Spherical Branes Research Articles

Over-extremal brane shells from string theory?

We demonstrate that, if the usual phenomenological compactifications of IIB string theory with warped throats and anti-branes make sense, there must exist spherical brane shells in 4d that are overcharged. They correspond to classical over-extremal objects but without the usual naked singularities. The objects are made from D3-particles that puff into spherical five-branes that stabilise at finite radii in 4d and whose inside corresponds to the supersymmetric AdS vacuum. One can think of these shells as stabilised Brown–Teitelboim bubbles. We find that these objects can be significantly larger than the string scale depending on the details of the warped compactification.

Dynamical brane creation and annihilation via a background flux

We study the dynamical Myers effect by allowing the fuzzy (or the dynamical dielectric brane) coordinates to be time dependent. We find three novel kinds of the dynamical spherical dielectric branes depending on their respective excess energies. The first represents a dynamical spherical brane carrying a negative excess energy (having a lower bound) with its radius oscillating periodically between two given non-zero values. The second is the one with zero excess energy and whose time dependence can be expressed in terms of a simple function. This particular dynamical spherical configuration represents the dielectric brane creation and/or annihilation like a photon in the presence of a background creating an electron-position pair and then annihilating back to a photon. The third is the one carrying positive excess energy and the radius can also oscillate periodically between two non-zero values but, unlike the first kind, it passes zero twice for each cycle. Each of the above can also be interpreted as the time evolution of a semi-spherical D-brane-anti semi-spherical D-brane system.

Supersymmetric Yang-Mills, spherical branes, and precision holography

Using supersymmetric localization we compute the free energy and BPS Wilson loop vacuum expectation values for planar maximally supersymmetric Yang-Mills theory on Sd in the strong coupling limit for 2 ≤ d < 6. The same calculation can also be performed in supergravity using the recently found spherical brane solutions. We find excellent agreement between the two sets of results. This constitutes a non-trivial precision test of holography in a non-conformal setting. The free energy of maximal SYM on S6 diverges in the strong coupling limit which might signify the onset of little string theory. We show how this divergence can be regularized both in QFT and in supergravity. We also consider d = 7 with a small negative ’t Hooft coupling and show that the free energy and Wilson loop vacuum expectation value agree with the results from supergravity after addressing some subtleties.

Spherical branes

We construct new solutions of ten-dimensional supergravity with sixteen super-charges which describe the backreaction of Dp-branes with spherical worldvolume. These solutions are holographically dual to the (p + 1)-dimensional maximally supersymmetric Yang-Mills theory on Sp+1. The finite size of the sphere provides an IR cut-off for the gauge theory which is manifested in the supergravity solution as a smooth cap-off of the geometry. In the UV the size of the sphere plays no role and the backgrounds asymptote to the well-known supergravity solutions that describe the near-horizon limit of flat Dp-branes. We compute the on-shell action of our spherical brane solutions and show that it is in agreement with recent supersymmetric localization results for the free energy of maximal SYM theory on Sp+1.

D-brane solutions under market panic

The relativistic quantum mechanic approach is used to develop stock market dynamics. The relativistic is conceptional here as the meaning of big external volatility or volatility shock on a financial market. We used a differential geometry approach with the parallel transport of prices to obtain a direct shift of the stock price movement. The prices are represented here as electrons with different spin orientation. Up and down orientations of the spin particle are likened here to an increase or a decrease of stock prices. The parallel transport of stock prices is enriched by Riemann curvature, which describes some arbitrage opportunities in the market. To solve the stock-price dynamics, we used the Dirac equation for bispinors on the spherical brane-world. We found out that when a spherical brane is abbreviated to the disk on the equator, we converge to the ideal behavior of financial market where Black–Scholes as well as semi-classical equations are sufficient. Full spherical brane-world scenarios can describe non-equilibrium market behavior where all arbitrage opportunities as well as transaction costs are taken into account. Real application of the model to the option pricing was done. The model developed in this paper brings quantitative different results of option pricing dynamics in the case of nonzero Riemann curvature.

Construction of multiple spherical branes cosmological scenario

The general solution of Einstein's gravity equation in $D$ dimensions for an anisotropic and spherically symmetric matter distribution is calculated in a bulk with a position dependent cosmological constant. Results for $n$ concentric $(D\ensuremath{-}2)$-branes with arbitrary mass, radius, and pressure with different cosmological constant between branes are found. It is shown how the different cosmological constants contribute to the effective mass of each brane. It is also shown that the equation of state for each brane influences the dynamics of branes, which can be divided into eras according to the dominant matter. This scenario can be used to model the universe in the $D=5$ case, which may present a phenomenology richer than the current models. The evolution law of the branes is studied, and the anisotropic pressure that removes divergences is found. The Randall-Sundrum metric in an outside-the-region in the flat branes limit is also derived.

Scalar Field Dark Matter from Two Concentric Spherical Branes Universe

The Scalar Field Dark Matter (SFDM) model has provided to be a very successful one to explain the large scale structure of the Universe. Nevertheless, one of the main problems of the SFDM model is the ultralight mass of the scalar field mΦ ∼ 10−22eV. In this work we explore a five-dimensional Universe with a special topology with the aim to explain this mass using the Randal-Sumdrum prescription for the hierarchy problem using two branes. In this model we show two limits where the branes have mutual interaction and have no interaction. We analyze the Friedmann equations and the linear corrections introduced by this model.

D-brane potentials from multi-trace deformations in AdS/CFT

It is known that certain AdS boundary conditions allow smooth initial data to evolve into a big crunch. To study this type of cosmological singularity, one can use the dual quantum field theory, where the non-standard boundary conditions are reflected by the presence of a multi-trace potential unbounded below. For specific AdS_4 and AdS_5 models, we provide a D-brane (or M-brane) interpretation of the unbounded potential. Using probe brane computations, we show that the AdS boundary conditions of interest cause spherical branes to be pushed to the boundary of AdS in finite time, and that the corresponding potential agrees with the multi-trace deformation of the dual field theory. Systems with expanding spherical D3-branes are related to big crunch supergravity solutions by a phenomenon similar to geometric transition.

GRAVITATIONAL FIELD OF SPHERICAL BRANES

The warped solution of Einstein's equations corresponding to the spherical brane in five-dimensional AdS is considered. This metric represents interiors of black holes on both sides of the brane and can provide gravitational trapping of physical fields on the shell. It is found that the analytic form of the coordinate transformations from the Schwarzschild to co-moving frame that exists only in five dimensions. It is shown that in the static coordinates active gravitational mass of the spherical brane, in agreement with Tolman's formula, is negative, i.e. such objects are gravitationally repulsive.

Accelerating branes and brane temperature

We define the local acceleration and jerk of a relativistic brane in an ambient spacetime, and construct from them a dimensionless parameter λ that must be small for an interpretation of brane acceleration as local Unruh temperature. As examples, we discuss (i) open rotating branes, for which , (ii) closed spherical branes expanding in Minkowski spacetime, for which when the worldvolume is either an Einstein static universe or de Sitter space, in which case the brane temperature equals the Gibbons–Hawking temperature, (iii) closed spherical branes in anti-de Sitter spacetime, for which a maximally symmetric worldvolume is anti-de Sitter, Minkowski or de Sitter according to whether the magnitude of the brane acceleration is less than, equal to or greater than a ‘critical’ value, and (iv) the BTZ black hole, viewed as a membrane.

Casimir densities for two spherical branes in Rindler-like spacetimes

Wightman function, the vacuum expectation values of the field square and the energy-momentum tensor are evaluated for a scalar field obeying the Robin boundary conditions on two spherical branes in (D+1)-dimensional Rindler-like spacetime $Ri\times S^{D-1}$, with a two-dimensional Rindler spacetime $Ri$. This spacetime approximates the near horizon geometry of (D+1)-dimensional black hole. By using the generalized Abel-Plana formula, the vacuum expectation values are presented as the sum of single brane and second brane induced parts. Various limiting cases are studied. The vacuum forces acting on the branes are decomposed into the self-action and interaction terms. The interaction forces are investigated as functions of the brane locations and coefficients in the boundary conditions.

Surface Casimir densities on a spherical brane in Rindler-like spacetimes

Abstract The vacuum expectation value of the surface energy–momentum tensor is evaluated for a scalar field obeying Robin boundary condition on a spherical brane in ( D + 1 ) -dimensional spacetime Ri × S D − 1 , where Ri is a two-dimensional Rindler spacetime. The generalized zeta function technique is used in combination with the contour integral representation. The surface energies on separate sides of the brane contain pole and finite contributions. Analytic expressions for both these contributions are derived. For an infinitely thin brane in odd spatial dimensions, the pole parts cancel and the total surface energy, evaluated as the sum of the energies on separate sides, is finite. For a minimally coupled scalar field the surface energy–momentum tensor corresponds to the source of the cosmological constant type.

Strings, dipoles and fuzzy spheres

I discuss a scaling limit, where open strings in the WZW-model behave as dipoles with charges confined to a spherical brane and projected to the lowest Landau level. Then I show how the joining and splitting interactions of these dipoles are naturally described using the fuzzy sphere algebra.

Casimir densities for a spherical brane in Rindler-like spacetimes

Wightman function, the vacuum expectation values of the field square and the energy–momentum tensor are evaluated for a scalar field obeying mixed boundary condition on a spherical brane in ( D + 1 ) -dimensional Rindler-like spacetime Ri × S D − 1 , where Ri is a two-dimensional Rindler spacetime. This spacetime approximates the near horizon geometry of ( D + 1 ) -dimensional black hole in the large mass limit. The vacuum expectation values are presented as the sum of boundary-free and brane-induced parts. Further we extract from the Wightman function for the boundary-free geometry the corresponding function in the bulk R 2 × S D − 1 . For the latter geometry the vacuum expectation values of the field square and the energy–momentum tensor do not depend on the spacetime point. For the renormalization of these quantities we use zeta regularization technique. Various limiting cases of the brane-induced vacuum expectation values are investigated.

Logarithmic Corrections to the FRW Brane Cosmology from 5d Schwarzschild–de Sitter Black Hole

Thermodynamics of 5d SdS black hole is considered. Thermal fluctuations define the (sub-dominant) logarithmic corrections to black hole entropy and then to Cardy–Verlinde formula and to FRW brane cosmology. We demonstrate that logarithmic terms (which play the role of effective cosmological constant) change the behavior of 4d spherical brane in dS, SdS or Nariai bulk. In particularly, bounce Universe occurs or 4d dS brane expands to its maximum and then shrinks. The entropy bounds are also modified by next-to-leading terms. Out of braneworld context the logarithmic terms may suggest slight modification of standard FRW cosmology.

Decay modes of intersecting fluxbranes

Just as the single fluxbrane is quantum mechanically unstable to the nucleation of a locally charged spherical brane, so intersecting fluxbranes are unstable to various decay modes. Each individual element of the intersection can decay via the nucleation of a spherical brane, but uncharged spheres can also be nucleated in the region of intersection. For special values of the fluxes, however, intersecting fluxbranes are supersymmetric, and so are expected to be stable. We explicitly consider the instanton describing the decay modes of the two--element intersection (an F5-brane in the string theory context), and show that in dimensions greater than four the action for the decay mode of the supersymmetric intersection diverges. This observation allows us to show that stable intersecting fluxbranes should also exist in type 0A string theory.

On higher-dimensional fuzzy spherical branes

Matrix descriptions of higher-dimensional spherical branes are investigated. It is known that a fuzzy 2 k-sphere is described by the coset space SO(2 k+1)/ U( k) and has some extra dimensions. It is shown that a fuzzy 2 k-sphere is comprised of n k(k−1) 2 spherical D(2 k−1)-branes and has a fuzzy 2( k−1)-sphere at each point. We can understand the relationship between these two viewpoints by the dielectric effect. Contraction of the algebra is also discussed.

Supersymmetry and branes in M-theory plane waves

We study brane embeddings in M-theory plane waves and their supersymmetry. The relation with branes in AdS backgrounds via the Penrose limit is also explored. Longitudinal planar branes originate from AdS branes while giant gravitons of AdS spaces become spherical branes which are realized as fuzzy spheres in the massive matrix theory.

Higher-dimensional geometries from matrix brane constructions

Matrix descriptions of even-dimensional fuzzy spherical branes S 2 k in Matrix Theory and other contexts in type II superstring theory reveal, in the large N limit, higher-dimensional geometries SO(2 k+1)/ U( k), which have an interesting spectrum of SO(2 k+1) harmonics and can be up to 20-dimensional, while the spheres are restricted to be of dimension less than 10. In the case k=2, the matrix description has two dual field theory formulations. One involves a field theory living on the non-commutative coset SO(5)/ U(2) which is a fuzzy S 2 fibre bundle over a fuzzy S 4. In the other, there is a U( n) gauge theory on a fuzzy S 4 with O(n 3) instantons. The two descriptions can be related by exploiting the usual relation between the fuzzy two-sphere and U( n) Lie algebra. We discuss the analogous phenomena in the higher-dimensional cases, developing a relation between fuzzy SO(2 k)/ U( k) cosets and unitary Lie algebras.

From p-branes to fluxbranes and back

In this note we study aspects of the interplay between fluxbranes and p-branes. We describe how a fluxbrane can be physically realized as a limit of a brane-antibrane configuration, in a manner similar to the way a uniform electric field appears in between the plates of a capacitor. We also study the evolution of a fluxbrane after nucleation of p-branes. We find that Kaluza-Klein fluxbranes do relax by forming brane-antibrane pairs or spherical branes, but we also find that for fluxtubes with dilaton coupling in a different range, the field strength does not relax, instead it becomes stronger after each nucleation bounce. We speculate on a possible runaway instability of such fluxtubes an an eventual breakdown of their classical description.