We consider a model involving a 4-brane in a 6D bulk which carries sigma model fields. An axion field on the 4-brane cancels the pressure along one direction leading to an effective codimension-2 3-brane. For a range of parameters of the theory, we get a transverse space which is non-compact, providing a possible solution to the cosmological constant problem. A setup with two branes in a compact space is also treated. In this case, a mild fine-tuning between the radii of the two 4-branes is necessary. Finally, we explore the 4-brane problem in the Gauss-Codazzi formulation and we discuss general aspects of gravity in the presence of additional brane sources.
We determine the Killing spinors for a class of magnetic brane solutions with Minkowski worldvolume of the theory of AdS Einstein Maxwell theories in d dimensions. We also obtain curved magnetic brane solutions with Ricci-flat worldvolumes. If we demand that the curved brane solution admits Killing spinors, then its worldvolume must admit parallel spinors. Classes of Ricci-flat worldvolumes admitting parallel spinors are discussed.
This paper analyzes the effect of curved closed string backgrounds on the stability of D-branes within boundary string field theory. We identify the non-local open string background that implements shifts in the closed string background and analyze the tachyonic sector off-shell. The renormalization group flow reveals some characteristic properties, which are expected for a curved background, like the absence of a stable space-filling brane. In 3-dimensions we describe tachyon condensation processes to lower-dimensional branes, including a curved 2-dimensional brane. We argue that this 2-brane…
We consider null bosonic p-branes in curved space-times. Some exact solutions of the classical equations of motion and of the constraints for the null membrane in general stationary, axially symmetrical, four dimensional, gravity background are found.
We discuss the relation between supersymmetric gauge theory of branes and supergravity; as it was discovered in D-brane physics, and as it appears in Matrix theory, with emphasis on motion in curved backgrounds. We argue that gauged sigma model Lagrangians can be used as definitions of Matrix theory in curved space. Lecture given at Strings '97; June 20, 1997.
We study semiclassical strings in the near horizon geometry of certain curved branes. We investigate the rigidly rotating strings in the near horizon geometry of NS5-branes wrapped on AdS3 x S3 and in the presence of background NS-NS flux. We study several string solutions corresponding to giant magnon, single spike and more general folded strings for the fundamental string in this background. We comment that in the S-dual background the situation changes drastically.
In this paper we first derive solutions which can be interpreted as branes wrapping nontrivial curved manifolds, and then study their cosmological implications. We find that at early times the branes tend to shrink the internal manifold, while allowing the ``unwrapped'' dimensions to expand in congruence with what has already been observed in the case when the internal manifold is flat (tori). However, at late times the internal curvature terms become important leading to potentially interesting differences.
An action for supersymmetric D0-branes in curved backgrounds is obtained by dimensional reduction of N=1 ten-dimensional supergravity coupled to super Yang-Mills system to 0+1 dimensions. The resultant action exhibits the coset-space symmetry $\frac{SO(9,9+n)}{SO(9)\times SO(9+n)}\times U(1)$ where $n=N^{2}-1$ is the dimension of the SU(N) gauge group.
Oblique Dp-branes in the maximally supersymmetric type IIB plane-wave background are constructed in terms of boundary states, as well as from the open string point of view. These Dp-branes, whose existence was anticipated by Hikida and Yamaguchi from general supersymmetry arguments, have an isometry that is a subgroup of the diagonal SO(4) symmetry of the background. The oblique D3-brane is found to preserve four dynamical and four kinematical supersymmetries while the oblique D5-brane preserves one half of both the dynamical and kinematical supersymmetries. We also discuss the open-string bou…
We discuss non-linear instantons in supersymmetric field theories on curved spaces arising from D-branes. Focusing on D3-branes and four-dimensional field theories, we derive the supersymmetry conditions and show the intimate relation between the instanton solutions and the non-linearly realized supersymmetries of the field theory. We demonstrate that field theories with non-linearly realized supersymmetries are coupled to supergravity backgrounds in a similar fashion as those with linearly realized supersymmetries, and provide details on how to derive such couplings from a type II perspective…
We construct p-brane solutions with non-trivial world volume metrics and show that applied to supergravity theories, they will lead to threshold BPS bound states of intersecting solutions. However applied to certain specific values of the couplings in cosmological (a,b)-models non-trivial solutions can be constructed.
We obtain actions for N D-branes occupying points in a manifold with arbitrary Kahler metric. In one complex dimension, the action is uniquely determined (up to second order in commutators) by the requirement that it reproduce the masses of stretched strings and by imposing supersymmetry. These conditions are very restrictive in higher dimensions as well. The results provide a noncommutative extension of Kahler geometry.
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.
We give a simple method to calculate the semiclassical $D$-brane boundary states of the bosonic string propagating in an arbitrary curved spacetime in a perturbative approach in which the metric $g_{AB}$ and the constant antisymmetric Kalb-Ramond field $b_{AB}$ form the general background which is treated exactly. As an important particular case, it is shown that at the first order perturbation theory there are $D$-brane coherent states in the $d$-dimensional {\em AdS} spacetime if certain conditions are fulfilled by the boundary projectors.
Some recent literature has examined the holographic-induced cosmology of a brane universe in the background of an anti-de Sitter-black hole geometry. In this regard, curved-brane scenarios have begun to receive considerable attention. Our current interest is in a formal discrepancy that exists between two such works by Padilla (hep-th/0111247) and Youm (hep-th/0111276). In particular, these authors have incorporated different values for a conformal factor that is used to relate the thermodynamics of the relevant (AdS bulk and CFT brane) spacetimes. After a more general review, we clarify this …
These lectures provide an introduction to the microscopic description of branes in curved backgrounds. After a brief reminder of the flat space theory, the basic principles and techniques of (rational) boundary conformal field theory are presented in the second lecture. The general formalism is then illustrated through a detailed discussion of branes on compact group manifolds. In the final lecture, many more recent developments are reviewed, including some results for non-compact target spaces.
The nondeterminantal forms of the Born-Infeld and related brane actions in which the gauge fields couple to both an induced metric and an intrinsic metric are generalised by letting either or both metrics be dynamical. The resulting actions describe ` brane world' and cosmological scenarios in which the gauge fields are confined to the brane, while gravity propagates in both the world-volume and the bulk. In particular, for actions involving a nonsymmetric ` metric', nonsymmetric gravity propagates on the worldvolume. For 3-branes with a symmetric metric, conformal (Weyl) gravity propagates on…
We find exact D-brane configurations in the Nappi-Witten background using the boundary state approach and describe how they are related by T-duality transformations. We also show that the classical boundary conditions of the associated sigma model correspond to a field dependent automorphism relating the chiral currents and discuss the correspondence between the boundary state approach and the sigma model approach.
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 find exact tachyon kink solutions of DBI type effective action describing an unstable D5-brane with worldvolume gauge field turned on in a curved background. The background of interest is the ten-dimensional lift of the Salam-Sezgin vacuum and, in the asymptotic limit, it approaches ${\rm R}^{1,4}\times {\rm T}^2\times {\rm S}^3$. The solutions are identified as composites of lower-dimensional D-branes and fundamental strings, and, in the BPS limit, they become a D4D2F1 composite wrapped on ${\rm R}^{1,2}\times {\rm T}^2$ where ${\rm T}^2$ is inside ${\rm S}^3$. In one class of solutions we…
We investigate the properties of the AdS D1-branes which are the bound states of a curved D1-brane with $n$ fundamental strings (F1) in the $AdS_3$ spacetime, and the AdS D2-branes which are the axially symmetric bound states of a curved D2-brane with $m$ D0-branes and $n$ fundamental strings in the $AdS_3 \times S^3$ spacetime. We see that, while the AdS D1-branes asymptotically approach to the event horizon of the $AdS_3$ spacetime the AdS D2-branes will end on it. As the near horizon geometry of the F1/NS5 becomes the spacetime of $AdS_3 \times S^3 \times T^4$ with NS-NS three form turned o…
We describe a simple method for generating new string solutions for which the brane worldvolume is a curved space. As a starting point we use solutions with NS-NS charges combined with 2-d CFT's representing different parts of space-time. We illustrate our method with many examples, some of which are associated with conformally invariant sigma models. Using U-duality, we also obtain supergravity solutions with RR charges which can be interpreted as D-branes with non-trivial worldvolume geometry. In particular, we discuss the case of a D5-brane wrapped on AdS_3 x S^3, a solution interpolating b…
We construct novel $7d$ supersymmetric gauge theories which include a Chern-Simons-like term on curved spaces. In order to so, we examine the supersymmetry constraints for E7-branes in type IIA$^*$ theory, rather than making use of an off-shell supergravity. We find two classes of solutions to the constraints, expressed in terms of a $G_2$-structure with non-vanishing intrinsic torsion. The supersymmetric gauge theories are then obtained by coupling flat gauge theory to such supersymmetric backgrounds. Various examples are given, including round and squashed $S^7$ as well as $S^3 \times M_4$ w…
A generic property of curved manifolds is the existence of focal points. We show that branes located at focal points of the geometry satisfy special properties. Examples of backgrounds to which our discussion applies are AdS_m x S^n and plane wave backgrounds. As an example, we show that a pair of AdS_2 branes located at the north and south pole of the S^5 in AdS_5 x S^5 are half supersymmetric and that they are dual to a two-monopole solution of N=4 SU(N) SYM theory. Our second example involves spacelike branes in the (Lorentzian) plane wave. We develop a modified lightcone gauge for the open…
The non-abelian Dirac-Born-Infeld action is used to construct the D2-brane from multiple D0-branes in the curved spacetimes. After choosing the matrix elements as the coordinates of the D0-branes we obtain a simple formula of the Lagrangian for the system in a class of the curved background. Using the formula we first re-examine the system in the flat spacetime and show that, in addition to the fuzzy tube and fuzzy spike which were found in the previous literature, there is the fuzzy wormhole solution. Next, we apply the formula to the system in the geometry of the NS5-branes background. A sol…
Braneworld effective action is constructed by two different methods based respectively on the Dirichlet and Neumann boundary value problems. The equivalence of these methods is shown due to nontrivial duality relations between special boundary operators of these two problems. Previously known braneworld action algorithms in two-brane Randall-Sundrum model are generalized to curved branes with deSitter and Anti-deSitter geometries.
We study fermions coupled to Yang-Mills matrix models from the point of view of emergent gravity. The matrix model Dirac operator provides an appropriate coupling for fermions to the effective gravitational metric for general branes with nontrivial embedding, albeit with a non-standard spin connection. This generalizes previous results for 4-dimensional matrix models. Integrating out the fermions in a nontrivial geometrical background induces indeed the Einstein-Hilbert action of the effective metric, as well as additional terms which couple the Poisson tensor to the Riemann tensor, and a dila…
We discuss general supersymmetric brane configurations in flux backgrounds of string and M-theory and derive a necessary condition for the worldvolume theory to be supersymmetric on a given curved manifold. This condition resembles very much the conditions found from coupling a supersymmetric field theory to off-shell supergravity but can be derived in any dimension and for up to sixteen supercharges. Apart from the topological twist, all couplings appearing in the supersymmetry condition are linked to fluxes in the bulk. We explicitly derive the condition for D3-, M2- and M5-branes, in which …
A survey is given of the formulation of a $σ$-model describing an open string moving in general target space background fields and coupling to both a matrix-valued D-brane position and a matrix-valued gauge field on the D-brane. The equations of motion for the D-brane and the gauge field are derived from the conformal invariance condition on the string world sheet in lowest order of $\ap$. The ordering problem of the involved matrices is solved. In addition to our previous work we discuss a conflict between the classical T-duality rules and renormalization. The calculation of the RG $β$-functi…
We study spacetime singularities in a general five-dimensional braneworld with curved branes satisfying four-dimensional maximal symmetry. The bulk is supported by an analog of perfect fluid with the time replaced by the extra coordinate. We show that contrary to the existence of finite distance singularities from the brane location in any solution with flat (Minkowski) branes, in the case of curved branes there are singularity-free solutions for a range of equations of state compatible with the null energy condition.
Curved, intersecting brane configurations satisfying the type IIA supergravity equations of motion are found. In eleven dimensions, the models are interpreted in terms of orthogonally intersecting M5--branes, where the world--volumes are curved due to the effects of one or more massless scalar fields. Duality symmetries are employed to generate further type II and heterotic solutions. Some cosmological implications are discussed.
We construct a supergravity dual to the cascading $SU(N+M) x SU(N)$ supersymmetric gauge theory (related to fractional D3-branes on conifold according to Klebanov et al) in the case when the 3-space is compactified on $S^3$ and in the phase with unbroken chiral symmetry. The size of $S^3$ serves as an infrared cutoff on the gauge theory dynamics. For a sufficiently large $S^3$ the dual supergravity background is expected to be nonsingular. We demonstrate that this is indeed the case: we find a smooth type IIB supergravity solution using a perturbation theory that is valid when the radius of $S…
Starting with the Nambu-Goto action of the braneworld embedded in a curved bulk, we derive the precise expressions for the quantum induced effects due to small fluctuations of the brane. To define the brane fluctuations invariantly, we introduce the Riemannian coordinate system for the subspace normal to the braneworld. It will turn out that we can systematically incorporate the effects of bulk curvature, and that the induced effects depend on the extrinsic curvature and the normal-connection gauge field as well as on bulk curvature components at the brane.
It appears that having our own brane to somehow interact with other branes could give rise to quite an interesting system and that that interaction could lead to some observable effects. We consider the question of whether or not these signatures of interaction between the branes can be observed. To answer this question, we investigate the effect induced by the inflaton in the WMAP7 data using the warm inflationary model. In this model, slow-roll and perturbation parameters are given in terms of the inflaton thermal distribution. We show that this distribution depends on the orbital radius of …
We present a three dimensional novel massive N=2 super Yang-Mills action as a low energy effective worldvolume description of the D2-branes on a pp-wave. The action contains the Myers term, mass terms for three Higgs, and terms mixing the electric fields with other two Higgs. We derive the action in three different ways, from the M-theory matrix model, from the supermembrane action, and from the Dirac-Born-Infeld action. We verify the consistent mutual agreement and comment how each approach is complementary to another. In particular, we give the eleven dimensional geometric interpretation of …
We argue that black p-branes will occur in the collision of D0-branes at Planckian energies. This extents the Amati, Ciafaloni and Veneziano and 't Hooft conjecture that black holes occur in the collision of two light particles at Planckian energies. We discuss a possible scenario for such a process by using colliding plane gravitational waves. D-branes in the presence of black holes are discussed. M(atrix) theory and matrix string in curved space are considered. A violation of quantum coherence in M(atrix) theory is noticed.
We investigate further our recent proposal for the form of the matrix theory action in weak background fields. Using Seiberg's scaling argument we relate the matrix theory action to a low-energy system of many D0-branes in an arbitrary but weak NS-NS and R-R background. The resulting multiple D0-brane action agrees with the known Born-Infeld action in the case of a single brane and gives an explicit formulation of many additional terms which appear in the multiple brane action. The linear coupling to an arbitrary background metric satisfies the nontrivial consistency condition suggested by Dou…
We search for exact tachyon kink solutions of DBI type effective action describing an unstable D-brane with worldvolume gauge field turned in both the flat and a curved background. There are various kinds of solutions in the presence of electromagnetic fields in the flat space, such as periodic arrays, topological tachyon kinks, half kinks, and bounces. We identify a BPS object, D($p$-1)F1 bound state, which describes a thick brane with string flux density. The curved background of interest is the ten-dimensional lift of the Salam-Sezgin vacuum and, in the asymptotic limit, it approaches ${\rm…
We consider the low-energy limit of the two-dimensional theory on multiple M2-branes suspended between a flat M5-brane and a curved M5-brane. We argue that it is described by an $\mathcal{N}=(2,2)$ supersymmetric Landau-Ginzburg model with the superpotential determined by the shape of the curved M5-branes, which flows in the low-energy limit to a Kazama-Suzuki coset model. We provide evidence by studying ground states and BPS spectra of the systems.
Embedding of a bosonic and/or fermionic p-brane into a generic curved $D$-dimensional spacetime is considered. In contradistinction to the bosonic p-brane case, when there are no constraints on a generic curving whatsoever, the usual superbrane can be embedded into a curved spacetime of a restricted curving only. A generic curving is achieved by extending the odd sector of a superbrane as to transform w.r.t. $\bar{SL}(D,R)$, i.e. $\bar{Diff}(D,R)$ infinite-component spinorial representations. Relevant constructions in the D=3 case are considered.
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 systematically analyze supersymmetric D-branes in the type IIB plane wave background using Green-Schwarz superstring theory. We find several new supersymmetric oblique and curved D-branes. The supersymmetries preserved by various configurations of these D-branes including their intersections are also identified. In particular, we show that $D_+$-branes of type (+,-,n,n) for n=1,2,3,4 preserve 4 dynamical supersymmetries by introducing gauge field excitations and newly discovered oblique D5- and D7-branes also preserve four or two dynamical supersymmetries with gauge field condensates. Furth…
A consistent truncation of IIB on S^5 has been obtained in the sector of the metric and the 4-form potential. The ansatz contains 20 scalars and all 15 gauge fields of ${\cal N}=8$ gauged supergravity in five dimensions. With this fully non-linear ansatz, the calculations for n-point correlators of super Yang-Mills (SYM) theory via AdS/CFT are simpler than those in the literature that use {\em linear} ansatz followed by non-linear field redefinitions. We work out the SYM operators that couple to the scalars by expanding the Dirac-Born-Infeld (DBI) action plus Wess-Zumino (WZ) terms around an $…
We study a $D_p$-brane in a parallelizable NS-NS background. The article starts with a brief review of the non-associative deformation of $D$-brane worldvolume in presence of torsion \cite{cornalba}. We suggest an alternative form and heuristic derivation of the open string metric for weakly curved backgrounds, by promoting the constant two-form in the flat space formula to a dynamical two-form and then Taylor expanding the bulk fields in Riemann Normal Coordinates at the origin. For weakly curved backgrounds, terms only upto the leading order in the NS-NS field strength or torsion contribute.…
We point out that when a D-brane is placed in an NS-NS B field background with non-vanishing field strength (H=dB) along the D-brane worldvolume, the coordinate of one end of the open string does not commute with that of the other in the low energy limit. The degrees of the freedom associated with both ends are not decoupled and accordingly, the effective action must be quite different from that of the ordinary noncommutative gauge theory for a constant B background. We construct an associative and noncommutative product which operates on the coordinates of both ends of the string and propose …
We obtain the action for a curved superconformal abelian M5 brane with the background R-symmetry gauge field turned on. We then restrict ourselves to superconformal M5 brane on a sphere times flat Minkowski space. We choose R-symmetry SO(1,4) instead of SO(5), which enables us to partially twist on Minkowski space and replace it by some curved Lorentzian manifold. We obtain M5 brane actions on $M_{1,1} \times S^4$ and $M_{1,2} \times S^3$ where actions and all fields, including the background gauge field, are real. Dimensional reduction along time gives real 5d SYM actions with nonabelian gene…
We consider the non-Abelian action for the dynamics of $N Dp'$-branes in the background of $M Dp$-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 imp…
We generalise the standard, flat p-brane solutions sourced by a dilaton and a form field, by taking the worldvolume to be a curved Einstein space, such as (anti-)de Sitter space. Our method is based on reducing the p-branes to domain walls and then allowing these domain walls to be curved. For de Sitter worldvolumes this extends some recently constructed warped de Sitter non-compactifications. We restrict our analysis to solutions that possess scaling behavior and demonstrate that these scaling solutions are near-horizon limits of a more general solution. Finally, our framework can equally be …
We construct a broad family of exact solutions to the five-dimensional Einstein equations coupled to a scalar field with an exponential potential. Embedding a three-brane in these bulk space-times in a particular way we obtain a class of self-tuned curved brane worlds in which the vacuum energy on the brane is gravitationally idle, the four-dimensional geometry being insensitive to the value of the brane tension. This self-tuning arises from cancellations, enforced by the junction conditions, between the scalar field potential, the brane vacuum energy and the matter on the brane. Finally, we s…
We consider the actions for ten--dimensional $p$--branes and $D$--branes in an arbitrary curved background and discuss some of their properties. We comment on how the $SL(2,R)$ duality symmetry acts on the five--brane actions.
Fate of branes in external fields is reviewed. Spontaneous creation of the Brane World in $AdS_{5}$ with external field is described. The resulting Brane World consists of a flat 4d spatially finite expanding Universe and curved expanding "regulator" branes. All branes have a positive tension.
In this thesis we study the AdS3 Wess-Zumino-Novikov-Witten model. We compute the Operator Product Expansion of primary fields as well as their images under the spectral flow automorphism in all sectors of the model by considering it as a Wick rotation of the H3+ coset model. We argue that the symmetries of the affine algebra require a truncation which establishes the closure of the fusion rules on the Hilbert space of the theory. These results are then used to discuss the factorization of four point functions by applying the bootstrap approach. We also study the modular properties of the mode…
We construct the holographic dual for $\mathcal N=4$ SYM on $\rm S^4$ and $\rm AdS_4$ coupled to massive $\mathcal N=2$ supersymmetric quenched flavor fields on a codimension-1 defect, which is $\rm S^3$ and $\rm AdS_3$, respectively. The holographic description is in terms of a D3/probe D5 brane system. We set up and reduce the BPS equations for D5-brane embeddings with arbitrary supersymmetric deformations and partly solve them at the non-linear level. The remaining equations are solved explicitly in a small-mass expansion. We compute the contribution of the defect fields to the partition fu…
We construct a model for dilatonic brane worlds with constant curvature on the brane, i.e. a non-zero four-dimensional cosmological constant, given in function of the dilaton coupling and the cosmological constant of the bulk. We compare this family of solutions to other known dilatonic domain wall solutions and apply a self-tunning mechanism to check the stability of our solutions under quantum fluctuations living on the brane.
An intense study of the relationship between certain quantum theories of gravity realized on curved backgrounds and suitable gauge theories, has been originated by a remarkable conjecture put forward by Maldacena almost one year ago. Among the possible curved vacua of superstring or M-theory, spaces having the form of an Anti-de Sitter space-time times a compact Einstein manifold, have been playing a special role in this correspondence, since the quantum theory realized on them, in the original formulation of the conjecture, was identified with the effective superconformal theory on the world …
In the presence of a D-brane a string theory develops a new subsector. We show that for curved D-branes the corresponding sector is a (partially twisted) topological field theory. We use this result to compute the degeneracy of 2-branes wrapped around $K3$ cycles as well as 3-branes wrapped around CY threefold vanishing 3-cycles. In both cases we find the degeneracy is in accord with expectation. The counting of BPS states of a gas of 0-branes in the presence of a 4-brane in $K3$ is considered and it is noted that the effective 0-brane charge is shifted by 1, due to a quantum correction. This …
In this paper, we adopt the method of quantum fields in curved spacetime to quantize a free scalar matter field in the braneworld background whose warped factor is of the form that could generate Pöschl-Teller potential. Then we consider the interaction between the scalar field $ϕ(x)$ and a classical scalar source $ρ(x)$ with the form $\mathcal{H}_I=\sqrt{-g}\tilde{g}ρ(x)ϕ(x)$. The corresponding S-matrix is given and the number of particles generated by the source is obtained. Furthermore, we get the {particle numbers} in the cases that only ground state mode of the field could be detected and…
We investigate the deformation of D-brane world-volumes in curved backgrounds. We calculate the leading corrections to the boundary conformal field theory involving the background fields, and in particular we study the correlation functions of the resulting system. This allows us to obtain the world-volume deformation, identifying the open string metric and the noncommutative deformation parameter. The picture that unfolds is the following: when the gauge invariant combination ω= B + F is constant one obtains the standard Moyal deformation of the brane world-volume. Similarly, when dω= 0 one o…
