118824196
Heterotic kink solitons and their worldvolume action
A bstractWe present a formalism for computing the higher-order corrections to the worldvolume action of a co-dimension one kink soliton embedded in five-dimensional heterotic M-theory. The geometry of heterotic M-theory, as well as the effective theory which describes a five-brane wrapping a holomorphic curve by a topological kink in a scalar field, is reviewed. Using this formalism, the explicit worldvolume action is computed to second order in two expansion parameters — one describing the “warp” of the heterotic geometry and the second the fluctuation length of the soliton hypersurface. The result is expressed in terms of the trace of the extrinsic curvature and the intrinsic curvature scalar.
118976087
Superbranes and superembeddings
Abstract We review a geometrical approach to the description of the dynamics of superparticles, superstrings and, in general, of super- p -branes, Dirichlet branes and the M5-brane, which is based on a generalization of the elements of surface theory to the description of the embedding of supersurfaces into target superspaces. Being manifestly supersymmetric in both, the superworldvolume of the brane and the target superspace, this approach unifies the Neveu–Schwarz–Ramond and the Green–Schwarz formulation and provides the fermionic κ -symmetry of the Green–Schwarz-type superbrane actions with a clear geometrical meaning of standard worldvolume local supersymmetry. The dynamics of superbranes is encoded in a generic superembedding condition. Depending on the superbrane and the target-space dimension, the superembedding condition produces either only off-shell constraints (as in the case of N =1 superparticles and N =1 superstrings), or also results in the full set of the superbrane equations of motion (as, for example, in the case of the M-theory branes). In the first case worldvolume superspace actions for the superbranes can be constructed, while in the second case only component or generalized superfield actions are known. We describe the properties of the doubly supersymmetric brane actions and show how they are related to the standard Green–Schwarz formulation. In the second part of the article basic geometrical grounds of the (super)embedding approach are considered and applied to the description of the M2-brane and the M5-brane. Various applications of the superembedding approach are reviewed.
1706400
Kappa-symmetric higher-derivative terms in brane actions
Using the superembedding formalism we construct supermembrane actions with higher-derivative terms which can be viewed as possible higher-order terms in effective actions. In particular, we provide the first example of an action for an extended supersymmetric object with fully κ-symmetric extrinsic curvature terms.
10613835
Open string gravity
We present a new application of Boundary String Field Theory: calculating the induced-gravity action on a D-brane. Using a simple quadratic tachyon potential to model a D-brane fluctuating in the flat target space we derive the effective action in terms of the extrinsic curvature to all orders in α'. We identify both the Born-Infeld structure as well as the Einstein-Hilbert term at order α'. This corroborates the conjectured existence of the latter term in the brane-world scenarios.
118399104
The supermultiplet of boundary conditions in supergravity
Boundary conditions in supergravity on a manifold with boundary relate the bulk gravitino to the boundary supercurrent, and the normal derivative of the bulk metric to the boundary energy-momentum tensor. In the 3D N = 1 setting, we show that these boundary conditions can be stated in a manifestly supersymmetric form. We identify the Extrinsic Curvature Tensor Multiplet, and show that boundary conditions set it equal to (a conjugate of) the boundary supercurrent multiplet. Extension of our results to higher-dimensional models (including the Randall-Sundrum and Horava-Witten scenarios) is discussed.
119237669
Dynamics of the infinitely-thin kink
Abstract We consider the dynamics of the domain-wall kink soliton, in particular we study the zero mode of translation. In the infinitely-thin kink limit, we show that the zero mode is almost completely frozen out, the only remnant being a dynamically constrained four-dimensional mode of a single but arbitrary frequency. In relation to this result, we show that the usual mode expansion for dealing with zero modes – implicit collective coordinates – is not in fact a completely general expansion, and that one must use instead a traditional generalised Fourier analysis.
35869443
Effective actions for bosonic topological defects.
We consider a gauge field theory which admits {ital p}-dimensional topological defects, expanding the equations of motion in powers of the defect thickness. In this way we derive an effective action and effective equation of motion for the defect in terms of the coordinates of the {ital p}-dimensional world surface defined by the history of the core of the defect.
394473
Curvature corrections to dynamics of domain walls.
The most usual procedure for deriving curvature corrections to effective actions for topological defects is subjected to a critical reappraisal. A logically unjustified step (leading to overdetermination) is identified and rectified, taking the standard domain wall case as an illustrative example. Using the appropriately corrected procedure, we obtain a new exact (analytic) expression for the corresponding effective action contribution of quadratic order in the wall width, in terms of the intrinsic Ricci scalar $R$ and the extrinsic curvature scalar $K$. The result is proportional to $cK^2-R$ with the coefficient given by $c\simeq 2$. The resulting form of the ensuing dynamical equations is obtained in terms of the second fundamental form and the Dalembertian of its trace, K. It is argued that this does not invalidate the physical conclusions obtained from the "zero rigidity" ansatz $c=0$ used in previous work.
119181269
The worldvolume action of kink solitons in AdS spacetime
A bstractA formalism is presented for computing the higher-order corrections to the worldvolume action of co-dimension one solitons. By modifying its potential, an explicit “kink” solution of a real scalar field in AdS spacetime is found. The formalism is then applied to explicitly compute the kink worldvolume action to quadratic order in two expansion parameters-associated with the hypersurface fluctuation length and the radius of AdS spacetime respectively. Two alternative methods are given for doing this. The results are expressed in terms of the trace of the extrinsic curvature and the intrinsic scalar curvature. In addition to conformal Galileon interactions, we find a non-Galileon term which is never sub-dominant. This method can be extended to any conformally flat bulk spacetime.
18168398
Galileon as a local modification of gravity
In the Dvali-Gabadadze-Porrati (DGP) model, the "self-accelerating" solution is plagued by a ghost instability, which makes the solution untenable. This fact, as well as all interesting departures from general relativity (GR), are fully captured by a four-dimensional effective Lagrangian, valid at distances smaller than the present Hubble scale. The 4D effective theory involves a relativistic scalar pi, universally coupled to matter and with peculiar derivative self-interactions. In this paper, we study the connection between self-acceleration and the presence of ghosts for a quite generic class of theories that modify gravity in the infrared. These theories are defined as those that at distances shorter than cosmological, reduce to a certain generalization of the DGP 4D effective theory. We argue that for infrared modifications of GR locally due to a universally coupled scalar, our generalization is the only one that allows for a robust implementation of the Vainshtein effect-the decoupling of the scalar from matter in gravitationally bound systems-necessary to recover agreement with solar-system tests. Our generalization involves an internal Galilean invariance, under which pi's gradient shifts by a constant. This symmetry constrains the structure of the pi Lagrangian so much so that in 4D there exist only five terms that can yield sizable nonlinearities without introducing ghosts. We show that for such theories in fact there are "self-accelerating" de Sitter solutions with no ghostlike instabilities. In the presence of compact sources, these solutions can support spherically symmetric, Vainshtein-like nonlinear perturbations that are also stable against small fluctuations. We investigate a possible infrared completion of these theories at scales of order of the Hubble horizon, and larger. There are however some features of our theories that may constitute a problem at the theoretical or phenomenological level: the presence of superluminal excitations; the extreme subluminality of other excitations, which makes the quasistatic approximation for certain solar-system observables unreliable due to Cherenkov emission; the very low strong-interaction scale for pi pi scatterings.
119113396
Generalizing Galileons
The Galileons are a set of terms within four-dimensional effective field theories, obeying symmetries that can be derived from the dynamics of a 3 + 1-dimensional flat brane embedded in a 5-dimensional Minkowski Bulk. These theories have some intriguing properties, including freedom from ghosts and a nonrenormalization theorem that hints at possible applications in both particle physics and cosmology. In this brief review article, we will summarize our attempts over the last year to extend the Galileon idea in two important ways. We will discuss the effective field theory construction arising from co-dimension greater than one flat branes embedded in a flat background the multiGalileons and we will then describe symmetric covariant versions of the Galileons, more suitable for general cosmological applications. While all these Galileons can be thought of as interesting four-dimensional field theories in their own rights, the work described here may also make it easier to embed them into string theory, with its multiple extra dimensions and more general gravitational backgrounds. Generalizing Galileons 2
17061129
Supersymmetric Galileons
Galileon theories are of considerable interest since they allow for stable violations of the null energy condition. Since such violations could have occurred during a highenergy regime in the history of our universe, we are motivated to study supersymmetric extensions of these theories. This is carried out in this paper, where we construct generic classes of N = 1 supersymmetric Galileon Lagrangians. They are shown to admit non-equivalent stress-energy tensors and, hence, vacua manifesting differing conditions for violating the null energy condition. The temporal and spatial fluctuations of all component fields of the supermultiplet are analyzed and shown to be stable on a large number of such backgrounds. In the process, we uncover a surprising connection between conformal Galileon and ghost condensate theories, allowing for a deeper understanding of both types of theories.
119236957
Derrick’s theorem beyond a potential
Scalar field theories with derivative interactions are known to possess solitonic excitations, but such solitons are generally unsatisfactory because the effective theory fails precisely where nonlinearities responsible for the solitons are important. A new class of theories possessing (internal) galilean invariance can in principle bypass this difficulty. Here, we show that these galileon theories do not possess stable solitonic solutions. As a by-product, we show that no stable solitons exist for a different class of derivatively coupled theories, describing for instance the infrared dynamics of superfluids, fluids, solids and some k-essence models.
118627727
DBI and the Galileon reunited
We derive the relativistic generalization of the Galileon, by studying the brane position modulus of a relativistic probe brane embedded in a five- dimensional bulk. In the appropriate Galilean contraction limit, we recover the complete Galileon generalization of the DGP decoupling theory and its conformal extension. All higher order interactions for the Galileon and its relativistic generalization naturally follow from the brane tension, induced curvature, and the Gibbons-Hawking-York boundary terms associated with all bulk Lovelock invariants. Our approach makes the coupling to gravity straightforward, in particular allowing a simple rederivation of the nonmini- mal couplings required by the Covariant Galileon. The connection with the Lovelock invariants makes the well-defined Cauchy problem manifest, and gives a natural unification of four dimensional effective field theories of the DBI type and the Galileon type.
11430554
Multifield Galileons and higher codimension branes
In the decoupling limit, the Dvali-Gabadadze-Porrati model reduces to the theory of a scalar field $\ensuremath{\pi}$, with interactions including a specific cubic self-interaction---the Galileon term. This term, and its quartic and quintic generalizations, can be thought of as arising from a probe 3-brane in a five-dimensional bulk with Lovelock terms on the brane and in the bulk. We study multifield generalizations of the Galileon and extend this probe-brane view to higher codimensions. We derive an extremely restrictive theory of multiple Galileon fields, interacting through a quartic term controlled by a single coupling, and trace its origin to the induced brane terms coming from Lovelock invariants in the higher codimension bulk. We explore some properties of this theory, finding de Sitter like self-accelerating solutions. These solutions have ghosts if and only if the flat space theory does not have ghosts. Finally, we prove a general nonrenormalization theorem: multifield Galileons are not renormalized quantum mechanically to any loop in perturbation theory.
17301596
Stability and superluminality of spherical DBI Galileon solutions
The Dirac-Born-Infeld (DBI) Galileons are a generalization of the Galileon terms, which extend the internal Galilean symmetry to an internal relativistic symmetry, and can also be thought of as generalizations of DBI which yield second order field equations. We show that, when considered as local modifications to gravity, such as in the Solar System, there exists a region of parameter space in which spherically symmetric static solutions exist and are stable. However, these solutions always exhibit superluminality, casting doubt on the existence of a standard Lorentz invariant UV completion.
117031129
Lectures on Supergravity p-branes
We review the properties of classical p-brane solutions to supergravity theories, i.e. solutions that may be interpreted as Poincare-invariant hyperplanes in spacetime. Topics covered include the distinction between elementary/electric and solitonic/magnetic solutions, examples of singularity and global structure, relations between mass densities, charge densities and the preservation of unbroken supersymmetry, diagonal and vertical Kaluza-Klein reduction families, Scherk-Schwarz reduction and domain walls, and the classification of multiplicities using duality symmetries.
16122181
Eleven-dimensional supergravity on a manifold with boundary
Abstract In this paper, we present a systematic analysis of eleven-dimensional supergravity on a manifold with boundary, which is believed to be relevant to the strong coupling limit of the E 8 × E 8 heterotic string. Gauge and gravitational anomalies enter at a very early stage, and require a refinement of the standard Green-Schwarz mechanism for their cancellation. This uniquely determines the gauge group to be a copy of E 8 for each boundary component, fixes the gauge coupling constant in terms of the gravitational constant, and leads to several striking new tests of the hypothesis that there is a consistent quantum M -theory with eleven-dimensional supergravity as its low-energy limit.
5092777
The Universe as a domain wall
It is shown that the effective five-dimensional theory of the strongly coupled heterotic string is a gauged version of N=1 five-dimensional supergravity with four-dimensional boundaries. For the universal supermultiplets, this theory is explicitly constructed by a generalized dimensional reduction procedure on a Calabi-Yau manifold. A crucial ingredient in the reduction is the retention of a {open_quotes}non-zero mode{close_quotes} of the four-form field strength, leading to the gauging of the universal hypermultiplet by the graviphoton. We show that this theory has an exact three-brane domain wall solution which reduces to Witten{close_quote}s {open_quotes}deformed{close_quotes} Calabi-Yau background upon linearization. This solution consists of two parallel three-branes with sources provided by the four-dimensional boundary theories and constitutes the appropriate background for a reduction to four dimensions. Four-dimensional space-time is then identified with the three-brane world volume. {copyright} {ital 1999} {ital The American Physical Society}
8652477
Heterotic M-theory in five dimensions
Abstract We derive the five-dimensional effective action of strongly coupled heterotic string theory for the complete (1,1) sector of the theory by performing a reduction, on a Calabi-Yau three-fold, of M-theory on S 1 / Z 2 . A crucial ingredient for a consistent truncation is a non-zero-mode of the antisymmetric tensor field strength which arises due to magnetic sources on the orbifold planes. The correct effective theory is a gauged version of five-dimensional N = 1 supergravity coupled to Abelian vector multiplets, the universal hypermultiplet and four-dimensional boundary theories with gauge and gauge matter fields, The gauging is such that the dual of the four-form field strength in the universal multiplet is charged under a particular linear combination of the Abelian vector fields. In addition, the theory has potential terms for the moduli in the bulk as well as on the boundary. Because of these potential terms, the supersymmetric ground state of the theory is a multi-charged BPS three-brane domain wall, which we construct in general. We show that the five-dimensional theory together with this solution provides the correct starting point for particle phenomenology as well as early universe cosmology. As an application, we compute the four-dimensional N = 1 supergravity theory for the complete (1, 1) sector to leading non-trivial order by a reduction on the domain wall background. We find a correction to the matter field Kahler potential and threshold corrections to the gauge kinetic functions.
6936494
Moduli Spaces of Fivebranes on Elliptic Calabi-Yau Threefolds
We present a general method for calculating the classical moduli spaces of fivebranes wrapped on holomorphic curves in elliptically fibered Calabi-Yau threefolds, in particular, in the context of heterotic M-theory. The cases of fivebranes wrapped purely on a fiber curve, purely on a curve in the base and, generically, on a curve with components both in the fiber and the base are each discussed in detail. The number of irreducible components of the fivebrane and their properties, such as their intersections and phase transitions in moduli space, follow from the analysis. Even though generic curves have a large number of moduli, we show that there are isolated curves that have no moduli associated with the Calabi-Yau threefold. We present several explicit examples, including cases which correspond to potentially realistic three family models with grand unified gauge group SU(5).
10994662
Non-perturbative vacua and particle physics in M-theory
In this letter, we introduce a general theory for the construction of particle physics theories, with three families and realistic gauge groups, within the context of heterotic M-theory. This is achieved using semi-stable holomorphic gauge bundles over elliptically fibered Calabi-Yau three-folds. Construction of realistic theories is facilitated by the appearance of non-perturbative five-branes in the vacuum. The complete moduli space of these five-branes is computed and their worldvolume gauge theory discussed. In the context of holomorphic gauge bundles, it is shown how grand unified gauge groups can be spontaneously broken to the gauge group of the standard model. These ideas are illustrated in an explicit SU(5) three-family example.
8626513
Holomorphic vector bundles and non-perturbative vacua in M-theory
We review the spectral cover formalism for constructing both U(n) and SU(n) holomorphic vector bundles on elliptically fibered Calabi-Yau three-folds which admit a section. We discuss the allowed bases of these three-folds and show that physical constraints eliminate Enriques surfaces from consideration. Relevant properties of the remaining del Pezzo and Hirzebruch surfaces are presented. Restricting the structure group to SU(n), we derive, in detail, a set of rules for the construction of three-family particle physics theories with phenomenologically relevant gauge groups. We show that anomaly cancellation generically requires the existence of non-perturbative vacua containing five-branes. We illustrate these ideas by constructing four explicit three-family non-perturbative vacua.
20900201
Vector Bundle Moduli and Small Instanton Transitions
We give the general presciption for calculating the moduli of irreducible, stable SU(n) holomorphic vector bundles with positive spectral covers over elliptically fibered Calabi-Yau threefolds. Explicit results are presented for Hirzebruch base surfaces B = r. The transition moduli that are produced by chirality changing small instanton phase transitions are defined and specifically enumerated. The origin of these moduli, as the deformations of the spectral cover restricted to the ``lift'' of the horizontal curve of the M5-brane, is discussed. We present an alternative description of the transition moduli as the sections of rank n holomorphic vector bundles over the M5-brane curve and give explicit examples. Vector bundle moduli appear as gauge singlet scalar fields in the effective low-energy actions of heterotic superstrings and heterotic M-theory.
8248466
Standard-M odelBundles on N on-Sim ply Connected Calabi{Yau Threefolds
A bstract:W egiveaproofoftheexistenceofG = SU (5),stableholom orphicvectorbundles on elliptically bered Calabi{Yau threefolds with fundam entalgroup Z 2. The bundles we construct have Euler characteristic 3 and an anom aly that can be absorbed by M -theory ve-branes.Such bundlesprovide the basisforconstructing the standard m odelin heterotic M -theory. They are also applicable to vacua ofthe weakly coupled heterotic string. W e explicitly presenta classofthreefam ily m odelswith gaugegroup SU (3)C SU (2)L U (1)Y .
14089156
Standard-model bundles
We describe a family of genus one fibered Calabi-Yau threefolds with fundamental group Z/2. On each Calabi-Yau Z in the family we exhibit a positive dimensional family of Mumford stable bundles whose symmetry group is the Standard Model group SU(3) × SU(2) × U(1) and which have c3 = 6. We also show that for each bundle V in our family, c2(Z) − c2(V ) is the class of an effective curve on Z. These conditions ensure that Z and V can be used for a phenomenologically relevant compactification of Heterotic M-theory. MSC 2000: 14D21, 14J32
55757695
Exploring positive monad bundles and a new heterotic standard model
A complete analysis of all heterotic Calabi-Yau compactifications based on positive two-term monad bundles over favourable complete intersection Calabi-Yau threefolds is performed. We show that the original data set of about 7000 models contains 91 standard-like models which we describe in detail. A closer analysis of Wilson-line breaking for these models reveals that none of them gives rise to precisely the matter field content of the standard model. We conclude that the entire set of positive two-term monads on complete intersection Calabi-Yau manifolds is ruled out on phenomenological grounds. We also take a first step in analyzing the larger class of non-positive monads. In particular, we construct a supersymmetric heterotic standard model within this class. This model has the standard model gauge group and an additional U(1)B−L symmetry, precisely three families of quarks and leptons, one pair of Higgs doublets and no anti-families or exotics of any kind.
16952322
Vector bundle extensions, sheaf cohomology, and the heterotic standard model
Stable, holomorphic vector bundles are constructed on an torus fibered, non-simply connected Calabi-Yau threefold using the method of bundle extensions. Since the manifold is multiply connected, we work with equivariant bundles on the elliptically fibered covering space. The cohomology groups of the vector bundle, which yield the low energy spectrum, are computed using the Leray spectral sequence and fit the requirements of particle phenomenology. The physical properties of these vacua were discussed previously. In this paper, we systematically compute all relevant cohomology groups and explicitly prove the existence of the necessary vector bundle extensions. All mathematical details are explained in a pedagogical way, providing the technical framework for constructing heterotic standard model vacua.
14899052
Kinky brane worlds
We present a toy model for five-dimensional heterotic M theory where bulk three-branes, originating in 11 dimensions from M five-branes, are modeled as kink solutions of a bulk scalar field theory. It is shown that the vacua of this defect model correspond to a class of topologically distinct M-theory compactifications. Topology change can then be analyzed by studying the time evolution of the defect model. In the context of a four-dimensional effective theory, we study in detail the simplest such process, that is, the time evolution of a kink and its collision with a boundary. We find that the kink is generically absorbed by the boundary thereby changing the boundary charge. This opens up the possibility of exploring the relation between more complicated defect configurations and the topology of brane-world models.