Born-Infeld Theory Research Articles

On the road to [formula omitted] supersymmetric Born–Infeld action

We analyze the exact perturbative solution of N=2 Born–Infeld theory which is believed to be defined by Ketovʼs equation. This equation can be considered as a truncation of an infinite system of coupled differential equations defining Born–Infeld action with one manifest N=2 and one hidden N=2 supersymmetries. We explicitly demonstrate that infinitely many new structures appear in the higher orders of the perturbative solution to Ketovʼs equation. Thus, the full solution cannot be represented as a function depending on a finite number of its arguments. We propose a mechanism for generating the new structures in the solution and show how it works up to 18-th order. Finally, we discuss two new superfield actions containing an infinite number of terms and sharing some common features with N=2 supersymmetric Born–Infeld action.

A fully general relativistic numerical simulation code for spherically symmetric matter

We present a fully general relativistic open-source code that can be used for simulating a system of spherically symmetric perfect fluid matter. It is based on the Arnowitt-Deser-Misner 3+1 formalism with maximal slicing and isotropic spatial coordinates. For hydrodynamic matter High Resolution Shock Capturing (HRSC) schemes with a monotonized central-difference limiter and approximated Riemann solvers are used in the Eulerian viewpoint. The accuracy and the convergence of our numerical code are verified by performing several test problems. These include a relativistic blast wave, relativistic spherical accretion of matter into a black hole, Tolman-Oppenheimer-Volkoff (TOV) stars and Oppenheimer-Snyder (OS) dust collapses. In particular, a dynamical code test is done for the OS collapse by explicitly performing numerical coordinate transformations between our coordinate 8system and the one used for the analytic solution. Finally, some TOV star solutions are presented for the Eddington-inspired Born-Infeld gravity theory.

Pulse Soliton Solutions of the Modified KdV and Born-Infeld Equations

In this work, we use the Bogning-Djeumen Tchaho-Kofane method to look for all solutions of shape Sechn- of the modified KdV and Born-Infeld Equations. n being a real number, we obtain the soliton solutions when n is positive and the non soliton solutions when n is negative.

Erratum to "Existence and multiplicity of solutions for the nonlinear Klein-Gordon equation coupled with Born-Infeld theory on bounded domain" [Differ. Equ. Appl. 4 (2012) 445-457

Erratum to "Existence and multiplicity of solutions for the nonlinear Klein-Gordon equation coupled with Born-Infeld theory on bounded domain" [Differ. Equ. Appl. 4 (2012) 445-457

Noncommutative geometry of multicore bions

We find new BPS solutions to the nonabelian theory on a world-volume of parallel D1-branes. Our solutions describe two parallel, separated bundles of N D1-branes expanding out to form a single orthogonal D3-brane. This configuration corresponds to two charge N magnetic monopoles in the world-volume of a single D3-brane, deforming the D3-brane into two parallel spikes. We obtain the emergent surface corresponding to our nonabelian D1-brane configuration and demonstrate, at finite N, a surprisingly accurate agreement with the shape of the D3-brane world-volume as obtained from the abelian Born-Infeld action. Our solution provides an explicit realization of topology change in noncommutative geometry at finite N.

Extended phase space thermodynamics for charged and rotating black holes and Born-Infeld vacuum polarization

We investigate the critical behaviour of charged and rotating AdS black holes in d spacetime dimensions, including effects from non-linear electrodynamics via the Born-Infeld action, in an extended phase space in which the cosmological constant is interpreted as thermodynamic pressure. For Reissner-Nordstrom black holes we find that the analogy with the Van der Walls liquid-gas system holds in any dimension greater than three, and that the critical exponents coincide with those of the Van der Waals system. We find that neutral slowly rotating black holes in four space-time dimensions also have the same qualitative behaviour. However charged and rotating black holes in three spacetime dimensions do not exhibit critical phenomena. For Born-Infeld black holes we define a new thermodynamic quantity B conjugate to the Born-Infeld parameter b that we call Born-Infeld vacuum polarization. We demonstrate that this quantity is required for consistency of both the first law of thermodynamics and the corresponding Smarr relation.

Thin-shell wormholes with a generalized Chaplygin gas in Einstein–Born–Infeld theory

We construct spherically symmetric thin-shell wormholes supported by a generalized Chaplygin gas in Born–Infeld electrodynamics coupled to Einstein gravity, and we analyze their stability under radial perturbations. For different values of the Born–Infeld parameter and the charge, we compare the results with those obtained in a previous work for Maxwell electrodynamics. The stability region in the parameter space reduces and then disappears as the value of the Born–Infeld parameter is modified in the sense of a larger departure from Maxwell theory.

Eddington-inspired Born-Infeld gravity: nuclear physics constraints and the validity of the continuous fluid approximation

In this paper we investigate the classical non-relativistic limit of the Eddington-inspired Born-Infeld theory of gravity. We show that strong bounds on the value of the only additional parameter of the theory κ, with respect to general relativity, may be obtained by requiring that gravity plays a subdominant role compared to electromagnetic interactions inside atomic nuclei. We also discuss the validity of the continuous fluid approximation used in this and other astrophysical and cosmological studies. We argue that although the continuous fluid approximation is expected to be valid in the case of sufficiently smooth density distributions, its use should eventually be validated at a quantum level.

Multiple solutions for the nonhomogeneous Klein–Gordon equation coupled with Born–Infeld theory on [formula omitted

In this paper we prove the existence of multiple solutions for the following nonhomogeneous Klein–Gordon equation coupled with Born–Infeld theory, {−Δu+[m2−(ω+ϕ)2]u=|u|q−2u+h(x),inR3,Δϕ+βΔ4ϕ=4π(ω+ϕ)u2,inR3, when 2<q<6.

Observational constraints on electromagnetic Born-Infeld cosmology

The cosmological model consisting of an electromagnetic Born-Infeld (BI) field coupled to a Robertson-Walker geometry is tested with the standard probes of SNIa, GRBs and direct Hubble parameter. The analysis shows that the inclusion of the nonlinear electromagnetic component does not contribute in a significative way to the observed expansion. The BI electromagnetic matter is considered with an abundance of ΩBI, that our best fit leads to ΩBI = 0.037 when tested with SNIa and the Hubble parameter data (0.1 < z < 1.75); while when tested with GRBs the result is of ΩBI = 0.304, which may indicate that this electrodynamics was important at epochs close to the appearance of large structure (z ≈ 7), although this late result has not as much reliability as that corresponding to the first two probes, since we know that the dispersion in GRBs data is still considerable. In view of these results we can rule out the electromagnetic Born-Infeld matter as the origin of the present accelerated expansion, this conclusion concerns exclusively the Born-Infeld theory.

Bouncing Eddington-inspired Born-Infeld cosmologies: An alternative to inflation?

We study the dynamics of a homogeneous and isotropic Friedmann-Robertson-Walker universe in the context of the Eddington-inspired Born-Infeld theory of gravity. We generalize earlier results, obtained in the context of a radiation dominated universe, to account for the evolution of a universe permeated by a perfect fluid with an arbitrary equation of state parameter $w$. We show that a bounce may occur for $\kappa >0$, if $w$ is time-dependent, and we demonstrate that it is free from tensor singularities. We argue that Eddington-inspired Born-Infeld cosmologies may be a viable alternative to the inflationary paradigm as a solution to fundamental problems of the standard cosmological model.

New Insights on the Matter-Gravity Coupling Paradigm

The coupling between matter and gravity in general relativity is given by a proportionality relation between the stress tensor and the geometry. This is an oriented assumption driven by the fact that both the stress tensor and the Einstein tensor are divergenceless. However, general relativity is in essence a nonlinear theory, so there is no obvious reason why the coupling to matter should be linear. On another hand, modified theories of gravity usually affect the vacuum dynamics, yet keep the coupling to matter linear. In this Letter, we address the implications of consistent nonlinear gravity-matter coupling. The Eddington-inspired Born-Infeld theory recently introduced by Bañados and Ferreira provides an enlightening realization of such coupling modifications. We find that this theory coupled to a perfect fluid reduces to general relativity coupled to a nonlinearly modified perfect fluid, leading to an ambiguity between modified coupling and modified equation of state. We discuss observational consequences of this degeneracy and argue that such a completion of general relativity is viable from both an experimental and theoretical point of view through energy conditions, consistency, and singularity-avoidance perspectives. We use these results to discuss the impact of changing the coupling paradigm.

The Dark Energy Properties of the Dirac–Born–Infeld Action

Introducing a new potential, we deduce a general Lagrangian for Dirac–Born– Infeld (DBI) inflation, in which the determinant of the induced metric naturally includes the kinetic energy and the potential energy. In particular, the potential energy and kinetic energy can convert into each other at any same order, which is in agreement with the limit of classical physics. We also present a general sound speed in the evolutions of the universe, and the exact expressions of energy-momentum tensor, pressure and density. Furthermore, from the results we obtain the new equation of states. The analytic form of the action that is consistent with data turns out to be surprisingly simple and easy to categorize. Finally, we examine properties of the dark energy and introduce a novel mechanism for realizing either quintessence or phantom dark energy dominated phases within a string theoretical context.

More on closed string induced higher derivative interactions on D-branes

In our continued efforts of matching full string computations with the corresponding effective field theory computations, we evaluate string theory correlators in closed forms. In particular, we consider a correlator between three SYM vertex operators and one Ramond-Ramond $C$-field vertex operator: $<V_{C}V_{\phi} V_AV_A>$. We show that the infinite number of massless poles of this amplitude can be reproduced by the Born-Infeld action, the Wess-Zumino terms, and their higher derivative corrections. More specifically we find, up to an on-shell ambiguity, two scalar field and two gauge field couplings to all orders in $\alpha'$ such that the infinite number of massless poles of the field theory amplitude exactly match the infinite number of massless poles of S-matrix elements of $<V_{C}V_{\phi} V_AV_A>$. We comment on close intertwinedness of an open string and a closed string that must be behind the matching.

Nonlinear self-duality in $ \mathcal{N} = 2 $ supergravity

For nonlinear models of an Abelian vector supermultiplet coupled to N = 2 supergravity in four dimensions, we formulate the self-duality equation which expresses invariance under U(1) duality rotations. In the flat space limit, this equation reduces to the N = 2 self-duality equation proposed in hep-th/0001068. We also give an example of a self-dual locally supersymmetric model containing a higher-derivative extension of the Born-Infeld action at the component level.

Eddington-inspired Born-Infeld gravity: Astrophysical and cosmological constraints

In this letter we compute stringent astrophysical and cosmological constraints on a recently proposed Eddington-inspired Born-Infeld theory of gravity. We find, using a generalized version of the Zel'dovich approximation, that in this theory a pressureless cold dark matter fluid has a non-zero effective sound speed. We compute the corresponding effective Jeans length and show that it is approximately equal to the fundamental length of the theory $R_*=\kappa^{1/2} G^{-1/2}$, where $\kappa$ is the only additional parameter of theory with respect to general relativity and $G$ is the gravitational constant. This scale determines the minimum size of compact objects which are held together by gravity. We also estimate the critical mass above which pressureless compact objects are unstable to colapse into a black hole, showing that it is approximately equal to the fundamental mass $M_* = \kappa^{1/2} c^2 G^{-3/2}$, and we show that the maximum density attainable inside stable compact stars is roughly equal to the fundamental density $\rho_*=\kappa^{-1} c^2$, where $c$ is the speed of light in vacuum. We find that the mere existence of astrophysical objects of size $R$ which are held together by their own gravity leads to the constraint $\kappa < G R^2$. In the case of neutron stars this implies that $\kappa < 10^{-2} \, {\rm m^5 \, kg^{-1} \, s^{-2}}$, a limit which is stronger by about 10 orders of magnitude than big bang nucleosynthesis constraints and by more than 7 orders of magnitude than solar constraints.

Practically linear analogs of the Born-Infeld and other nonlinear theories

I discuss theories that describe fully nonlinear physics, while being practically linear (PL), in that they require solving only linear differential equations. These theories may be interesting in themselves as manageable nonlinear theories. But, they can also be chosen to emulate genuinely nonlinear theories of special interest, for which they can serve as approximations. The idea can be applied to a large class of nonlinear theories, exemplified here with a PL analogs of scalar theories, and of Born-Infeld (BI) electrodynamics. The general class of such PL theories of electromagnetism are governed by a Lagrangian L=-(1/2)F_mnQ^mn+ S(Q_mn), where the electromagnetic field couples to currents in the standard way, while Qmn is an auxiliary field, derived from a vector potential that does not couple directly to currents. By picking a special form of S(Q_mn), we can make such a theory similar in some regards to a given fully nonlinear theory, governed by the Lagrangian -U(F_mn). A particularly felicitous choice is to take S as the Legendre transform of U. For the BI theory, this Legendre transform has the same form as the BI Lagrangian itself. Various matter-of-principle questions remain to be answered regarding such theories. As a specific example, I discuss BI electrostatics in more detail. As an aside, for BI, I derive an exact expression for the short-distance force between two arbitrary point charges of the same sign, in any dimension.

Dark matter, infinite statistics, and quantum gravity

We elaborate on our proposal regarding a connection between global physics and local galactic dynamics via quantum gravity. This proposal calls for the concept of MONDian dark matter which behaves like cold dark matter at cluster and cosmological scales but emulates modified Newtonian dynamics (MOND) at the galactic scale. In the present paper, we first point out a surprising connection between the MONDian dark matter and an effective gravitational Born-Infeld theory. We then argue that these unconventional quanta of MONDian dark matter must obey infinite statistics, and the theory must be fundamentally non-local. Finally, we provide a possible top-down approach to our proposal from the Matrix theory point of view.

Tensor instability in the Eddington-inspired Born-Infeld theory of gravity

In this paper, we consider an extension to Eddington's proposal for the gravitational action. We study tensor perturbations of a homogeneous and isotropic space-time in the Eddington regime, where modifications to Einstein gravity are strong. We find that the tensor mode is linearly unstable deep in the Eddington regime and discuss its cosmological implications.

Loop variables and gauge invariant exact renormalization group equations for (open) string theory

An exact renormalization group equation is written down for the world sheet theory describing the bosonic open string in general backgrounds. Loop variable techniques are used to make the equation gauge invariant. This is worked out explicitly up to level 3. The equation is quadratic in the fields and can be viewed as a proposal for a string field theory equation. As in the earlier loop variable approach, the theory has one extra space dimension and mass is obtained by dimensional reduction. Being based on the sigma model RG, it is background independent. It is intriguing that in contrast to BRST string field theory, the gauge transformations are not modified by the interactions up to the level calculated. The interactions can be written in terms of gauge invariant field strengths for the massive higher spin fields and the non-zero mass is essential for this. This is reminiscent of Abelian Born–Infeld action (along with derivative corrections) for the massless vector field, which is also written in terms of the field strength.