D3-D7 System Research Articles

Holographic Chern-Simons defects

We study SU(N) Yang-Mills-Chern-Simons theory in the presence of defects that shift the Chern-Simons level from a holographic point of view by embedding the system in string theory. The model is a D3-D7 system in Type IIB string theory, whose gravity dual is given by the AdS soliton background with probe D7-branes attaching to the AdS boundary along the defects. We holographically renormalize the free energy of the defect system with sources, from which we obtain the correlation functions for certain operators naturally associated to these defects. We find interesting phase transitions when the separation of the defects as well as the temperature are varied. We also discuss some implications for the Fractional Quantum Hall Effect and for two-dimensional QCD.

Entanglement entropy and differential entropy for massive flavors

Abstract In this paper we compute the holographic entanglement entropy for massive flavors in the D3-D7 system, for arbitrary mass and various entangling region geometries. We show that the universal terms in the entanglement entropy exactly match those computed in the dual theory using conformal perturbation theory. We derive holographically the universal terms in the entanglement entropy for a CFT perturbed by a relevant operator, up to second order in the coupling; our results are valid for any entangling region geometry. We present a new method for computing the entanglement entropy of any top-down brane probe system using Kaluza-Klein holography and illustrate our results with massive flavors at finite density. Finally we discuss the differential entropy for brane probe systems, emphasising that the differential entropy captures only the effective lower-dimensional Einstein metric rather than the ten-dimensional geometry.

Shock waves in Lifshitz-like spacetimes

We construct shock waves for Lifshitz-like geometries in four- and fivedimensional effective theories as well as in D3-D7 and D4-D6 brane systems. The solutions to the domain wall profile equations are found. Further, the study makes a connection with the implications for the quark-gluon plasma formation in heavy-ion collisions. According to the holographic approach, the multiplicity of particles produced in heavy-ion collisions can be estimated by the area of the trapped surface formed in shock wave collisions. We calculate the areas of trapped surfaces in the geometry of two colliding Lifshitz domain walls. Our estimates show that for five-dimensional cases with certain values of the critical exponent the dependence of multiplicity on the energy of colliding ions is rather close to the experimental data $$ \mathrm{\mathcal{M}} $$ ∼ s 0.15 observed at RHIC and LHC.

Embedding massive flavor in ABJM

We add massive fundamental matter to the ABJM model by adding D6-branes wrapped asymptotically over RP3. We find two types of solutions at finite temperature, one that enters the black hole and one that ends before the black hole. We analyze the behavior of the free energy as a function of temperature, and find that the system exhibits a phase transition between the two types of solutions, similar to what happens in the D3-D7 system. We also analyze the meson spectrum in the model and find several massive scalar modes, again, quite like the D3-D7 system. We end with a calculation of the conductivities in the two phases.

Consistent reduction of charged D3-D7 systems

We provide a consistent reduction to five dimensions of the system of D3-branes at Calabi-Yau singularities coupled to D7-branes with world-volume gauge flux. The D3-branes source the dual to would-be conformal quiver theories. The D7-branes, which are homogeneously distributed in their transverse directions, are dual to massless matter in the fundamental representation at finite (baryon) density. We provide the five-dimensional action and equations of motion, and discuss a few sub-truncations. The reduction can be used in the study of transport properties and stability of D3-D7 charged systems.

Noncritical holographic QCD in external electric field

We investigate behavior of a noncritical model in external electric field and explore its phase structure in the quenched approximation N f ≪ N c . We compute the conductivity of QCD plasma in this model and compare it with the predictions of Sakai–Sugimoto model, D3–D7 system and lattice simulations. We find that, while the behavior of conductivity in noncritical model as a function of temperature and baryon density is similar to those of D3–D7 system, the phase diagram of noncritical model resembles the phase diagram of Sakai–Sugimoto model.

Deconstructing holographic liquids

We argue that there exist simple effective field theories describing the long-distance dynamics of holographic liquids. The degrees of freedom responsible for the transport of charge and energy–momentum are Goldstone modes. These modes are coupled to a strongly coupled infrared (IR) sector through emergent gauge and gravitational fields. The IR degrees of freedom are described holographically by the near-horizon part of the metric, whereas the Goldstone bosons are described by a field-theoretical Lagrangian. In the cases where the holographic dual involves a black hole, this picture allows for a direct connection between the holographic prescription where currents live on the boundary and the membrane paradigm where currents live on the horizon. The zero-temperature sound mode in the D3–D7 system is also re-analyzed and re-interpreted within this formalism.

D3-D7 quark-gluon plasmas at finite baryon density

We present the string dual to SU(Nc) N=4 SYM, coupled to Nf massless fundamental flavors, at finite temperature and baryon density. The solution is determined by two dimensionless parameters, both depending on the 't Hooft coupling $\lambda_h$ at the scale set by the temperature T: $\epsilon_h\sim\lambda_h Nf/Nc$, weighting the backreaction of the flavor fields and $\tilde\delta\sim\lambda_h^{-1/2}nb/(Nf T^3)$, where $nb$ is the baryon density. For small values of these two parameters the solution is given analytically up to second order. We study the thermodynamics of the system in the canonical and grand-canonical ensembles. We then analyze the energy loss of partons moving through the plasma, computing the jet quenching parameter and studying its dependence on the baryon density. Finally, we analyze certain "optical" properties of the plasma. The whole setup is generalized to non abelian strongly coupled plasmas engineered on D3-D7 systems with D3-branes placed at the tip of a generic singular Calabi-Yau cone. In all the cases, fundamental matter fields are introduced by means of homogeneously smeared D7-branes and the flavor symmetry group is thus a product of abelian factors.

Quantum phase transition in a Dp-Dq system

Using the top-down approach, we study intersecting Dp-Dq brane configuration in string theory and find examples, where there can be a quantum phase transition at zero temperature induced by the violation of the Breitenlohner-Freedman bound at IR, which is done essentially by a combination of charge density and magnetic fields. In particular, there exists a Berezinskii-Kosterlitz-Thouless (BKT) type of transition for D3-D5 and D5-D5 systems. The study of the BKT type of transition is initiated by Jensen et al. [Phys. Rev. Lett. 105, 041601 (2010)] for a D3-D5 system with nonzero charge density and a magnetic field. Here, we show that one can have the BKT transition for a D3-D5 system even in the absence of charge density but requires multiple magnetic fields. In this case the field theory lives in $2+1$ dimensions, whereas for the D5-D5 type, the transition requires the presence of both the charge density and magnetic fields and the dual field theory lives on a $3+1$ dimensional spacetime. We also study the D3-D7 system but it does not show the BKT type of transition.

Holographic Roberge-Weiss transitions

We investigate N=4 SYM coupled to fundamental flavours at nonzero imaginary quark chemical potential in the strong coupling and large N limit, using gauge/gravity duality applied to the D3-D7 system, treating flavours in the probe approximation. The interplay between Z(N) symmetry and the imaginary chemical potential yields a series of first-order Roberge-Weiss transitions. An additional thermal transition separates phases where quarks are bound/unbound into mesons. This results in a set of Roberge-Weiss endpoints: we establish that these are triple points, determine the Roberge-Weiss temperature, give the curvature of the phase boundaries and confirm that the theory is analytic in mu^2 when mu^2~0.

Holographic integral equations and walking technicolor

We study chiral symmetry breaking in the holographic D3-D7 system in a simple model with an arbitrary running coupling. We derive equations for the D7 embedding and show there is a light pion. In particular we present simple integral equations, involving just the running coupling and the quark self energy, for the quark condensate and the pion decay constant. We compare these to the Pagels-Stokar or constituent quark model equivalent. We discuss the implications for walking Technicolour theories. We also perform a similar analysis in the four dimensional field theory whose dual is the non-supersymmetric D3-D5 system and propose that it represents a walking theory in which the quark condensate has dimension 2 + sqrt{3}.

D3-D7 quark-gluon plasmas

We present the string dual to finite temperature SU(Nc) = 4 SYM coupled to massless fundamental matter introduced by Nf D7 branes, with Abelian flavor symmetry. The analytic solution includes the backreaction of the flavors up to second order in the parameter that weighs the internal flavor loops, h = (λhNf)/(8π2Nc), λh being the 't Hooft coupling at the temperature of the dual Quark-Gluon Plasma. We study the thermodynamics of the system and its departure from conformality, which is a second order effect. We then analyze the energy loss of partons moving through the plasma, finding that the fundamental degrees of freedom enhance the jet quenching. The whole setup is generalized to D3-D7 systems with D3-branes placed at the tip of a generic singular Calabi-Yau cone over a five-dimensional Sasaki-Einstein manifold. We finally provide the equations for the inclusion of massive flavors in the = 4 SYM plasma.

On string theory duals of Lifshitz-like fixed points

We present type IIB supergravity solutions which are expected to be dual to certain Lifshitz-like fixed points with anisotropic scale invariance. They are expected to describe a class of D3-D7 systems and their finite temperature generalizations are straightforward. We show that there exist solutions that interpolate between these anisotropic solutions in the IR and the standard AdS5 solutions in the UV. This predicts anisotropic RG flows from familiar isotropic fixed points to anisotropic ones. In our case, these RG flows are triggered by a non-zero theta-angle in Yang-Mills theories that linearly depends on one of the spatial coordinates. We study the perturbations around these backgrounds and discuss the possibility of instability. We also holographically compute their thermal entropies, viscosities, and entanglement entropies.

Fractional quantum Hall effect via holography: Chern-Simons, edge states and hierarchy

We present three holographic constructions of fractional quantum Hall effect (FQHE) via string theory. The first model studies edge states in FQHE using supersymmetric domain walls in = 6 Chern-Simons theory. We show that D4-branes wrapped on 1 or D8-branes wrapped on 3 create edge states that shift the rank or the level of the gauge group, respectively. These holographic edge states correctly reproduce the Hall conductivity. The second model presents a holographic dual to the pure U(N)k (Yang-Mills-)Chern-Simons theory based on a D3-D7 system. Its holography is equivalent to the level-rank duality, which enables us to compute the Hall conductivity and the topological entanglement entropy. The third model introduces the first string theory embedding of hierarchical FQHEs, using IIA string on 2/Zn.

Gravity dual of a quantum Hall plateau transition

We show how to model the transition between distinct quantum Hall plateaus in terms of D-branes in string theory. A low energy theory of 2+1 dimensional fermions is obtained by considering the D3-D7 system, and the plateau transition corresponds to moving the branes through one another. We study the transition at strong coupling using gauge/gravity duality and the probe approximation. Strong coupling leads to a novel kind of plateau transition: at low temperatures the transition remains discontinuous due to the effects of dynamical symmetry breaking and mass generation, and at high temperatures is only partially smoothed out.

Planar quark scattering at strong coupling and universality

We discuss scattering of fundamental matter in the planar and strong coupling limit via the AdS/CFT correspondence, generalizing the recently proposed calculation for adjoint matter due to Alday and Maldacena [arXiv:0705.0303]. Color decomposition of quark amplitudes is a key property allowing to repeat the procedure in the case of fundamental matter and to derive the relation of these strong coupling amplitudes to minimal area problems. We present the results for two different D3-D7 systems, one is only conformal in the planar limit and the other is exactly conformal. Our results suggest a universal behavior of scattering amplitudes at strong coupling and planar limit (both for gluons and quarks).

Erratum: Supergravity analysis of the hybrid inflation model from a D3–D7 system [Phys. Rev. D 69, 106001 (2004)

The slow-roll inflation is a beautiful paradigm, yet the inflaton potential can hardly be sufficiently flat when unknown gravitational effects are taken into account. However, the hybrid inflation models constructed in D = 4 N = 1 supergravity can be consistent with N = 2 supersymmetry, and can be naturally embedded into string theory. This article discusses the gravitational effects carefully in the string model, using D = 4 supergravity description. We adopt the D3--D7 system of Type IIB string theory compactified on K3 x T^2/Z_2 orientifold for definiteness. It turns out that the slow-roll parameter can be sufficiently small despite the non-minimal Kahler potential of the model. The conditions for this to happen are clarified in terms of string vacua. We also find that the geometry obtained by blowing up singularity, which is necessary for the positive vacuum energy, is stabilized by introducing certain 3-form fluxes.

Supergravity analysis of the hybrid inflation model from a D3-D7 system

Slow-roll inflation is a beautiful paradigm, yet the inflaton potential can hardly be sufficiently flat when unknown gravitational effects are taken into account. However, the hybrid inflation models constructed in $D=4,$ $\mathcal{N}=1$ supergravity can be consistent with $\mathcal{N}=2$ supersymmetry, and can be naturally embedded into string theory. This article discusses the gravitational effects carefully in the string model, using a $D=4$ supergravity description. We adopt the D3-D7 system of type IIB string theory compactified on a $K3\ifmmode\times\else\texttimes\fi{}{T}^{2}/{Z}_{2}$ orientifold for definiteness. It turns out that the slow-roll parameter can be sufficiently small despite the nonminimal K\"ahler potential of the model. The conditions for this to happen are given in terms of string vacua. We also find that the geometry obtained by blowing up the singularity, which is necessary for the positive vacuum energy, is stabilized by introducing certain three-form fluxes.

Semi-simple unification on / orientifold in the type IIB supergravity

The semi-simple unification model based on SU(5)_GUT \times U(3)_H gauge group is an interesting extension of the minimal SU(5)_GUT grand unification theory (GUT), since it solves the two serious problems in the standard GUT: the triplet-doublet splitting problem and the presence of dangerous dimension five operators for proton decay. Here, the extra U(3)_H gauge interaction plays a crucial role on the GUT breaking. In this paper, we show that the full multiplet structure of the U(3)_H sector required for the desired GUT breaking is reproduced naturally on T^6/Z_12 orientifold in the type IIB supergravity with a D3-D7 system. The SU(5)_GUT vector multiplet lives on D7-branes and the U(3)_H sector resides on D3-branes. We also show that various interesting features in the original SU(5)_GUT \times U(3)_H model are explained in the present brane-world scenario. A possible extension to the type IIB string theory is also discussed.

New type IIB vacua and their F-theory interpretation

We discuss a D3-D7 system in type IIB string theory. The near-horizon geometry is described by AdS 5× X 5 where X 5 is a U(1) bundle over a Kähler-Einstein complex surface S with positive first Chern class c 1>0. The surface S can either be P 1× P 1 , P 2 or P n 1,…,n k , a blow up of P 2 at k points with 3≤ k≤8. The P 2 corresponds to the maximally supersymmetric AdS 5× S 5 vacuum while the other cases lead to vacua with less supersymmetries. In the F-theory context they can be viewed as compactifications on elliptically fibered almost Fano 3-folds.