New knotted solutions of Maxwell's equations

In this note we have further developed the study of topologically non-trivial solutions of vacuum electrodynamics. We have discovered a novel method of generating such solutions by applying conformal transformations with complex parameters on known solutions expressed in terms of Bateman's variables. This has enabled us to get a wide class of solutions from the basic configuration like constant electromagnetic fields and plane-waves. We have introduced a covariant formulation of the Bateman's construction and discussed the conserved charges associated with the conformal group as well as a set of four types of conserved helicities. We have also given a formulation in terms of quaternions. This led to a simple map between the electromagnetic knotted and linked solutions into flat connections of $SU(2)$ gauge theory. We have computed the corresponding CS charge in a class of solutions and it takes integer values.Comment: version accepted for publication in J. Phys. A. minor changes: references added, new figure added, typos correcte

Can the Hagedorn Phase Transition be explained from Matrix Model for Strings?

The partition function of BFSS matrix model is studied for two different classical backgrounds upto 1-loop level. One of the backgrounds correspond to a membrane wrapped around a compact direction and another to a localized cluster of $D0$-branes. It is shown there exist phase transitions between these two configurations - but only in presence of an IR cut-off. The low temperature phase corresponds to a string (wrapped membrane) phase and so we call this the Hagedorn phase transition. While the presence of an IR cut-off seemingly is only required for perturbative analysis to be valid, the physical necessity of such a cut-off can be seen in the dual supergravity side. It has been argued from entropy considerations that a finite size horizon must develop even in an extremal configuration of D0-branes, from higher derivative $O(g_s)$ corrections to supergravity. It can then be shown that the Hagedorn like transition exists in supergravity also. Interestingly the perturbative analysis also shows a second phase transition back to a string phase. This is also reminiscent of the Gregory-Laflamme instability.Comment: minor change

Extremal Horizons with Reduced Symmetry: Hyperscaling Violation, Stripes, and a Classification for the Homogeneous Case

Classifying the zero-temperature ground states of quantum field theories with finite charge density is a very interesting problem. Via holography, this problem is mapped to the classification of extremal charged black brane geometries with anti-de Sitter asymptotics. In a recent paper [1], we proposed a Bianchi classification of the extremal near-horizon geometries in five dimensions, in the case where they are homogeneous but, in general, anisotropic. Here, we extend our study in two directions: we show that Bianchi attractors can lead to new phases, and generalize the classification of homogeneous phases in a way suggested by holography. In the first direction, we show that hyperscaling violation can naturally be incorporated into the Bianchi horizons. We also find analytical examples of "striped" horizons. In the second direction, we propose a more complete classification of homogeneous horizon geometries where the natural mathematics involves real four-algebras with three dimensional sub-algebras. This gives rise to a richer set of possible near-horizon geometries, where the holographic radial direction is non-trivially intertwined with field theory spatial coordinates. We find examples of several of the new types in systems consisting of reasonably simple matter sectors coupled to gravity, while arguing that others are forbidden by the Null Energy Condition. Extremal horizons in four dimensions governed by three-algebras or four-algebras are also discussed.Comment: 58 pages, 1 figure and 1 cartoon. v2: references adde

Strong Coupling BCS Superconductivity and Holography

We attempt to give a holographic description of the microscopic theory of a BCS superconductor. Exploiting the analogy with chiral symmetry breaking in QCD we use the Sakai-Sugimoto model of two D8 branes in a D4 brane background with finite baryon number. In this case there is a new tachyonic instability which is plausibly the bulk analog of the Cooper pairing instability. We analyze the Yang-Mills approximation to the non-Abelian Born-Infeld action. We give some exact solutions of the non-linear Yang-Mills equations in flat space and also give a stability analysis, showing that the instability disappears in the presence of an electric field. The holograhic picture also suggests a dependence of $T_c$ on the number density which is different from the usual (weak coupling) BCS. The flat space solutions are then generalized to curved space numerically and also, in an approximate way, analytically. This configuration should then correspond to the ground state of the boundary superconducting (superfluid) ground state. We also give some preliminary results on Green functions computations in the Sakai - Sugimoto model without any chemical potentialComment: minor revisions, numerical analysis has been redone to obtain some solutions to the complete set of equations, version accepted in Nuclear Physics

Properties of CFTs dual to Charged BTZ black-hole

We study properties of strongly coupled CFT's with non-zero background electric charge in 1+1 dimensions by studying the dual gravity theory - which is a charged BTZ black hole. Correlators of operators dual to scalars, gauge fields and fermions are studied at both T=0 and $T\neq 0$. In the $T=0$ case we are also able to compare with analytical results based on $AdS_2$ and find reasonable agreement. In particular the correlation between log periodicity and the presence of finite spectral density of gapless modes is seen. The real part of the conductivity (given by the current-current correlator) also vanishes as $\omega \rightarrow 0$ as expected. The fermion Green's function shows quasiparticle peaks with approximately linear dispersion but the detailed structure is neither Fermi liquid nor Luttinger liquid and bears some similarity to a "Fermi-Luttinger" liquid. This is expected since there is a background charge and the theory is not Lorentz or scale invariant. A boundary action that produces the observed non-Luttinger-liquid like behavior ($k$-independent non-analyticity at $\omega=0$) in the Greens function is discussed.Comment: major changes: paper reformatted, connection with Fermi-Luttinger liquid theory explored, comparison with expected behavior in 1+1 dimension added, rigorous numerical analysis for finite temperature don

Entangled Dilaton Dyons

Einstein-Maxwell theory coupled to a dilaton is known to give rise to extremal solutions with hyperscaling violation. We study the behaviour of these solutions in the presence of a small magnetic field. We find that in a region of parameter space the magnetic field is relevant in the infra-red and completely changes the behaviour of the solution which now flows to an $AdS_2\times R^2$ attractor. As a result there is an extensive ground state entropy and the entanglement entropy of a sufficiently big region on the boundary grows like the volume. In particular, this happens for values of parameters at which the purely electric theory has an entanglement entropy growing with the area, $A$, like $A \log(A)$ which is believed to be a characteristic feature of a Fermi surface. Some other thermodynamic properties are also analysed and a more detailed characterisation of the entanglement entropy is also carried out in the presence of a magnetic field. Other regions of parameter space not described by the $AdS_2\times R^2$ end point are also discussed.Comment: Some comments regarding comparison with weakly coupled Fermi liquid changed, typos corrected and caption of a figure modifie

Bianchi Attractors: A Classification of Extremal Black Brane Geometries

Extremal black branes are of interest because they correspond to the ground states of field theories at finite charge density in gauge/gravity duality. The geometry of such a brane need not be translationally invariant in the spatial directions along which it extends. A less restrictive requirement is that of homogeneity, which still allows points along the spatial directions to be related to each other by symmetries. In this paper, we find large new classes of homogeneous but anisotropic extremal black brane horizons, which could naturally arise in gauge/gravity dual pairs. In 4+1 dimensional spacetime, we show that such homogeneous black brane solutions are classified by the Bianchi classification, which is well known in the study of cosmology, and fall into nine classes. In a system of Einstein gravity with negative cosmological term coupled to one or two massive Abelian gauge fields, we find solutions with an additional scaling symmetry, which could correspond to the near-horizon geometries of such extremal black branes. These solutions realize many of the Bianchi classes. In one case, we construct the complete extremal solution which asymptotes to AdS space.Comment: Minor changes and a reference added. 43 Pages, 6 Figure