distances inversely proportional to masses that are not exponentially suppressed. The hierarchy between the gravitational and weak interactions is neverth…
The dynamics of a classical branelike object in a curved background is derived from the covariant stress-energy conservation of the brane matter. The world sheet equations and boundary conditions are obtained in the pole-dipole approximation, where nontrivial brane thickness gives rise to its intrinsic angular momentum. It is shown that intrinsic angular momentum couples to both, the background curvature and the brane orbital degrees of freedom. The whole procedure is manifestly covariant with respect to spacetime diffeomorphisms and world sheet reparametrizations. In addition, two extra gauge…
We discuss the dynamics of linear, scalar perturbations in an almost Friedmann-Robertson-Walker braneworld cosmology of Randall-Sundrum type II using the 1+3 covariant approach. We derive a complete set of frame-independent equations for the total matter variables, and a partial set of equations for the non-local variables which arise from the projection of the Weyl tensor in the bulk. The latter equations are incomplete since there is no propagation equation for the non-local anisotropic stress. We supplement the equations for the total matter variables with equations for the independent cons…
Some observational constraints on the brane-world based on predictions from specific models in five dimensions, have been recently reported, both on local and cosmological scales. In order to identify the origins of these constraints, the equations of motion of the brane-world are translated to the most general, model-independent (or "covariant"), formulation of the theory, based only on the Einstein-Hilbert action for the bulk geometry, the confinement of the standard gauge interactions and the exclusive probing of the extra dimensions by the gravitational field. In the case of the binary pul…
In this work, we extend a theory which describes a linearly self-dual exact 3-form field in six dimensional spacetime within the formalism of arXiv:1511.08220 and arXiv:1903.12196 to an action which fully describes an M5-brane in the eleven-dimensional supergravity background. The action we obtain has all the required symmetries including kappa-symmetry. Although the derivation of the action and the proof the symmetries do not require one to express the action explicitly in terms of the original field contents, we also give an initial attempt to give this expression.
We propose a complete Born-Infeld-like action for a bosonic 5-brane with the worldvolume chiral field in a background of gravitational and antisymmetric gauge fields of D=11 supergravity. When the five-brane couples to a three-rank antisymmetric gauge field local worldvolume symmetries of the five-brane require the addition to the action of an appropriate Wess-Zumino term. To preserve general coordinate and Lorentz invariance of the model we introduce a single auxiliary scalar field. The auxiliary field can be eliminated by gauge fixing a corresponding local symmetry at the price of the loss o…
The covariant quantization of massless D=11 superparticle (M0-brane) in its twistor-like Lorentz harmonic formulation is used to clarify the origin and some properties of the Berkovits pure spinor approach to quantum superstring and to search for hidden symmetries of D=11 supergravity. In the twistor like Lorentz harmonic formulation, the SO(16) symmetry is seen already at the classical level. The quantization produces the linearized supergravity multiplet as 128+128=256 component Majorana spinor of SO(16) and also shows an indirect argument in favor of the possible E8 symmetry.
We study the properties of the covariant supersymmetric and kappa-symmetric action for a system of N nearly coincident M0-branes (mM0 system) in flat eleven dimensional (11D) superspace and obtain supersymmetric equations for this dynamical system. Although a single M0-brane is the massless 11D superparticle, center of energy motion of the mM0 system is characterized by a nonnegative constant mass M constructed from the matrix fields describing the relative motion of mM0 constituents. We show that a bosonic solution of the mM0 equations can be supersymmetric iff this effective mass vanishes, M…
In discussions of Bousso's Covariant Entropy Bound, the Null Energy Condition is always assumed, as a sufficient {\em but not necessary} condition which helps to ensure that the entropy on any lightsheet shall necessarily be finite. The spectacular failure of the Strong Energy Condition in cosmology has, however, led many astrophysicists and cosmologists to consider models of dark energy which violate {\em all} of the energy conditions, and indeed the current data do not completely rule out such models. The NEC also has a questionable status in brane cosmology: it is probably necessary to viol…
The eikonal operator was originally introduced to describe the effect of tidal excitations on higher-genus elastic string amplitudes at high energy. In this paper we provide a precise interpretation for this operator through the explicit tree-level calculation of generic inelastic transitions between closed strings as they scatter off a stack of parallel Dp-branes. We perform this analysis both in the light-cone gauge, using the Green-Schwarz vertex, and in the covariant formalism, using the Reggeon vertex operator. We also present a detailed discussion of the high energy behaviour of the cova…
We generalize the current algebra of constraints of U-duality-covariant critical superstrings to include the generator responsible for the dynamics of the fundamental brane. This allows us to define $κ$ symmetry and to write a worldvolume action in Hamiltonian form that is manifestly supersymmetric in the target space. The Lagrangian form of this action is generally covariant, but the worldvolume metric has fewer components than expected.
The treatment of higher order perturbations of branes is considered using a covariant variational approach. This covariant variational approach brings to the forefront the geometric structure of the underlying perturbation theory, as opposed to a more commonly used `direct approach', that ignores the variational origin. In addition, it offers a clear calculational advantage with respect to so called `gauge fixed' treatments that distinguish tangential and normal modes, as it emphasizes the symmetries of the geometric models that describe the brane dynamics. We restrict our attention to a brane…
Using a fully covariant treatment for the description of the bulk geometry, we study the brane cosmological evolution in the presence of a smooth bulk matter distribution. We focus on the case of a Friedmann-Robertson-Walker (FRW) brane, invariantly characterized by the existence of a six-dimensional group of isometries acting on 3D spacelike orbits. With a FRW brane, the bulk geometry can be regarded as the 5D generalization of the \emph{inhomogeneous orthogonal family of Locally Rotationally Symmetric (LRS)} spacetimes. We show that, for \emph{any bulk matter configuration}, the expansion ra…
To exhibit the possible origin of the inner complexity of the Berkovits's pure spinor approach, we consider the covariant BRST quantization of the D=11 massless superparticle (M0-brane) in its spinor moving frame or twistor-like Lorentz harmonics formulation. The presence of additional twistor-like variables (spinor harmonics) allows us to separate covariantly the first and the second class constraints. After taking into account the second class constraints by means of Dirac brackets and after further reducing the first class constraints algebra, the dynamical system is described by the cohomo…
We first review self-dual (chiral) gauge field theories by studying their Lorentz non-covariant and Lorentz covariant formulations. We next construct a non-Abelian self-dual two-form gauge theory in six dimensions with a spatial direction compactified on a circle. This model reduces to the Yang-Mills theory in five dimensions for a small compactified radius R. The model also reduces to the Lorentz-invariant Abelian self-dual two-form theory when the gauge group is Abelian. The model is expected to describe multiple 5-branes in M-theory. We also discuss its decompactified limit, covariant formu…
