Brane Solutions Research Articles

Thick brane in mimetic-like gravity

We analyze a five-dimensional braneworld governed by a mimetic-like gravity, a plausible candidate for explaining dark matter. Within this scenario, we examine Friedmann-Lemaître-Robertson-Walker (FLRW) branes and find that constant curvature and Minkowskian solutions are possible. We then show that the mimetic model leads to kink-like and lump-like thick brane solutions without the need for spontaneous symmetry breaking. Its stability against small perturbations is also verified.

Galilean fluids from non-relativistic gravity

The 1/c-expansion of general relativity appropriately sourced by matter can be used to derive an action principle for Newtonian gravity. The gravitational part of this action is known as non-relativistic gravity (NRG). It is possible to source NRG differently and in such a way that one can construct solutions that are not described by Newtonian gravity (as they do not admit a notion of absolute time). It is possible to include a negative cosmological constant such that NRG admits a non-relativistic AdS solution. This non-relativistic AdS vacuum has Killing vectors that form the Galilean conformal algebra and a boundary that admits a conformal class of Newton-Cartan geometries. This begs the question of whether there exists an analogue of the fluid/gravity correspondence for NRG. In this paper we derive a non-relativistic AdS brane solution of NRG and confirm that it corresponds to the 1/c2-expansion of the AdS black brane geometry. We perform a Galilean boost of the non-relativistic AdS brane and derive the associated boundary energy-momentum tensor. We then show that this is the energy-momentum tensor of a massless Galilean fluid and explain how this is linked to the conformal isometries of the boundary. Along the way, we also present several new results for the theory of non-relativistic gravity itself. In particular we present a rewriting that greatly shortens and simplifies the equations of motion of the NRG action.

A holographic model of magnetohydrodynamics with fortuitous SO(3) symmetry

We study magnetohydrodynamics using holography. The gravity model is closely related to the STU supergravity in five dimensions and admits an analytical black brane solution carrying the conserved charge dual to the magnetic 1-form symmetry of the magnetohydrodynamic system. The black brane solution features a fortuitous SO(3) symmetry, providing a new symmetry principle for describing the magnetohydrodynamics. Since the bulk theory contains multiple 2-form gauge fields, the resistivity becomes matrix-valued. We find that the antisymmetric part of the resistivity matrix exhibits novel features depending on the UV cut-off of the theory. We also compute the shear and bulk viscosities and find that the bulk viscosity is proportional to the shear viscosity. Remarkably, the proportionality constant is exactly what is required for conformality, despite the zeroth-order energy-momentum tensor not being trace-free.

Brane profiles of non-supersymmetric strings

We connect the indications of 2D CFT for branes in non-supersymmetric strings to actual spacetime profiles, taking the bulk tadpole potentials into account. We find exact solutions for the uncharged branes that spread in the internal intervals of Dudas-Mourad vacua for non-tachyonic orientifolds and heterotic strings. These solutions involve suitable dressings of the uncharged branes of the nine-dimensional tadpole-free theory. Similar exact results for uncharged branes that are transverse to the internal space, or for charged branes, appear more challenging. Nevertheless, we identify their large-distance behavior, which is determined by linearized equations, and show that it is compatible with the CFT analysis in all expected cases. We also provide some hints on the leading back-reaction of the form-fields.

Quantum chaos in the presence of nonconformality

The behavior of a chaotic system and its effect on existing quantum correlation has been holographically studied in the presence of nonconformality. Keeping in mind the gauge/gravity duality framework, the nonconformality in the dual field theory has been introduced by considering a Liouville type dilaton potential for the gravitational theory. The resulting black brane solution is associated with a parameter η which represents the deviation from conformality. The parameters of chaos, namely, the Lyapunov exponent and butterfly velocity are computed by following the well-known shock wave analysis. The obtained results reveal that the presence of nonconformality leads to suppression of the chaotic nature of a system. Further, for a particular value of the nonconformal parameter η, the system achieves Lyapunov stability resulting from the vanishing of both the Lyapunov exponent as well as butterfly velocity. Interestingly, this particular value of η matches with the previously given upper bound of η known as Gubser bound in the literature. The effects of chaos and nonconformality on the existing correlation of a thermofield doublet state have been quantified by holographically computing the thermomutual information in both the presence and absence of the shock wave. Furthermore, the entanglement velocity is also computed, and the effect of nonconformality on it has been observed. Finally, the obtained results for the Lyapunov exponent and the butterfly velocity have also been computed from the pole-skipping analysis. The results from the two approaches agree with each other. Published by the American Physical Society 2024

Braneworld black holes with ModMax electrodynamics on the brane

In this study, we investigate ModMax electrodynamics localized within the Randall–Sundrum II and Dvali–Gabadadze–Porrati branes, deriving corresponding 3-brane spacetime solutions that conform to the effective Einstein equations in each specific scenario. We construct solutions for charged black holes within the effective Einstein equation framework in both braneworld scenarios. The examination explores the trajectories of charged objects in this spacetime, underscoring the significance of the nonlinear parameter. Our analysis uncovers the fact that, similar to the prior ModMax black hole investigation, the nonlinear parameter plays a pivotal role in suppressing the effective charge of the black hole, due to its definite positive value.

More holographic M5 branes in AdS7 × S4

We study classical M5 brane solutions in the probe limit in the AdS7×S4 spacetime geometry with worldvolume 3-form flux. These solutions describe the holography of codimension-4 defects in the 6d boundary dual N=(0,2) supersymmetric gauge theories. Starting from some half-BPS solutions which follow stricter BPS conditions, we find a general 116-BPS solution. We show how some of the giant-like M5 brane solutions here may be related to the codimension-2 surface operators in the 4d gauge theory.

Intersecting end of the world branes

Dynamical cobordisms implement the swampland cobordism conjecture in the framework of effective field theory, realizing codimension-1 end of the world (ETW) branes as singularities at finite spacetime distance at which scalars diverge to infinite field space distance. ETW brane solutions provide a useful probe of infinity in moduli/field spaces and the associated swampland constraints, such as the distance conjecture.We construct explicit solutions describing intersecting ETW branes in theories with multiple scalars and general potentials, so that different infinite field space limits coexist in the same spacetime, and can be simultaneously probed by paths approaching the ETW brane intersection. Our class of solutions includes physically interesting examples, such as intersections of Witten’s bubbles of nothing in toroidal compactifications, generalizations in compactifications on products of spheres, and possible flux dressings thereof (hence including charged objects at the ETW branes). From the cobordism perspective, the intersections can be regarded as describing the end of the world for end of the world branes, or as boundary domain walls interpolating between different ETW brane boundary conditions for the same bulk theory.

Black branes in asymptotically Lifshitz spacetimes with arbitrary exponents in κ -Horndeski gravity

In this work, we consider Horndeski gravity deformed by a parameter in its kinetic terms embedded in asymptotically Lifshitz spacetimes. We obtain black brane solutions in this geometry and study their thermodynamical properties. We show that the κ deformation on the Horndeski kinetic terms allows for arbitrary values of the critical exponents characteristic of Lifshitz spacetimes. These solutions present local and global thermodynamical stabilities. Published by the American Physical Society 2024

Bulk modified gravity from a thermal CFT by the conformal flow

We construct a bulk spacetime from a boundary conformal field theory, O(N) free scalar model, at finite temperature using a smearing technique, called a conformal flow. The bulk metric is constructed from the thermal two-point function of the smeared boundary elementary field in such a way that it can be interpreted as an information metric associated with the boundary thermofield double state. Near the boundary (UV region), an asymptotically anti–de Sitter (AdS) spacetime is obtained with a leading order perturbation of scalar mode. Based on the falloff behavior of the perturbations and the O(N) symmetry in the conformal field theory, we argue that the corresponding bulk theory is a modified gravity with scalar mode such as f(R) gravity rather than Einstein’s general relativity coupled minimally to matter fields. Moving to the Einstein frame, we show that the metric is asymptotically the same as the AdS black brane solution. On the other hand, deep in the bulk (IR region), the spacetime turns out to be conformally equivalent to the near horizon limit of AdS extremal black brane, though it is no longer a solution of f(R) gravity, and hence more general classes of modified gravity need to be considered. Published by the American Physical Society 2024

Thick Branes in Horndeski Gravity

We investigate thick brane solutions in the Horndeski gravity. In this setup, we found analytical solutions, applying the first-order formalism to two scalar fields where the first field comes from the nonminimal scalar-tensor coupling and the second is due to the matter contribution sector. With these analytical solutions, we evaluate the symmetric thick brane solutions in Horndeski gravity with four-dimensional geometry. In such a setup, we evaluate the gravity fluctuations to find “almost massless modes,” for any values of the Horndeski parameters. These modes were used to compute the corrections to the Newtonian potential and evaluate the limit four-dimensional gravity.

The effect of three matters on KSS bound

In this paper, we introduce the black brane solutions in anti-de Sitter (AdS) space in four-dimensional (4D) Einstein–Gauss–Bonnet–Yang–Mills theory in the presence of string cloud and quintessence. Shear viscosity to entropy density ratio is computed via fluid–gravity duality, as a transport coefficient for this model.

Brane nucleation in supersymmetric models

This paper explores the process of vacuum decay in supersymmetric models related to flux compactifications. In particular, we describe these instabilities within supersymmetric Lagrangians for a single three-form multiplet. This multiplet combines scalar fields, representing the moduli fields in four dimensions, with 3-form fields that influence the potential for these moduli via the integer flux of their associated 4-form field strength. Furthermore, using supersymmetry as a guide we obtain the form of the couplings of these fields to the membranes that act as sources to the 3-form potentials. Adding small supersymmetry breaking terms to these Lagrangians one can obtain instanton solutions describing the decay of the vacua in these models by the formation of a membrane bubble. These instantons combine the usual Coleman-de Luccia and the Brown-Teitelboim formalisms in a single unified model. We study simple numerical examples of theories with and without gravity in this new framework and generalize known Euclidean methods to accomodate the simulataneous inclusion of scalar fields and charged membranes to these instanton solutions. Moreover, we show explicitly in these examples how one recovers the static supersymmetric solutions in the limiting case where the supersymmetry breaking terms vanish. In this limit, the bubble becomes infinite and flat and represents a hybrid between the usual supersymmetric domain walls of field theory models and the brane solutions interpolating between the supersymmetric vacua; a sort of dressed supermembrane BPS solution. Finally, we briefly comment on the implications of these solutions in cosmological models based on the String Theory Landscape where these type of 4d effective theories could be relevant in inflationary scenarios.

Thick branes via higher order field theory models with exponential and power-law tails

In this work, we obtain exact thick brane models in 4+1 dimensions generated by higher order field theory kinks, inspired by specific potentials for phi ^{10} and phi ^{18} models. We verify that the geodesic equation along the fifth dimension confirms the confining effects of the scalar field on the brane for all of these models. These models provide new solutions with exponential and power-law tails which live in different topological sectors. We show that the resulting branes of specific exponential law models do not possess Z_2-symmetry. Furthermore, we examine the stability of the thick branes, by determining the sign of the w^2 term in the expansion of the potential for the resulting Schrödinger-like equation. It turns out that two of the three models of the phi ^{10} brane are stable, while another contains unstable modes for certain ranges of the model parameters. We also show that the brane solution from the specific phi ^{18} models are stable, while the others involve neutral equilibrium. The asymptotic behaviour of the brane solutions are also discussed.

AdS black brane coupled to non-abelian logarithmic gauge theory and color DC conductivity

In this paper, we consider Einstein–Hilbert gravity in the presence of cosmological constant and non-abelian nonlinear electromagnetic field of logarithmic type that is minimally coupled to gravity. First, black brane solution of this model is introduced and then color non-abelian DC conductivity is calculated for this solution by using AdS/conformal field theory (CFT) duality. Our result recovers the Yang–Mills model in λ → 0 limit.

Holographic aspects of non-minimal RFμα(a)F(a)μα black brane

In this paper, we consider Einstein–Hilbert gravity in the presence of cosmological constant and an electric field of Yang–Mills type, which is minimally coupled to gravity. We couple the Ricci scalar to the Yang–Mills invariant to obtain a modified theory of gravity. The black brane solution of this model is introduced up to the first order of the [Formula: see text] term. Then, the color non-Abelian direct current (DC) conductivity and the ratio of shear viscosity to entropy density are calculated for this solution. Our results recover the Yang–Mills Schwarzschild AdS black brane in the limit of [Formula: see text].

D3-brane supergravity solutions from Ricci-flat metrics on canonical bundles of Kähler–Einstein surfaces

D3 brane solutions of type IIB supergravity can be obtained by means of a classical Ansatz involving a harmonic warp factor, H(textbf{y},bar{textbf{y}}) multiplying at power -1/2 the first summand, i.e., the Minkowski metric of the D3 brane world-sheet, and at power 1/2 the second summand, i.e., the Ricci-flat metric on a six-dimensional transverse space mathcal {M}_6, whose complex coordinates y are the arguments of the warp factor. Of particular interest is the case where mathcal {M}_6={text {tot}}[ Kleft[ left( mathcal {M}_Bright) right] is the total space of the canonical bundle over a complex Kähler surface mathcal {M}_B. This situation emerges in many cases while considering the resolution à la Kronheimer of singular manifolds of type mathcal {M}_6=mathbb {C}^3/Gamma , where Gamma subset mathrm {SU(3)} is a discrete subgroup. When Gamma = mathbb {Z}_4, the surface mathcal {M}_B is the second Hirzebruch surface endowed with a Kähler metric having mathrm {SU(2)times U(1)} isometry. There is an entire class {text {Met}}(mathcal{F}mathcal{V}) of such cohomogeneity one Kähler metrics parameterized by a single function mathcal{F}mathcal{K}(mathfrak {v}) that are best described in the Abreu–Martelli–Sparks–Yau (AMSY) symplectic formalism. We study in detail a two-parameter subclass {text {Met}}(mathcal{F}mathcal{V})_{textrm{KE}}subset {text {Met}}(mathcal{F}mathcal{V}) of Kähler–Einstein metrics of the aforementioned class, defined on manifolds that are homeomorphic to S^2times S^2, but are singular as complex manifolds. Actually, {text {Met}}(mathcal{F}mathcal{V})_{textrm{KE}}subset {text {Met}}(mathcal{F}mathcal{V})_{textrm{ext}}subset {text {Met}}(mathcal{F}mathcal{V}) is a subset of a four parameter subclass {text {Met}}(mathcal{F}mathcal{V})_{textrm{ext}} of cohomogeneity one extremal Kähler metrics originally introduced by Calabi in 1983 and translated by Abreu into the AMSY action-angle formalism.{text {Met}}(mathcal{F}mathcal{V})_{textrm{ext}} contains also a two-parameter subclass {text {Met}}(mathcal{F}mathcal{V})_{textrm{ext}mathbb {F}_2} disjoint from {text {Met}}(mathcal{F}mathcal{V})_{textrm{KE}} of extremal smooth metrics on the second Hirzebruch surface that we rederive using constraints on period integrals of the Ricci 2-form. The Kähler–Einstein nature of the metrics in {text {Met}}(mathcal{F}mathcal{V})_{textrm{KE}} allows the construction of the Ricci-flat metric on their canonical bundle via the Calabi Ansatz, which we recast in the AMSY formalism deriving some new elegant formulae. The metrics in {text {Met}}(mathcal{F}mathcal{V})_{textrm{KE}} are defined on the base manifolds of U(1) fibrations supporting the family of Sasaki–Einstein metrics textrm{SEmet}_5 introduced by Gauntlett et al. (Adv Theor Math Phys 8:711–734, 2004), and already appeared in Gibbons and Pope (Commun Math Phys 66:267–290, 1979). However, as we show in detail using Weyl tensor polynomial invariants, the six-dimensional Ricci-flat metric on the metric cone of {mathcal M}_5 in {text {Met}}(textrm{SE})_5 is different from the Ricci-flat metric on {text {tot}}[ Kleft[ left( mathcal {M}_{textrm{KE}}right) right] constructed via Calabi Ansatz. This opens new research perspectives. We also show the full integrability of the differential system of geodesics equations on mathcal {M}_B thanks to a certain conserved quantity which is similar to the Carter constant in the case of the Kerr metric.

Gravity and matter on a pure geometric thick polynomial f(R) brane

In this paper, the solutions of the pure geometric thick $f(R)$ brane are investigated. The formulation of $f(R)$ is chosen as $f(R)=\sum_{i=1}^{n}a_{i}R^{i}+\Lambda$. For the certain value of $n$, the brane solution can be calculated, and when $n=3$, $n=4$, and $n=10$, the thick brane solutions are presented. The solutions is stable under linear tensor fluctuation. The zero mode of gravity and scalar field can be localized on thick $f(R)$ branes naturally. The zero mode of vector field and left-chiral fermion can be localized on thick $f(R)$ branes by introducing the coupling with scalar curvature $R$ of spacetime, and the massive resonant modes can be quasilocalized on the brane with the large coupling coefficients.

Effective action of a self-interacting scalar field on brane

In extra dimensional theories, the four-dimensional field theory is reduced from a fundamental field theory in the bulk spacetime by integrating the extra dimensional part. In this paper we investigate the effective action of a self-interacting scalar field on a brane in the five-dimensional thick braneworld scenario. We consider two typical thick brane solutions and obtain the Pöschl–Teller and harmonic potentials of the Kaluza–Klein (KK) modes, respectively. The analytical mass spectra and wave functions along extra dimension of the KK modes are obtained. Further, the effective coupling constant between different KK particles, cross section, and decay rate for some processes of the KK particles are related to the fundamental coupling in five dimensions and the new physics energy scale. Some interesting properties of these interactions are found with these calculations. The KK particles with higher mode have longer lifetime, and they almost do not interact with ordinary matter on the brane if their mode numbers are large enough. Thus, these KK particles with higher modes might be a candidate of dark matter.

Holographic anisotropic background in 5D Einstien–Gauss–Bonnet gravity

In this paper, we extend the work on the AdS/QCD model to quadratic gravity to gain insight into the influence of gravity. We obtain an anisotropic black brane solution to a 5D Einstein–Gauss–Bonnet-two Maxwell-dilaton system. The background is specified by an arbitrary exponent, a dilaton field, a time component of the first Maxwell field, and a magnetic component of the second Maxwell field. The system in three cases has been investigated and in each case the effect of the parameter of theory, the anisotropic parameter has been considered. The blackening function supports the thermodynamical phase transition between small/large and AdS/large black brane for a suitable chemical potential and other parameters.