Showing papers in "Physical Review D in 1997"

M theory as a matrix model: A conjecture

Abstract: We suggest and motivate a precise equivalence between uncompactified 11-dimensional $M$ theory and the $N=\ensuremath{\infty}$ limit of the supersymmetric matrix quantum mechanics describing $D0$ branes. The evidence for the conjecture consists of several correspondences between the two theories. As a consequence of supersymmetry the simple matrix model is rich enough to describe the properties of the entire Fock space of massless well separated particles of the supergravity theory. In one particular kinematic situation the leading large distance interaction of these particles is exactly described by supergravity. The model appears to be a nonperturbative realization of the holographic principle. The membrane states required by $M$ theory are contained as excitations of the matrix model. The membrane world volume is a noncommutative geometry embedded in a noncommutative spacetime.

Towards the theory of reheating after inflation

Abstract: Reheating after inflation occurs due to particle production by the oscillating inflaton field. In this paper we briefly describe the perturbative approach to reheating, and then concentrate on effects beyond the perturbation theory. They are related to the stage of parametric resonance, which we call preheating. It may occur in an expanding universe if the initial amplitude of oscillations of the inflaton field is large enough. We investigate a simple model of a massive inflaton field $\ensuremath{\varphi}$ coupled to another scalar field $\ensuremath{\chi}$ with the interaction term ${g}^{2}{\ensuremath{\varphi}}^{2}{\ensuremath{\chi}}^{2}$. Parametric resonance in this model is very broad. It occurs in a very unusual stochastic manner, which is quite different from parametric resonance in the case when the expansion of the universe is neglected. Quantum fields interacting with the oscillating inflaton field experience a series of kicks which, because of the rapid expansion of the universe, occur with phases uncorrelated to each other. Despite the stochastic nature of the process, it leads to exponential growth of fluctuations of the field $\ensuremath{\chi}$. We call this process stochastic resonance. We develop the theory of preheating taking into account the expansion of the universe and back reaction of produced particles, including the effects of rescattering. This investigation extends our previous study of reheating after inflation. We show that the contribution of the produced particles to the effective potential $V(\ensuremath{\varphi})$ is proportional not to ${\ensuremath{\varphi}}^{2}$, as is usually the case, but to $|\ensuremath{\varphi}|$. The process of preheating can be divided into several distinct stages. In the first stage the back reaction of created particles is not important. In the second stage back reaction increases the frequency of oscillations of the inflaton field, which makes the process even more efficient than before. Then the effects related to scattering of $\ensuremath{\chi}$ particles on the oscillating inflaton field terminate the resonance. We calculate the number density of particles ${n}_{\ensuremath{\chi}}$ produced during preheating and their quantum fluctuations $〈{\ensuremath{\chi}}^{2}〉$ with all back reaction effects taken into account. This allows us to find the range of masses and coupling constants for which one can have efficient preheating. In particular, under certain conditions this process may produce particles with a mass much greater than the mass of the inflaton field.

$CPT$ violation and the standard model

Abstract: Spontaneous $\mathrm{CPT}$ breaking arising in string theory has been suggested as a possible observable experimental signature in neutral-meson systems. We provide a theoretical framework for the treatment of low-energy effects of spontaneous $\mathrm{CPT}$ violation and the attendant partial Lorentz breaking. The analysis is within the context of conventional relativistic quantum mechanics and quantum field theory in four dimensions. We use the framework to develop a $\mathrm{CPT}$-violating extension to the minimal standard model that could serve as a basis for establishing quantitative $\mathrm{CPT}$ bounds.

An all sky analysis of polarization in the microwave background

Abstract: Using the formalism of spin-weighted functions we present an all-sky analysis of polarization in the cosmic microwave background (CMB). Linear polarization is a second-rank symmetric and traceless tensor, which can be decomposed on a sphere into spin $\ifmmode\pm\else\textpm\fi{}2$ spherical harmonics. These are the analogues of the spherical harmonics used in the temperature maps and obey the same completeness and orthogonality relations. We show that there exist two linear combinations of spin $\ifmmode\pm\else\textpm\fi{}2$ multipole moments which have opposite parities and can be used to fully characterize the statistical properties of polarization in the CMB. Magnetic-type parity combination does not receive contributions from scalar modes and does not cross correlate with either temperature or electric-type parity combination, so there are four different power spectra that fully characterize statistical properties of CMB. We present their explicit expressions for scalar and tensor modes in the form of line of sight integral solution and numerically evaluate them for a representative set of models. These general solutions differ from the expressions obtained previously in the small scale limit both for scalar and tensor modes. A method to generate and analyze all-sky maps of temperature and polarization is given and the optimal estimators for various power spectra and their corresponding variances are discussed.

Statistics of cosmic microwave background polarization

Abstract: We present a formalism for analyzing a full-sky temperature and polarization map of the cosmic microwave background. Temperature maps are analyzed by expanding over the set of spherical harmonics to give multipole moments of the two-point correlation function. Polarization, which is described by a second-rank tensor, can be treated analogously by expanding in the appropriate tensor spherical harmonics. We provide expressions for the complete set of temperature and polarization multipole moments for scalar and tensor metric perturbations. Four sets of multipole moments completely describe isotropic temperature and polarization correlations; for scalar metric perturbations one set is identically zero, giving the possibility of a clean determination of the vector and tensor contributions. The variance with which the multipole moments can be measured in idealized experiments is evaluated, including the effects of detector noise, sky coverage, and beam width. Finally, we construct coordinate-independent polarization two-point correlation functions, express them in terms of the multipole moments, and derive small-angle limits.

Deeply Virtual Compton Scattering

Abstract: We study in QCD the physics of deeply virtual Compton scattering (DVCS){emdash}the virtual Compton process in the large s and small t kinematic region. We show that DVCS can probe a new type of {ital off-forward} parton distributions. We derive an Altarelli-Parisi-type of evolution equations for these distributions. We also derive their sum rules in terms of nucleon form factors of the twist-two quark and gluon operators. In particular, we find that the second sum rule is related to fractions of the nucleon spin carried separately by quarks and gluons. We estimate the cross section for DVCS and compare it with the accompanying Bethe-Heitler process at CEBAF and HERMES kinematics. {copyright} {ital 1997} {ital The American Physical Society}

Nongaussian Isocurvature Perturbations from Inflation

Abstract: We present a class of very simple inflationary models of two scalar fields which leads to non-Gaussian isothermal perturbations with a ``blue'' spectrum, $ng1.$ One of the models is inspired by supersymmetric theories where light scalar fields naturally acquire masses $\ensuremath{\sim}H$ during inflation. Another model presumes that one of the fields has a nonminimal interaction with gravity $\ensuremath{\xi}R{\ensuremath{\sigma}}^{2}.$ By a slight modification of parameters of these models one can obtain either Gaussian isothermal perturbations, or non-Gaussian adiabatic perturbations with $ng1.$

Nonforward parton distributions

Abstract: Applications of perturbative QCD to deeply virtual Compton scattering and hard exclusive electroproduction processes require a generalization of usual parton distributions for the case when long-distance information is accumulated in nonforward matrix elements of quark and gluon light-cone operators. They describe two types of nonperturbative functions parameterizing such matrix elements: double distributions F(x,y;t) and nonforward distribution functions F{_}/zeta (X;t), discuss their spectral properties, evolution equations which they satisfy, basic uses and general aspects of factorization for hard exclusive processes.

Neutralino relic density including coannihilations

Abstract: We evaluate the relic density of the lightest neutralino, the lightest supersymmetric particle, in the minimal supersymmetric extension of the standard model. For the first time, we include all coannihilation processes between neutralinos and charginos for any neutralino mass and composition. We use the most sophisticated routines for integrating the cross sections and the Boltzmann equation. We properly treat (sub)threshold and resonant annihilations. We also include one-loop corrections to neutralino masses. We find that coannihilation processes are important not only for light Higgsino-like neutralinos, as pointed out before, but also for heavy Higgsinos and for mixed and gauginolike neutralinos. Indeed, coannihilations should be included whenever {vert_bar}{mu}{vert_bar}{approx_lt}2{vert_bar}M{sub 1}{vert_bar}, independently of the neutralino composition. When {vert_bar}{mu}{vert_bar}{approximately}{vert_bar}M{sub 1}{vert_bar}, coannihilations can increase or decrease the relic density in and out of the cosmologically interesting region. We find that there is still a window of light Higgsino-like neutralinos that are viable dark matter candidates and that coannihilations shift the cosmological upper bound on the neutralino mass from 3 to 7 TeV. {copyright} {ital 1997} {ital The American Physical Society}

Correspondence principle for black holes and strings

Abstract: For most black holes in string theory, the Schwarzschild radius in string units decreases as the string coupling is reduced. We formulate a correspondence principle, which states that (i) when the size of the horizon drops below the size of a string, the typical black hole state becomes a typical state of strings and D-branes with the same charges, and (ii) the mass does not change abruptly during the transition. This provides a statistical interpretation of black hole entropy. This approach does not yield the numerical coefficient, but gives the correct dependence on mass and charge in a wide range of cases, including neutral black holes. {copyright} {ital 1997} {ital The American Physical Society}

CP violation and baryogenesis due to heavy Majorana neutrinos

Abstract: We analyze the scenario of baryogenesis through leptogenesis induced by the out-of-equilibrium decays of heavy Majorana neutrinos and pay special attention to $\mathrm{CP}$ violation. Extending a recently proposed resummation formalism for two-fermion mixing to decay amplitudes, we calculate the resonant phenomenon of $\mathrm{CP}$ violation due to the mixing of two nearly degenerate heavy Majorana neutrinos. Solving numerically the relevant Boltzmann equations, we find that the isosinglet Majorana mass may range from 1 TeV up to the grand unification scale, depending on the mechanism of $\mathrm{CP}$ violation and/or the flavor structure of the neutrino mass matrix assumed. Finite temperature effects and possible constraints from the electric dipole moment of electron and other low-energy experiments are briefly discussed.

Intrinsic glue distribution at very small x

Abstract: We compute the distribution functions for gluons at very small x and not too large values of transverse momenta. We extend the McLerran-Venugopalan model by using renormalization group methods to integrate out effects due to those gluons which generate an effective classical charge density for Weizs{umlt a}cker-Williams fields. We argue that this model can be extended from the description of nuclei at small x to the description of hadrons at yet smaller values of x. This generates a Lipatov-like enhancement for the intrinsic gluon distribution function and a nontrivial transverse momentum dependence as well. We estimate the transverse momentum dependence for the distribution functions, and show how the issue of unitarity is resolved in lepton-nucleus interactions. {copyright} {ital 1997} {ital The American Physical Society}

Factorization for hard exclusive electroproduction of mesons in QCD

Abstract: We formulate and prove a QCD factorization theorem for hard exclusive electroproduction of mesons in QCD. The proof is valid for the leading power in Q and all logarithms. This generalizes previous work on vector meson production in the diffractive region of small x. The amplitude is expressed in terms of off-diagonal generalizations of the usual parton densities. The full theorem applies to all kinds of meson and not just to vector mesons. The parton densities used include not only the ordinary parton density, but also ! ,

Improved parton distributions from global analysis of recent deep inelastic scattering and inclusive jet data

Abstract: The impact of recent precision measurements of DIS structure functions and inclusive jet production at the Fermilab Tevatron on the global QCD analysis of parton distribution functions is studied in detail. Particular emphasis is placed on exploring the range of variation of the gluon distribution $G(x,Q)$ allowed by these new data. The strong coupling of $G(x,Q)$ with ${\ensuremath{\alpha}}_{s}$ is fully taken into account. A new generation of CTEQ parton distributions, CTEQ4, is presented. It consists of the three standard sets [modified minimal subtraction $(\overline{\mathrm{MS}})$, deep inelastic scattering (DIS), and leading order (LO)], a series that gives a range of parton distributions with corresponding ${\ensuremath{\alpha}}_{s}$'s, and a set with a low starting value of $Q$. Previously obtained gluon distributions that are consistent with the high ${E}_{t}$ jet cross section are also discussed in the context of this new global analysis.

CDM models with a smooth component

Abstract: The inflationary prediction of a flat Universe is at odds with current determinations of the matter density $({\ensuremath{\Omega}}_{M}\ensuremath{\simeq}0.2\ensuremath{-}0.4).$ This dilemma can be resolved if a smooth component contributes the remaining energy density $({\ensuremath{\Omega}}_{X}=1\ensuremath{-}{\ensuremath{\Omega}}_{M}).$ We parametrize the smooth component by its equation of state, ${p}_{X}=w{\ensuremath{\rho}}_{X},$ and show that $X$CDM with $w\ensuremath{\simeq}\ensuremath{-}0.6,$ ${\ensuremath{\Omega}}_{M}\ensuremath{\simeq}0.3,$ and $h\ensuremath{\simeq}0.7$ is the best fit to all present cosmological data. Together, the position of the peak in the CMB angular power spectrum and the type Ia supernova magnitude-redshift diagram provide a crucial test of $X$CDM.

Precision SUSY measurements at CERN LHC

Abstract: If supersymmetry exists at the electroweak scale, then it should be discovered at the CERN Large Hadron Collider (LHC). Determining masses of supersymmetric particles, however, is more difficult. In this paper, methods are discussed to determine combinations of masses and of branching ratios precisely from experimentally observable distributions. In many cases such measurements alone can greatly constrain the particular supersymmetric model and determine its parameters with an accuracy of a few percent. Most of the results shown correspond to one year of running at LHC at ``low luminosity,'' ${10}^{33}{\mathrm{cm}}^{\mathrm{\ensuremath{-}}2}{\mathrm{s}}^{\mathrm{\ensuremath{-}}1}.$

Phenomenology of forward hadrons in deep inelastic scattering: Fracture functions and its Q 2 evolution

Abstract: We analyze recent data on the production of forward neutrons in deep inelastic scattering at DESY HERA in the framework of a perturbative QCD description for semi-inclusive processes, which includes fracture functions. Using a model estimate for the nonperturbative piece of the fragmentation process, in fairly good agreement with the available data, we analyze the ${Q}^{2}$ dependence of the resulting fracture functions, which is driven by nonhomogeneous evolution equations. We also propose a measurement of the pion production cross section in the target fragmentation region as a new test of perturbative QCD, which in this case predicts also a different ${Q}^{2}$ evolution with respect to the one given by the usual Altarelli-Parisi equations.

Minimal length uncertainty relation and ultraviolet regularization

Abstract: Studies in string theory and quantum gravity suggest the existence of a finite lower limit $\ensuremath{\Delta}{x}_{0}$ to the possible resolution of distances, at the latest on the scale of the Planck length of ${10}^{\ensuremath{-}35}$ m. Within the framework of the Euclidean path integral we explicitly show ultraviolet regularization in field theory through this short distance structure. Both rotation and translation invariance can be preserved. An example is studied in detail.

Black holes with unusual topology

Abstract: Einstein's equations with a negative cosmological constant admit solutions which are asymptotically anti\char21{}de Sitter space. Matter fields in anti\char21{}de Sitter space can be in stable equilibrium even if the potential energy is unbounded from below, violating the weak energy condition. Hence there is no fundamental reason that black hole horizons should have a spherical topology. In anti\char21{}de Sitter space Einstein's equations admit black hole solutions where the horizon can be a Riemann surface with genus $g.$ The case $g=0$ is the asymptotically anti\char21{}de Sitter black hole first studied by Hawking and Page, which has a spherical topology. The genus one black hole has a new free parameter entering the metric, the conformal class to which the torus belongs. The genus $gg1$ black hole has no other free parameters apart from the mass and the charge. All such black holes exhibit a natural temperature which is identified as the period of the Euclidean continuation and there is a mass formula connecting the mass with the surface gravity and the horizon area of the black hole. The Euclidean action and entropy are computed and used to argue that the mass spectrum of states is positive definite.

Black hole greybody factors and D-brane spectroscopy

Abstract: Black holes do not Hawking-radiate strictly blackbody radiation due to well-known frequency-dependent greybody factors. These factors arise from frequency-dependent potential barriers outside the horizon which filter the initially blackbody spectrum emanating from the horizon. D-brane bound states, in a thermally excited state corresponding to near-extremal black holes, also do not emit blackbody radiation: The bound state radiation spectrum encodes the energy spectrum of its excitations. We study a near-extremal five-dimensional black hole. We show that in a wide variety of circumstances including both neutral and charged emission, the effect of the greybody filter is to transform the blackbody radiation spectrum precisely into the bound state radiation spectrum. Implications of this result for the information puzzle in the context of near-extremal black hole dynamics are discussed.

CMB anisotropies: Total angular momentum method

Abstract: of the Boltzmann equations brings out the geometric and model-independent aspects of temperature and polarization anisotropy formation. Large angle scalar polarization provides a robust means to distinguish between isocurvature and adiabatic models for structure formation in principle. Vector modes have the unique property that the CMB polarization is dominated by magnetic-type parity at small angles ~a factor of 6 in power compared with 0 for the scalars and 8/13 for the tensors! and hence potentially distinguishable independent of the model for the seed. The tensor modes produce a different sign from the scalars and vectors for the temperature-polarization correlations at large angles. We explore conditions under which one perturbation type may dominate over the others including a detailed treatment of the photon-baryon fluid before recombination. @S0556-2821~97!00614-0#

Structure of resonance in preheating after inflation

Abstract: We consider preheating in the theory $1/4 \lambda \phi^4 + 1/2 g^2\phi^2\chi^2 $, where the classical oscillating inflaton field $\phi$ decays into $\chi$-particles and $\phi$-particles. The parametric resonance which leads to particle production in this conformally invariant theory is described by the Lame equation. It significantly differs from the resonance in the theory with a quadratic potential. The structure of the resonance depends in a rather nontrivial way on the parameter $g^2/\lambda$. We construct the stability/instability chart in this theory for arbitrary $g^2/\lambda$. We give simple analytic solutions describing the resonance in the limiting cases $g^2/\lambda\ll 1$ and $g^2/\lambda \gg 1$, and in the theory with $g^2=3\lambda$, and with $g^2 =\lambda$. From the point of view of parametric resonance for $\chi$, the theories with $g^2=3\lambda$ and with $g^2 =\lambda$ have the same structure, respectively, as the theory $1/4 \lambda \phi^4$, and the theory $\lambda /(4 N) (\phi^2_i)^2$ of an N-component scalar field $\phi_i$ in the limit $N \to \infty$. We show that in some of the conformally invariant theories such as the simplest model $1/4 \lambda\phi^4$, the resonance can be terminated by the backreaction of produced particles long before $ $ or $ $ become of the order $\phi^2$. We analyze the changes in the theory of reheating in this model which appear if the inflaton field has a small mass.

'Sum over surfaces' form of loop quantum gravity

Abstract: We derive a spacetime formulation of quantum general relativity from (Hamiltonian) loop quantum gravity. In particular, we study the quantum propagator that evolves the three-geometry in proper time. We show that the perturbation expansion of this operator is finite and computable order by order. By giving a graphical representation in the manner of Feynman of this expansion, we find that the theory can be expressed as a sum over topologically inequivalent (branched, colored) two-dimensional (2D) surfaces in 4D. The contribution of one surface to the sum is given by the product of one factor per branching point of the surface. Therefore branching points play the role of elementary vertices of the theory. Their value is determined by the matrix elements of the Hamiltonian constraint, which are known. The formulation we obtain can be viewed as a continuum version of Reisenberger's simplicial quantum gravity. Also, it has the same structure as the Ooguri-Crane-Yetter 4D topological field theory, with a few key differences that illuminate the relation between quantum gravity and topological quantum field theory. Finally, we suggest that certain new terms should be added to the Hamiltonian constraint in order to implement a ``crossing'' symmetry related to 4D diffeomorphism invariance.

Axiomatic approach to electromagnetic and gravitational radiation reaction of particles in curved spacetime

Abstract: The problem of determining the electromagnetic and gravitational ``self-force'' on a particle in a curved spacetime is investigated using an axiomatic approach. In the electromagnetic case, our key postulate is a ``comparison axiom,'' which states that whenever two particles of the same charge $e$ have the same magnitude of acceleration, the difference in their self-force is given by the ordinary Lorentz force of the difference in their (suitably compared) electromagnetic fields. We thereby derive an expression for the electromagnetic self-force which agrees with that of DeWitt and Brehme as corrected by Hobbs. Despite several important differences, our analysis of the gravitational self-force proceeds in close parallel with the electromagnetic case. In the gravitational case, our final expression for the (reduced order) equations of motion shows that the deviation from geodesic motion arises entirely from a ``tail term,'' in agreement with recent results of Mino et al. Throughout the paper, we take the view that ``point particles'' do not make sense as fundamental objects, but that ``point particle equations of motion'' do make sense as means of encoding information about the motion of an extended body in the limit where not only the size but also the charge and mass of the body go to zero at a suitable rate. Plausibility arguments for the validity of our comparison axiom are given by considering the limiting behavior of the self-force on extended bodies.

Lorentz-invariant actions for chiral p-forms

Abstract: We demonstrate how a Lorentz-covariant formulation of the chiral p-form model in D=2(p+1) containing infinitely many auxiliary fields is related to a Lorentz-covariant formulation with only one auxiliary scalar field entering a chiral p-form action in a nonpolynomial way. The latter can be regarded as a consistent Lorentz-covariant truncation of the former. We make the Hamiltonian analysis of the model based on the nonpolynomial action and show that the Dirac constraints have a simple form and are all first class. In contrast with the Siegel model the constraints are not the square of second-class constraints. The canonical Hamiltonian is quadratic and determines the energy of a single chiral p-form. In the case of D=2 chiral scalars the constraint can be improved by use of a {open_quotes}twisting{close_quotes} procedure (without the loss of the property to be first class) in such a way that the central charge of the quantum constraint algebra is zero. This points to the possible absence of an anomaly in an appropriate quantum version of the model. {copyright} {ital 1997} {ital The American Physical Society}

How to measure CMB power spectra without losing information

Abstract: A new method for estimating the angular power spectrum ${C}_{l}$ from cosmic microwave background (CMB) maps is presented, which has the following desirable properties. (1) It is unbeatable in the sense that no other method can measure ${C}_{l}$ with smaller error bars. (2) It is quadratic, which makes the statistical properties of the measurements easy to compute and use for estimation of cosmological parameters. (3) It is computationally faster than rival high-precision methods such as the nonlinear maximum-likelihood technique, with the crucial steps scaling as ${n}^{2}$ rather than ${n}^{3}$, where $n$ is the number of map pixels. (4) It is applicable to any survey geometry whatsoever, with arbitrary regions masked out and arbitrary noise behavior. (5) It is not a ``black-box'' method, but quite simple to understand intuitively: it corresponds to a high-pass filtering and edge softening of the original map followed by a straight expansion in truncated spherical harmonics. It is argued that this method is computationally feasible even for future high-resolution CMB experiments with $n\ensuremath{\sim}{10}^{6}$--${10}^{7}$. It is shown that ${C}_{l}$ computed with this method is useful not merely for graphical presentation purposes, but also as an intermediate (and arguably necessary) step in the data analysis pipeline, reducing the data set to a more manageable size before the final step of constraining Gaussian cosmological models and parameters --- while retaining all the cosmological information that was present in the original map.

Gravitational radiation reaction to a particle motion

Abstract: A small mass particle traveling in a curved spacetime is known to trace a background geodesic in the lowest order approximation with respect to the particle mass. In this paper, we discuss the leading order correction to the equation of motion of the particle, which presumably describes the effect of gravitational radiation reaction. We derive the equation of motion in two different ways. The first one is an extension of the well-known formalism by DeWitt and Brehme developed for deriving the equation of motion of an electrically charged particle. Constructing the conserved rank two symmetric tensor, and integrating it over the interior of the world tube surrounding the orbit, we derive the equation of motion. Although the calculation in this approach is straightforward, it contains less rigorous points. In contrast to the electromagnetic case, in which there are two different charges, i.e., the electric charge and the mass, the gravitational counterpart has only one charge. This fact prevents us from using the same renormalization scheme that was used in the electromagnetic case. In order to overcome this difficulty, we put an ansatz in evaluating the integral ofthe conserved tensor on a three spatial volume which defines the momentum of the small particle. To make clear the subtlety in the first approach, we then consider the asymptotic matching of two different schemes, i.e., the internal scheme in which the small particle is represented by a spherically symmetric black hole with tidal perturbations and the external scheme in which the metric is given by small perturbations on the given background geometry. The equation of motion is obtained from the consistency condition of the matching. We find that in both ways the same equation of motion is obtained. The resulting equation of motion is analogous to that derived in the electromagnetic case. We discuss implications of this equation of motion. PACS number(s): 04.30.Db, 04.25.-g

New Goldstone multiplet for partially broken supersymmetry

Abstract: The partial spontaneous breaking of rigid $N=2$ supersymmetry implies the existence of a massless $N=1$ Goldstone multiplet. In this paper we show that the spin-$(1/2,1)$ Maxwell multiplet can play this role. We construct its full nonlinear transformation law and find the invariant Goldstone action. The spin-$1$ piece of the action turns out to be of Born-Infeld-type, and the full superfield action is duality invariant. This leads us to conclude that the Goldstone multiplet can be associated with a D-brane solution of superstring theory for $p=3$. In addition, we find that $N=1$ chirality is preserved in the presence of the Goldstone-Maxwell multiplet. This allows us to couple it to $N=1$ chiral and gauge field multiplets. We find that arbitrary K\"ahler and superpotentials are consistent with partially broken $N=2$ supersymmetry.