In this paper we study dynamical supersymmetry breaking in absence of gravity with the matter content of the minimal supersymmetric standard model. The hidden sector of the theory is a strongly coupled gauge theory, realized in terms of microscopic variables which condensate to form mesons. The supersymmetry breaking scalar potential combines F, D terms with instanton generated interactions in the Higgs-mesons sector. We show that for a large region in parameter space the vacuum breaks in addition to supersymmetry also electroweak gauge symmetry. We furthermore present local D-brane configurations that realize these supersymmetry breaking patterns.
Intersecting D-brane models seem to be one of the most promising avenues to embed the Standard Model physics within the string context. We review here different aspects of these models. Topics include the question of SUSY and quasi-SUSY in intersecting brane models, model-building, the brane recombination interpretation of the SM Higgs mechanism, Yukawa couplings, the lowering of the string scale and possible new Z's accessible to accelerators.
We study the modular symmetry in four-dimensional low-energy effective field theory, which is derived from type IIB magnetized D-brane models and type IIA intersecting D-brane models. We analyze modular symmetric behaviors of perturbative terms and non-perturbative terms induced by D-brane instanton effects. Anomalies are also investigated and such an analysis on anomalies suggests corrections in effective field theory.
We present a simple mechanism by which supersymmetry can be dynamically broken in intersecting brane models, naturally generating an exponentially small scale. Rather than utilize either non-Abelian gauge dynamics or D-instantons, our mechanism uses worldsheet instantons to generate the small scale in a hidden sector.
We propose a unification scenario for supersymmetric intersecting brane models. The quarks and leptons are embedded into adjoint representations of SO(32), which are obtained and break by type I string compactified on orbifolds. Its single unified gauge coupling can give rise to different gauge couplings below the unification scale, due to effects of magnetic fluxes. The crucial mechanism is brane recombination preserving supersymmetry.
We provide a simple low energy description of recombination of intersecting D-branes using super Yang-Mills theory. The recombination is realized by condensation of an off-diagonal tachyonic fluctuation localized at the intersecting point. The recombination process is equivalent to brane-antibrane annihilation, thus our result confirms Sen's conjecture on tachyon condensation, although we work in the super Yang-Mills theory whose energy scale is much lower than alpha'. We also discuss the decay width of non-parallelly separated D-branes.
Starting with a new bosonization scheme for the βγCFT of the super-conformal ghosts, vertex operators are constructed for massless open string states in the intersecting D-brane world. These vertex operators satisfy all requirements for a consistent RNS formulation of superstring theories, so GSO projections can be properly taken.
We address dynamical supersymmetry breaking within a N=1 supersymmetric Standard-like Model based on a Z_2 x Z_2 Type IIA orientifold with intersecting D6-branes. The model possesses an additional, confining gauge sector with the USp(2)_A x USp(2)_B x USp(4) gauge group, where the gaugino condensation mechanism allows for the breaking of supersymmetry and stabilizes moduli. We derive the leading contribution to the non-perturbative effective superpotential and determine numerically the minima of the supergravity potential. These minima break supersymmetry and fix two undetermined moduli, which…
We consider intersecting brane solutions of the type IIB matrix model. It is shown that fermionic zero-modes arise on such backgrounds, localized at the brane intersections. They lead to chiral fermions in four dimensions under certain conditions. Such configurations reproduce many of the welcome features in similar string-theoretic constructions. Therefore they can be used to construct semi-realistic particle physics models in the framework of Yang-Mills matrix models. In particular, we present a brane configuration which realizes the correct chiral spectrum of the standard model in the matri…
We consider the intersecting D4-brane and anti-D4-brane model of holographic QCD, motivated by the model that has recently been suggested by Van Raamsdonk and Whyte. We analyze such D4-branes by the use of the action with a bi-fundamental ``tachyon'' field, so that we find the classical solutions describing the intersecting D4-branes and the U-shaped D4-branes. We show that the ``tachyon'' field in the bulk theory provides a current quark mass and a quark condensate to the dual gauge theory and that the lowest modes of mesons obtain mass via tachyon condensation. Then evaluating the properties…
We consider the interactions between Dp-branes intersecting at an arbitrary number of angles in the context of type II string theory. For cosmology purposes we concentrate in the theory on R^{3,1} x T^6. Interpreting the distance between the branes as the inflaton field, the branes can intersect at most at two angles on the compact space. If the configuration is non-supersymmetric we will have an interbrane potential that provides an effective cosmological inflationary epoch at the four dimensional intersection between the branes. The end of inflation occurs when the interbrane distance become…
A brane world model is investigated, in which there are many branes that may intersect and self intersect. One of the branes, being a 3-brane, represents our spacetime, while the other branes, if they intersect our brane world, manifest themselves as matter in our 3-brane. It is shown that such a matter encompasses dust of point particles and higher dimensional p-branes, and all those objects follow "geodesics" in the world volume swept by our 3-brane. We also point point out that such a model can be formulated in a background independent way, and that the kinetic term for gravity arises from …
We study N=1 supersymmetric four-dimensional solutions of massive Type IIA supergravity with intersecting D6-branes in the presence NS-NS three-form fluxes. We derive N=1 supersymmetry conditions for the D6-brane and flux configurations in an internal manifold $X_6$ and derive the intrinsic torsion (or SU(3)-structure) related to the fluxes. In the absence of fluxes, N=1 supersymmetry implies that D6-branes wrap supersymmetric three-cycles of $X_6$ that intersect at angles of SU(3) rotations and the geometry is deformed by SU(3)-structures. The presence of fluxes breaks the SU(3) structures to…
We study non-abelian discrete flavor symmetries, which can appear in magnetized brane models. For example, $D_4$, $Δ(27)$ and $Δ(54)$ can appear and matter fields with several representations can appear. We also study the orbifold background, where non-abelian flavor symmetries are broken in a certain way.
We present some phenomenology of a new class of intersecting D-brane models. Soft SUSY breaking terms for these models are calculated in the u - moduli dominant SUSY breaking approach (in type IIA). In this case, the dependence of the soft terms on the Yukawas and Wilson lines drops out. These soft terms have a different pattern compared to the usual heterotic string models. Phenomenological implications for dark matter are discussed.
We describe the construction of configurations of D6-branes wrapped on compact 3-cycles intersecting at points in non-compact Calabi-Yau threefolds. Such constructions provide local models of intersecting brane worlds, and describe sectors of four-dimensional gauge theories with chiral fermions. We present several classes of non-compact manifolds with compact 3-cycles intersecting at points, and discuss the rules required for model building with wrapped D6-branes. The rules to build 3-cycles are simple, and allow easy computation of chiral spectra, RR tadpoles and the amount of preserved super…
We present new classes of supersymmetric Standard-like models from type IIA $\IT^6/(\IZ_2\times \IZ_2)$ orientifold with intersecting D6-branes. D6-branes can wrap general supersymmetric three-cycles of $\IT^6=\IT^2\times \IT^2\times \IT^2$, and any $\IT^2$ is allowed to be tilted. The models still suffer from additional exotics, however we obtained solutions with fewer Higgs doublets, as well as models with all three families of left-handed quarks and leptons arising from the same intersecting sector, and examples of a genuine left-right symmetric model with three copies of left-handed and ri…
We study the matching conditions of intersecting brane worlds in Lovelock gravity in arbitrary dimension. We show that intersecting various codimension 1 and/or codimension 2 branes one can find solutions that represent energy-momentum densities localized in the intersection, providing thus the first examples of infinitesimally thin higher codimension braneworlds that are free of singularities and where the backreaction of the brane in the background is fully taken into account.
We study flavor structure and the coupling selection rule in intersecting D-brane configurations. We formulate the selection rule for Yukawa couplings and its extensions to generic n-point couplings. We investigate the possible flavor structure, which can appear from intersecting D-brane configuration, and it is found that their couplings are determined by discrete abelian symmetry. Our studies on the flavor structure and the coupling selection rule show that the minimal matter content of the supersymmetric standard model would have difficulty to derive realistic Yukawa matrices from stringy 3…
Starting from the non-supersymmetric, tachyon-free orientifold of type 0 string theory, we construct four-dimensional brane world models with D6-branes intersecting at angles on internal tori. They support phenomenologically interesting gauge theories with chiral fermions. Despite the theory being non-supersymmetric the perturbative scalar potential induced at leading order is shown to stabilize geometric moduli, leaving only the dilaton tadpole uncanceled. As an example we present a three generation model with gauge group and fermion spectrum close to a left-right symmetric extension of the S…
A three-family non-supersymmetric model with U(3)^3 gauge symmetry is analyzed in the context of intersecting D-branes. This is equivalent to the `trinification' model extended by three U(1) factors which survive as global symmetries in the low energy effective model. The Standard Model fermions are accommodated in the three possible bifundamental multiplets represented by strings with endpoints attached on different brane-stacks of this particular setup. Further, a natural Quark-Lepton hierarchy is realized due to the existence of the additional abelian symmetries
We show that contrary to first expectations realistic three generation supersymmetric intersecting brane world models give rise to phenomenologically interesting predictions about gauge coupling unification. Assuming the most economical way of realizing the matter content of the MSSM via intersecting branes we obtain a model independent relation among the three gauge coupling constants at the string scale. In order to correctly reproduce the experimentally known values of sin^2[theta_W(M_z)] and alpha_s(M_z) this relation leads to natural gauge coupling unification at a string scale close to t…
The structure of Yukawa coupling matrices is investigated in type IIA T^6/(Z_2 x Z_2) orientifold models with intersecting D-branes. Yukawa coupling matrices are difficult to be realistic in the conventional models in which the generation structure emerges by the multiple intersection of D-branes in the factorized T^6 = T^2 x T^2 x T^2. We study the new type of flavor structure, where Yukawa couplings are dynamically generated, and show this type of models lead to nontrivial structures of Yukawa coupling matrices, which can be realistic.
We study supersymmetric intersecting D6-branes wrapping 3-cycles in the Type IIA T^6/Z_4 orientifold background. As a new feature, the 3-cycles in this orbifold space arise both from the untwisted and the Z_2 twisted sectors. We present an integral basis for the homology lattice, H_3(M,Z), in terms of fractional 3-cycles, for which the intersection form involves the Cartan matrix of E8. We show that these fractional D6-branes can be used to construct supersymmetric brane configurations realizing a three generation Pati-Salam model. Via brane recombination processes preserving supersymmetry, th…
All the possible three-family ${\cal N}=1$ supersymmetric Pati-Salam models constructed with intersecting D6-branes from Type IIA orientifolds on $T^6/(\mathbb{Z}_2\times \mathbb{Z}_2)$ are recently presented in arXiv: 2112.09632. Taking models with largest wrapping number $5$ and approximate gauge coupling unification at GUT scale as examples, we show string scale gauge coupling unification can be realized through two-loop renormalization group equation running by introducing seven pairs of vector-like particles from ${\cal N}=2$ sector. The number of these introduced vector-like particles ar…
We compute Yukawa couplings in type IIa string theory compactified on a six-torus in the presence of intersecting D6-branes. The six-torus is generated by an SO(12) root lattice. Yukawa couplings are expressed as sums over worldsheet instantons. Our result extends known expressions to a non-factorisable torus. As an aside we also fill in some details for the factorisable torus and non-coprime intersection numbers.
We construct an N=1 supersymmetric three-family flipped SU(5) model from type IIA orientifolds on $T^6/(\Z_2\times \Z_2)$ with D6-branes intersecting at general angles. The spectrum contains a complete grand unified and electroweak Higgs sector. In addition, it contains extra exotic matter both in bi-fundamental and vector-like representations as well as two copies of matter in the symmetric representation of SU(5).
We construct the first three family N=1 supersymmetric string model with Standard Model gauge group SU(3)_C x SU(2)_L x U(1)_Y from an orientifold of type IIA theory on T^6/(Z_2 x Z_2) and D6-branes intersecting at angles. In addition to the minimal supersymmetric Standard Model particles, the model contains right-handed neutrinos, a chiral (but anomaly-free) set of exotic multiplets, and extra vector-like multiplets. We discuss some phenomenological features of this model.
We review the construction of chiral four-dimensional compactifications of type IIA string theory with intersecting D6-branes. Such models lead to four-dimensional theories with non-abelian gauge interactions and charged chiral fermions. We discuss the application of these techniques to building of models with spectrum as close as possible to the Standard Model, and review their main phenomenological properties. We also emphasize the advantages/disadvantages of carrying out this idea using supersymmetric of non-supersymmetric models.
We provide a pedagogical introduction to a recently studied class of phenomenologically interesting string models, known as Intersecting D-Brane Models. The gauge fields of the Standard-Model are localized on D-branes wrapping certain compact cycles on an underlying geometry, whose intersections can give rise to chiral fermions. We address the basic issues and also provide an overview of the recent activity in this field. This article is intended to serve non-experts with explanations of the fundamental aspects, and also to provide some orientation for both experts and non-experts in this acti…
We consider intersecting M-brane solutions of supergravity in eleven dimensions. Supersymmetry turns out to be a powerful tool in obtaining such solutions and their generalizations.
We compute the Yukawa couplings among chiral fields in toroidal Type II compactifications with wrapping D6-branes intersecting at angles. Those models can yield realistic standard model spectrum living at the intersections. The Yukawa couplings depend both on the Kahler and open string moduli but not on the complex structure. They arise from worldsheet instanton corrections and are found to be given by products of complex Jacobi theta functions with characteristics. The Yukawa couplings for a particular intersecting brane configuration yielding the chiral spectrum of the MSSM are computed as a…
We generalize solutions of Einstein's equations for intersecting branes in higher dimensional spacetimes to the nonstatic case, modeling an expanding universe. The relation between the Hubble rate, the brane tensions, and the bulk cosmological constant is similar to the case of a single 3-brane in a 5-dimensional spacetime. However, because the bulk inflates as well as the branes, this class of solutions suffers from Newton's constant tending toward zero on the TeV brane, where the Randall-Sundrum mechanism should solve the weak scale hierarchy problem. The strength of gravity remains constant…
A candidate supergravity solution of intersecting D7-branes with a five-dimensional intersecting domain (an I5-brane) is presented. This displays an enhanced Poincare symmetry and supersymmetry away from the brane cores. We also explore the possibility of a relation between the intersection region of D7-branes and conifolds through F-theory.
We construct intersecting D5-brane orbifold models that yield the (non-supersymmetric) standard model up to vector-like matter and charged-singlet scalars. The models are constrained by the requirement that twisted tadpoles cancel, and that the gauge boson coupled to the weak hypercharge $U(1)_Y$ does not get a string-scale mass via a generalised Green-Schwarz mechanism. Gauge coupling constant ratios close to those measured are easily obtained for reasonable values of the parameters, consistently with having the string scale close to the electroweak scale, as required to avoid the hierarchy p…
We study the non-linear realization of supersymmetry. We classify all lower dimensional operators, describing effective interactions of the Goldstino with Standard Model fields. Besides a universal coupling to the energy momentum tensor of dimension eight, there are additional model dependent operators whose strength is not determined by non-linear supersymmetry, within the effective field theory. Their dimensionality can be lower than eight, starting with dimension six, leading in general to dominant effects at low energies. We compute their coefficients in string models with D-branes at angl…
A supersymmetric Pati-Salam model with wrapping number equal to 5 has been constructed in Type IIA orientifolds on $\mathbf{T}^6/(\mathbb{Z}_2\times \mathbb{Z}_2)$ with intersecting D6-branes recently. In particular, the string-scale gauge coupling unification can be achieved due to the intermediate-scale vector-like particles from $\mathcal{N}=2$ sector. We calculate the supersymmetry breaking soft terms, and study the Standard Model (SM) fermion masses and mixings. There are nine pairs of Higgs doublets from $\mathcal{N}=2$ sector. Interestingly, we can explain the SM quark masses and mixing…
Intersecting D-brane models provide an attractive explanation of family replication in the context of string theory. We show, however, that the localization of fermion families at different brane intersections in the extra dimensions introduces flavour changing neutral currents mediated by the Kaluza-Klein excitations of the gauge fields. This is a generic feature in these models, and it implies stringent bounds on the mass of the lightest Kaluza-Klein modes (becoming severe when the compactification radii are larger than the string length). We present the full string calculation of four-fermi…
We analyze intersecting brane models on toroidal orbifolds T^4/Z_N(N=3,4,6). Focusing on several Higgsing processes of intersecting brane models, we have some insights into the matter spectrum on intersecting branes away from orientifold planes. The matter fields in the adjoint representations of the gauge group on branes can arise when brane intersects the orientifold images. Gauge group and matter spectrum are confirmed using Chan-Paton methods with the Higgsing processes.
The landscape of string vacua is very large, but generally expected to be finite in size. Enumerating the number and properties of the vacua is an important task for both the landscape and the swampland, in part to gain a deeper understanding of what is possible and "generic". We obtain an exact counting of distinct intersecting brane vacua of type IIA string theory on the $\mathbb{T}^6/\mathbb{Z}_2\times\mathbb{Z}_2$ orientifold. Care is taken to only count gauge-inequivalent brane configurations. Leveraging the recursive nature by which branes may be added together one-by-one, we use dynamic…
Discrete gauge symmetries in global intersecting D-brane models constrain the exact form of the perturbative as well as non-perturbative superpotential. We derive the complete set of conditions on the existence of discrete Zn gauge symmetries on toroidal orbifolds, T6/Z(N) and T6/Z(2)xZ(2M}, with fractional or rigid D6-branes on tilted tori, for which global models of particle physics are known. Several examples of global left-right symmetric and Pati-Salam models are presented. Some discrete `stringy' Zn symmetries are trivial from the field theory point of view, while others have not been id…
We discuss tree level three and four point scattering amplitudes in type II string models with matter fields localized at the intersections of D-brane wrapping cycles. Using conformal field theory techniques we calculate the four fermion amplitudes. These give "contact" interactions that can lead to flavour changing effects. We show how in the field theory limit the amplitudes can be interpreted as the exchange of Kaluza-Klein excitations, string oscillator states and stretched heavy string modes.
We study flavour issues in nonsupersymmetric intersecting brane models. Specifically, the purpose of the present paper is twofold: (i) to determine whether realistic flavour structures can be obtained in these models, and (ii) to establish whether the non-supersymmetric models address the gauge hierarchy problem. To this end, we find that realistic flavour structures, although absent at tree level, can arise even in the simplest models after effects of 4 fermion instanton--induced operators and radiative corrections have been taken into account. On the other hand, our analysis of flavour chang…
We construct the effective theory of intersecting branes and investigate the BPS monopoles in the theory. The monopoles obtained are the generalization of Nielsen-Olesen vortex. We study the properties of the solutions and interpret them as the D0-branes on the brane-intersections.
We analyze the perturbative stability of non-supersymmetric intersecting brane world models on tori. Besides the dilaton tadpole, a dynamical instability in the complex structure moduli space occurs at string disc level, which drives the background geometry to a degenerate limit. We show that in certain orbifold models this latter instability is absent as the relevant moduli are frozen. We construct explicit examples of such orbifold intersecting brane world models and discuss the phenomenological implications of a three generation Standard Model which descends naturally from an SU(5) GUT theo…
A model considered in the paper generalizes supergravity type model to the case of delocalized membrane sources. A generalization of intersecting p-brane solution with delocalized membranes is presented.
Intersecting D-brane models in string theory can naturally support the gauge and matter content of left-right symmetric extensions of the Standard Model with gauge symmetry SU(3)_c x SU(2)_L x SU(2)_R x U(1)_{B-L}. Considering such models as candidates for explaining the 2TeV excesses seen in Run-1 by both ATLAS and CMS, the minimal possible scale of supersymmetry breaking is determined by the requirement of precise one-loop gauge coupling unification. For the vector-like, bifundamental and (anti-)symmetric Higgs content of such brane configurations, this comes out fairly universally at around…
We construct intersecting D-branes as noncommutative solitons in bosonic and type II string theory. ``Defect'' branes which are D-branes containing bubbles of the closed string vacuum play an important role in the construction.
We identify configurations of intersecting branes that correspond to the meta-stable supersymmetry breaking vacua in the four-dimensional N=1 supersymmetric Yang-Mills theory coupled to massive flavors. We show how their energies, the stability properties, and the decay processes are described geometrically in terms of the brane configurations.
We present non-extreme generalisations of intersecting p-brane solutions of eleven-dimensional supergravity which upon toroidal compactification reduce to non-extreme static black holes in dimensions D=4, D=5 and 5<D<10, parameterized by four, three and two charges, respectively. The D=4 black holes are obtained either from non-extreme configuration of three intersecting five-branes with a boost along the common string or from non-extreme intersecting system of two two-branes and two five-branes. The D=5 black holes arise from three intersecting two-branes or from a system of intersecting two-…
We continue with the analysis of finite temperature corrections to the Tachyon mass in intersecting branes which was initiated in arxiv:1403.0389. In this paper we extend the computation to the case of intersecting D3-branes by considering a setup of two intersecting branes in flat-space background. A holographic model dual to BCS superconductor consisting of intersecting D8-branes in D4-brane background was proposed in arxiv:1104.2843. The background considered here is a simplified configuration of this dual model. We compute the one-loop Tachyon amplitude in the Yang-Mills approximation and …
We study supersymmetric intersecting configurations of D-branes with B-field backgrounds. Noncommutative D-brane or M-brane pairs can intersect supersymmetrically over (p-1)-brane, as well as over (p-2)-brane like ordinary branes. d=10 and d=11 supergravity solutions are obtained and the supersymmetry projection rule is examined. As an application we study a noncommutative D7-brane probe in noncommutative D3-brane background, intersecting at noncommutative plane, which describes BPS baryons of noncommutative gauge theory in the context of AdS/CFT correspondence.
We analyze six-dimensional supergravity theories coming from intersecting brane models on the toroidal orbifold T^4/Z_2. We use recently developed tools for mapping general 6D supergravity theories to F-theory to identify F-theory constructions dual to the intersecting brane models. The F-theory picture illuminates several aspects of these models. In particular, we have some new insight into the matter spectrum on intersecting branes, and analyze gauge group enhancement as branes approach orbifold points. These novel features of intersecting brane models are also relevant in four dimensions, a…
We discuss the phenomenology of a toy intersecting brane model where supersymmetry is dynamically broken in an open string hidden sector and gauge-mediated to the visible sector. Scalar masses ~ TeV are easily realizable, and R-symmetry is broken. These ideas are easily generalizable to other intersecting brane models.
We present two 1/8 supersymmetric intersecting p-brane solutions of 11-dimensional supergravity which upon compactification to four dimensions reduce to extremal dyonic black holes with finite area of horizon. The first solution is a configuration of three intersecting 5-branes with an extra momentum flow along the common string. The second describes a system of two 2-branes and two 5-branes. Related (by compactification and T-duality) solution of type IIB theory corresponds to a completely symmetric configuration of four intersecting 3-branes. We suggest methods for counting the BPS degenerac…
We discuss the application of general features of intersecting brane model constructions in cosmology. In particular, we describe a scenario for D-term inflation which arises straightforwardly in IBM constructions wherein open non-vectorlike strings play the role of the inflaton. We also show that baryogenesis driven by hidden sector mixed anomalies can naturally arise in intersecting brane models.
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…
BPS configurations of intersecting branes have many applications in string theory. We attempt to provide an introductory and pedagogical review of supergravity solutions corresponding to orthogonal BPS intersections of branes with an emphasis on eleven and ten space-time dimensions. Recent work on BPS solutions corresponding to non-orthogonally intersecting branes is also discussed. These notes are based on lectures given at the APCTP Winter School "Dualities of Gauge and String Theories", Korea, February 1997.
We construct a model describing BPS brane-systems using low energy effective theory of brane-antibrane system. Both parallel branes and intersecting branes can be treated by this model. After tachyon condensation, the dynamics of fluctuations around such brane-systems is supersymmetric if the degrees of freedom are restricted on the branes. The form of the tachyon potential and the application of this model to the black hole physics are discussed.
We give general intersecting brane solutions without assuming any restriction on the metric in supergravity coupled to a dilaton and antisymmetric tensor fields in arbitrary dimensions $D$. The result is a general class of intersecting brane solutions which interpolate the non-extreme solutions of type 1 and 2. We also discuss the relation of our solutions to the known single brane solution.
We find all possible static embeddings of a 4-brane in any dimension-6 spacetime with 4-dimensional Poincare symmetry and a negative cosmological constant, subject to orbifolding across the brane. Our new solutions allow intersecting branes at an angle determined by a new dynamical parameter. A collection of branes intersecting in one 3-brane allows an arbitrary excess angle that can be related to a vacuum density along the intersection. The 3-brane must be stabilized by additional fine-tuned interactions. We also note that localization of gravity is tied to the approximate fine tuning of the …
