All the 7 dynamical second order transport coefficients of the nonconformal fluids that correspond to Dp-branes with one or more world-volume directions compactified are derived via fluid/gravity correspondence. The conditions considered in this paper include D4-brane with 1, 2 or 3 compact directions, D3-brane with 1 or 2 compact directions, as well as D2-brane with 1 direction compactified. The derived second order transport coefficients satisfy the Haack-Yarom, Romatschke and Kleinert-Probst relations.
We develop the framework of boundary derivative expansion (BDE) formalism of fluid/gravity correspondence in compactified D4-brane system, which is a nonconformal background used in top-down holographic QCD models. Such models contain the D4-D6 model and the Sakai-Sugimoto (SS) model, with the background of the compactified black D4 branes under the near horizon limit. By using the dimensional reduction technique, we derive a 5D Einstein gravity minimally coupled with 3 scalar fields from the 10D D4-brane background. Following the BDE formalism of fluid/gravity correspondence in the conformal …
We derive all the dynamical second order transport coefficients for Dp-brane with $p$ from 1 to 6 within the framework of fluid/gravity correspondence in this paper. The D5 and D6-brane do not have dual relativistic fluids; D3-brane corresponds to 4-dimensional conformal relativistic fluid; D1, D2 and D4-brane separately correspond to nonconformal relativistic fluids of dimensions 2, 3 and 5. The Haack-Yarom relation only exists for Dp-branes with $p$ larger than 2 and is also satisfied by them. We also find that the Romatschke and Kleinert-Probst relations need to be generalized in order to b…
We develop the boundary derivative expansion (BDE) formalism of fluid/gravity correspondence to nonconformal version through the compactified, near-extremal black D4-brane. We offer an explicit calculation of 9 second order transport coefficients, i.e., the $τ_π,~τ_π^*,~τ_Π,~λ_{1,2,3}$ and $ξ_{1,2,3}$ for the strongly coupled, uncharged and nonconformal relativistic fluid which is the holographic dual of compactified, near extremal black D4-brane. We also show that the nonconformal fluid considered in this work is free of causal problem and admits the Haack-Yarom relation $4λ_1+λ_2=2ητ_π$.
The entanglement entropy of various geometries is calculated for the boundary theory dual to a stack of N Dp-branes. The entanglement entropies are readily expressed in terms of the effective coupling at the appropriate energy scales. The results are also compared to the entropy density of a black brane and some universal properties of holographic entropy are found.
We compute the vacuum one loop amplitude for two D-strings at an angle compactified on $T^2$ as a function of the transverse separation and the winding numbers. We show that in certain cases the amplitude is independent on whether the D-strings are compactified or not.
We examine the dynamics of a $Dp$-brane in the background of $k$ coincident, parallel $NS$5-branes which have had one of their common transverse directions compactified. We find that for small energy, bound orbits can exist at sufficiently large distances where there will be no stringy effects. The orbits are dependent upon the energy density, angular momentum and electric field. The analysis breaks down at radial distances comparable with the compactification radius and we must resort to using a modified form of the harmonic function in this region.
By using the boundary derivative expansion formalism of fluid/gravity correspondence, we study the chiral vortical effect from the compactified D4-branes with smeared D0-brane charge. This background corresponds to a strongly coupled, nonconformal relativistic fluid with a conserved vector current. The presence of the chiral vortical effect is induced by the addition of a Chern-Simons term in the bulk action. Except that the non-dissipative anomalous viscous coefficient and the sound speed rely only on the chemical potential, most of the other thermal and hydrodynamical quantities of the first…
We give a simple proof of the known S-duality of Heterotic String theory compactified on a T^6. Using this S-duality we calculate the tensions for a class of BPS 5-branes in Heterotic String theory on a circle. One of these, the Kaluza-Klein monopole, becomes tensionless when the radius of the circle is equal to the string length. We study the question of stability of the Heterotic NS5-brane with a transverse circle. For large radii the NS5-brane is absolutely stable. However for small radii it is only marginally stable. We also study the moduli space of 2 Kaluza-Klein monopoles and show that …
In the M(atrix) theory by making the expansions of the matrices around the membrane and four-brane solutions we derive the three- and five-dimensional gauge theories on the dual tori. The explicit forms of solutions yield the dual coordinates and each expansion is related to a toroidal compactification of the M(atrix) theory. From the derived Lorentz and gauge invariant actions the gauge coupling constants are shown to be characterized by the volume of the dual tori.
A supersymmetric non-Abelian self-dual gauge theory with the explicit introduction of Kaluza-Klein modes is proposed to give a classical description of multiple M5-branes on $R^5 \times S^1$. The gauge symmetry is parametrized by Lie-algebra valued 1-forms with the redundancy of a 0-form, and the supersymmetry transformations without gauge-fixing are given. We study BPS configurations involving KK modes, including M-waves and M2-branes with non-trivial distributions around the circle. Finally, this supersymmetric gauge theory of two-forms can be equipped with more general non-Abelian gerbes in…
We first calculate the holographic entanglement entropy of M5 branes on a circle and see that it has phase transition during decreasing the compactified radius. In particular, it is shown that the entanglement entropy scales as $N^3$. Next, we investigate the holographic entanglement entropy of D0+D4 system on a circle and see that it scales as $N^2$ at low energy, likes as a gauge theory with instantons. However, at high energy it transforms to a phase which scales as $N^3$, like as M5 branes system. We also present the general form of holographic entanglement entropy of Dp, ${\rm D_p+D_{p+4}…
We show that the same wrapping rules that have been derived for the branes of IIA and IIB string theory also apply to the branes of the toroidally compactified heterotic string theory. Moreover, we show that applying these wrapping rules to the IIA theory compactified over K3 is consistent with the well-known duality between the heterotic string theory compactified over T^4 and the IIA string theory compactified over K3. We derive a simple rule that relates, in any dimension, the T-duality representation of the branes of the toroidally compactified heterotic theory to the relevant R-symmetry r…
Solutions of the undeformed IKKT matrix model with structure R^{3,1} x K are presented, where the noncommutativity relates the compact with the non-compact space. The extra dimensions are stabilized by angular momentum, and the scales of K are generic moduli of the solutions. Explicit solutions are given for K= T^2, K= T^4, K = S^2 x T^2 and K = S^2 x S^2. Infinite towers of Kaluza-Klein modes may arise in some directions, along with an effective UV cutoff on the non-compact space. Deformations of these solutions carry NC gauge theory coupled to (emergent) gravity. Analogous solutions of the B…
Motivated by the recent D-brane constructions of world-volume monopoles and instantons, we study the supersymmetric SU(N) Yang-Mills theory on $S^1 \times R^{3+1}$, spontaneously broken by a Wilson loop. In addition to the usual N-1 fundamental monopoles, the N-th BPS monopole appears from the Kaluza-Klein sector. When all N monopoles are present, net magnetic charge vanishes and the solution can be reinterpreted as a Wilson-loop instanton of unit Pontryagin number. The instanton/multi-monopole moduli space is explicitly constructed, and seen to be identical to a Coulomb phase moduli space of …
We investigate the cosmological consequences of a two brane system embedded in a higher dimensional background spacetime with a compactified extra dimension described with an action that include the intrinsic curvature for each brane. We find that the dynamics of each brane is related to the other by means of cosmological restrictions that involve the scale factors, the equation of state parameters and the Hubble parameters of the two branes. We analyze the evolution of the scale factor and the equation of state parameter for the hidden brane when in the visible brane is present a cosmological…
We investigate the role of quantum fluctuations in the system composed of two branes bounding a region of AdS. It is shown that the modulus effective potential generated by quantum fluctuations of both brane and bulk fields is incapable of stabilizing the space naturally at the separation needed to generate the hierarchy. Consequently, a classical stabilization mechanism is required. We describe the proper method of regulating the loop integrals and show that, for large brane separation, the quantum effects are power suppressed and therefore have negligible affects on the bulk dynamics once a …
We compute Yukawa couplings in type IIB string theory compactified on a non factorisable six-torus in the presence of D9 branes and fluxes. The setting studied in detail, is obtained by T-dualising an intersecting brane configuration of type IIA theory compactified on a torus generated by the SO(12) root lattice. Particular deformations of such torus are taken into account and provide moduli dependent couplings. Agreement with the type IIA result is found in a non trivial way. The classical type IIB calculation gives also information on a factor accessible only by quantum computations on the t…
We develop and study a D-brane realization of 4D N=2 super Yang-Mills theory. It is a type IIB string theory compactified on R^6\times K3 and containing parallel 7-branes. It can also be regarded as a subsector of Vafa's F-theory compactified on K3\times K3 and is thus dual to the heterotic string on K3\times T^2. We show that the one-loop prepotential in this gauge theory is exactly equal to the interaction produced by classical closed string exchange. A monopole configuration corresponds to an open Dirichlet 5-brane wrapping around K3 with ends attached to two 7-branes.
The hamiltonian formulation of the supersymmetric closed 2-brane dual to the double compactified D=11 closed supermembrane is presented. The formulation is in terms of two U(1) vector fields related by the area preserving constraint of the SUSY 2-brane. Stable solutions of the field equations, which are local minima of the hamiltonian, are found. In the semiclassical approximation around the stable solutions the action becomes the reduction of D=10 Super-Maxwell to the worldvolume. The solutions carry RR charges as a type of magnetic charges associated with the worldvolume vector field. The ge…
We study compactified brane solutions of type R^4 x K in the IIB matrix model, and obtain explicitly the bosonic and fermionic fluctuation spectrum required to compute the one-loop effective action. We verify that the one-loop contributions are UV finite for R^4 x T^2, and supersymmetric for R^3 x S^1. The higher Kaluza-Klein modes are shown to have a gap in the presence of flux on T^2, and potential problems concerning stability are discussed.
We review exact results obtained for R^4 couplings in maximally supersymmetric type II string theories. These couplings offer a privileged scene to understand the rules of semiclassical calculus in string theory. Upon expansion in weak string coupling, they reveal an infinite sum of non-perturbative e^{-1/g} effects that can be imputed to euclidean D-branes wrapped on cycles of the compactification manifolds. They also shed light on the relation between Dp-branes and D-(p-2)branes, D-strings and (p,q) strings, instanton sums and soliton loops. The latter interpretation takes over in D<=6 in or…
We show how the brane wrapping rules, recently discovered in closed oriented string theories compactified on tori, are extended to the case of the Type IIA string compactified on K3. To this aim, a crucial role is played by the duality between this theory and the Heterotic string compactified on a four-dimensional torus T^4. We first show how the wrapping rules are applied to the T^4/Z_N orbifold limits of K3 by relating the D0 branes, obtained as D2 branes wrapping two-cycles, to the perturbative BPS states of the Heterotic theory on T^4. The wrapping rules are then extended to the solitonic …
We consider novel nonperturbative effects of type I theories compactified on singular ALE spaces obtained by adding NS branes. Such effects include a description of small $E_8$ instantons at singularities.
We construct the scalar profile for the non-abelian self dual string connecting two M5-branes compactified on a light-like circle. The construction is based on a conjectured modified version of Nahm's equations describing a D2-brane, with a magnetic field on it, suspended between two D4-branes. Turning on a constant magnetic field on the D2-brane corresponds to a boost in the eleventh direction. In the limit of infinite boost the D4-branes correspond to light-like compactified M5-branes. The solution for the scalar profile of the brane remains finite in this limit and displays all the correct …
The $D$-brane spectra in the Type IIB string theory compactified on $AdS_{p+2}\times S^{8-p}$ are computed using the K-theory approach. The results signal the existence of the mirror-symmetry-analogue for $D$-branes, analogous to that rised in the context of derived categories.
A new family of analytical solutions in a four dimensional static spacetime is presented for $f\left( R\right) $-gravity. In contrast to General Relativity, we find that a non trivial black string/ring solution is supported in vacuum power law $f\left( R\right) $-gravity for appropriate values of the parameters characterizing the model and when axisymmetry is introduced in the line element. For the aforementioned solution, we perform a brief investigation over its basic thermodynamic quantities.
The combined Einstein equations and scalar equation of motion in the Horava-Witten scenario of the strongly coupled heterotic string compactified on a Calabi-Yau manifold are solved in the presence of additional matter densities on the branes. We take into account the universal Calabi-Yau modulus phi with potentials in the 5-d bulk and on the 3-branes, and allow for an arbitrary coupling of the additional matter to phi and an arbitrary equation of state. No ad hoc stabilization of the five dimensional radius is assumed. The matter densities are assumed to be small compared to the potential for…
We show that the thin wall limit of the thick domain wall associated with a sine-Gordon soliton in a single non-compactified patch of 5-dimensional spacetime explicitly yields the Randall-Sundrum localized gravity two patch brane, with its discrete $Z_2$ symmetry arising from the discrete symmetry of the potential, and with the thin Minkowski brane $Λ_5+κ^2_5Λ^2_b/6=0$ relation between bulk and brane cosmological constants arising naturally without any need for fine tuning. Additionally we show that for an embedded thin de Sitter brane, localization of gravity is again possible provided the 5-…
As an extension to our previous work, we study the transport properties of the Witten-Sakai-Sugimoto model in the black D4-brane background with smeared D0-branes (D0-D4/D8 system). Because of the presence of the D0-branes, in the bubble configuration this model is holographically dual to 4d QCD or Yang-Mills theory with a Chern-Simons term. And the number density of the D0-branes corresponds to the coupling constant ($θ$ angle) of the Chern-Simons term in the dual field theory. In this paper, we accordingly focus on small number density of the D0-branes to study the sound mode in the black D0…
In the framework of Type IIB String Theory compactified on a general six-torus T6 with arbitrary complex structure, Yukawa couplings are determined for the chiral matter described by open strings ending on D9-branes having different oblique magnetization.
A mechanism for emergent gravity on brane solutions in Yang-Mills matrix models is exhibited. Newtonian gravity and a partial relation between the Einstein tensor and the energy-momentum tensor can arise from the basic matrix model action, without invoking an Einstein-Hilbert-type term. The key requirements are compactified extra dimensions with extrinsic curvature M^4 x K \subset R^D and split noncommutativity, with a Poisson tensor θ^{ab} linking the compact with the noncompact directions. The moduli of the compactification provide the dominant degrees of freedom for gravity, which are trans…
In the framework of low-energy effective actions of branes compactified on magnetized extra-dimensions, we determine Yukawa couplings for the chiral matter described by open strings attached to D9 branes having different oblique magnetization and living on a general torus T6 with an arbitrary complex structure. These results generalize the ones existing in literature.
We construct M-theory curves associated with brane configurations of SU(N), SO(N) and $Sp(2N)$ 5d supersymmetric gauge theories compactified on a circle. From the curves we can account for all the existing different SU(N) field theories with $N_f \leq 2 N$. This is the correct bound for $N \geq 3$. We remark on the exceptional case SU(2). The bounds obtained for SO(N) and $Sp(2N)$ are $N_f\leq N-4$ and $N_f\leq 2N+4$, respectively.
The D-brane spectrum of a class of $\Zop_2$ orbifolds of toroidally compactified Type IIA and Type IIB string theory is analysed systematically. The corresponding K-theory groups are determined and complete agreement is found. The charge densities of the various branes are also calculated.
It is shown that the dual of the double compactified D=11 Supermembrane and a suitable compactified D=10 Super 4D-brane with nontrivial wrapping on the target space may be formulated as noncommutative gauge theories. The Poisson bracket over the world-volume is intrinsically defined in terms of the minima of the hamiltonian of the theory, which may be expressed in terms of a non degenerate 2-form. A deformation of the Poisson bracket in terms of the Moyal brackets is then performed. A noncommutative gauge theory in terms of the Moyal star bracket is obtained. It is shown that all these theorie…
We present the formulation of the bosonic Hamiltonian M2-brane compactified on a twice punctured torus following the procedure proposed in \cite{mpgm14}. In this work we analyse two possible metric choice, different from the one used in \cite{mpgm14}, over the target space and study some of the properties of the corresponding Hamiltonian.
In the models of brane construction, the isometry of a compactified space might be broken by branes. In four-dimensional effective Lagrangian, the breaking of the isometry is seen as the spontaneous breaking of the corresponding effective symmetry. Then it seems natural to expect that there are various kinds of defects that will be implemented by the spontaneous symmetry breaking. These defects are parametrized by the brane positions. In this paper we consider two kinds of such ``brane defects'', which are formed by the local fluctuations of the locations of branes along their transversal dire…
We construct orientifolds of type IIA string theory. The theory is compactified on a T^6/Z_N times Z_M orbifold. In addition worldsheet parity in combination with a reflection of three compact directions is modded out. Tadpole cancellation requires to add D-6-branes at angles. The resulting four dimensional theories are N=1 supersymmetric and non-chiral.
We consider the effective action of M-theory compactified on a S^1/Z_2 orbifold with R^2 interaction in the Gauss-Bonnet combination. We derive equations of motion with source terms arising from the Gauss-Bonnet terms and find the M2-brane solution up to order κ^{2/3}. It receives a correction which depends on the orbifold coordinate in the same form as the gauge 5-brane solution.
We extend the search for fermionic subspaces of the bosonic string compactified on E8 X SO(16) lattices to include all fermionic D-branes. This extension constraints the truncation procedure previously proposed and relates the fermionic strings, supersymmetric or not, to the global structure of the SO(16) group. The specific properties of all the fermionic D-branes are found to be encoded in its universal covering, whose maximal toroid defines the configuration space torus of their mother bosonic theory.
This paper is an investigation of the effects of a thermal bulk fluid in brane world models compactified on AdS_5. Our primary purpose is to study how such a fluid changes the bulk dynamics and to compare these effects with those generated by matter localized to the branes. We find an exact cosmological solution for a thermally excited massless bulk field, as well as perturbative solutions with matter on the brane and in the bulk. We then perturb around these solutions to find solutions for a massive bulk mode in the limit where the bulk mass (m_B) is small compared to the AdS curvature scale …
It is shown that any anisotropic and inhomogeneous cosmological solution to the lowest-order, four-dimensional, dilaton-graviton string equations of motion may be employed as a seed to derive a curved, three-brane cosmological solution to five-dimensional heterotic M-theory compactified on a Calabi-Yau three-fold. This correspondence formally relates a weakly coupled string cosmology directly with a strongly coupled one. The asymptotic behaviour of a wide class of spatially homogeneous braneworlds is deduced. Similar solutions may be derived in toroidally compactified massive type IIA supergra…
We study a class of eight-supercharge little string theories (LSTs) on the world-volume of $N$ M5-branes with transverse space $\mathbb{S}^{1}\times (\mathbb{C}^2/\mathbb{Z}_M)$. These M-brane configurations compactified on a circle are dual to $M$ D5-branes intersecting $N$ NS5-branes on $\mathbb{T}^2\times \mathbb{R}^{7,1}$ as well as to F-theory compactified on a toric Calabi-Yau threefold $X_{N,M}$. We argue that the Kähler cone of $X_{N,M}$ admits three regions associated with weakly coupled quiver gauge theories of gauge groups $[U(N)]^M, [U(M)]^N$ and $[U(\frac{NM}{k})]^k$ where $k=\mbo…
We study a special combination of the compact directions of the spacetime (compactified on tori) and the worldsheet parity transformed of these directions. The transformations that change the compact part of the spacetime to this combination, are more general than the T-duality transformations. Many properties of this combination and also of the corresponding worldsheet fermions are studied. By using the boundary state formalism, we study the effects of the above transformations to D-branes. For the special cases the resulted branes reduce to the known mixed branes, or reduce to the modified m…
In the Matrix theories compactified on the $d$ dimensional torus with $d = 5, 6, 7$ which are described by the theories of D$d$-branes in the type IIA or IIB theory on the $d$ dimensional dual torus we analyze the BPS bound states of the background D$d$-brane with other objects by taking the matrix theory limit. Through the Nahm duality transformation the flux and the momentum multiplets for these BPS states are shown to be associated with the black holes and the black strings respectively from the viewpoint of the weakly coupled type IIA string theory compactified on the $d-1$ dimensional tor…
M(atrix) theory compactified on an orbifold ${\bf T}_9/{\bf Z}_2$ is studied. Via zero-brane parton scattering we find that each of the $2^9 = 512$ orbifold fixed points carry $-1/32$ units of zero-brane charge. The anomalous flux is cancelled by introducing a twisted sector consisting of 32 zero-branes that are spacetime supersymmetry singlets. These twisted sector zero-branes are nothing but gravitational waves propagating along the M-theory direction. There is no D0-partons in the untwisted sector, a fact consistent with holographic principle. For low-energy excitations, the orbifold compac…
In the paradigm with a small warped Spacelike Extra Dimensions (SED), the Higgs field is in general localized at a boundary of the SED (TeV-brane) where the gravity scale is redshifted to the TeV by a warp factor. If the SM gauge bosons and fermions propagate into the warped SED, one can generate the mass hierarchy for fermions. It is thus crucial to treat carefully the TeV-brane localized masses for such fermions, which is done in the literature by applying a regularization process suffering from a lack of consistency and more importantly being useless, as we demonstrate in detail in the pres…
In this note we study T-duality transformations for the NS5-brane and its orbifolds along angular directions. We identify a geometric charge for these configurations and show that it is interchanged with the H-flux under T-duality. We furthermore perform a supersymmetry analysis and find that T-duality can break supersymmetry, in agreement with earlier results in the literature. We contrast our findings to compactifications of the NS5-brane on tori, which have vanishing geometric charge and for which T-duality transformations along the compact directions preserve supersymmetry. This shows that…
By considering 5--dimensional cosmological models with a bulk filled with a perfect fluid and a cosmological constant, we have found regular instantonic solution which is free from any singularity at the origin of the extra--coordinate and describe 5--dimensional asymptotically anti de Sitter wormhole, when the bulk has a topology $ R \times S^4 $ and is filled with dust and a negative cosmological constant. Compactified brane-world instantons which are built up from such instantonic solution describe either a single brane or a string of branes. Their analytical continuation to the pseudo--Rie…
Exact Newtonian potential with an extra space dimension compactified on a circle is derived and studied. It is found that a point mass located at one side of the circle can generate almost the same strength of gravitational force at the other side. Combined with the brane-world scenarios, it means that although one can not see a particle which is confined to another brane, one can feel its gravity explicitly as if it were located on our brane. This leads to the conclusion that matter on all branes may contribute equally to the curvature of our brane. Therefore, dark matter is probably nothing …
Five and six dimensional SUSY gauge theories, with one or two compactified directions, are discussed. The 5d theories with the matter hypermultiplets in the fundamental representation are associated with the twisted $XXZ$ spin chain, while the group product case with the bi-fundamental matter corresponds to the higher rank spin chains. The Riemann surfaces for $6d$ theories with fundamental matter and two compact directions are proposed to correspond to the $XYZ$ spin chain based on the Sklyanin algebra. We also discuss the obtained results within the brane and geometrical engeneering framewor…
We formulate a six dimensional $U(1)$ gauge theory compactified on a (two dimensional) sphere $S^2$ with flux and localized brane sources. Profiles of the lowest Kaluza-Klein (KK) wavefunctions and their masses are derived analytically. In contrast to ordinary sphere compactifications, the above setup can lead to the degeneracy of and the sharp localizations of the linearly independent lowest KK modes, depending on the number of branes and their tensions. Moreover, it can naturally accommodate CP violation in Yukawa interactions.
Cosmic strings in the brane Universe have recently gained a great interest. I think the most interesting story is that future cosmological observations distinguish them from the conventional cosmic strings. If the strings are the higher-dimensional objects that can (at least initially) move along the compactified space, and finally settle down to (quasi-)degenerated vacua in the compactified space, then kinks should appear on the strings, which interpolate between the degenerated vacua. These kinks look like ``beads'' on the strings, which means that the strings turn into necklaces. Moreover, …
