Holographic Magnetic Star

A warm fermionic AdS star under a homogeneous magnetic field is explored. We obtain the relativistic Landau levels by using Dirac equation and use the Tolman-Oppenheimer-Volkoff (TOV) equation to study the physical profiles of the star. Bulk properties such as sound speed, adiabatic index, and entropy density within the star are calculated analytically and numerically. Bulk temperature increases the mass limit of the AdS star but external magnetic field has the opposite effect. The results are partially interpreted in terms of the pre-thermalization process of the gauge matter at the AdS boundary after the mass injection. The entropy density is found to demonstrate similar temperature dependence as the magnetic black brane in the AdS in certain limits regardless of the different nature of the bulk and Hawking temperatures. Total entropy of the AdS star is also found to be an increasing function of the bulk temperature and a decreasing function of the magnetic field, similar behaviour to the mass limit. Since both total entropy and mass limit are global quantities, they could provide some hints to the value of entropy and energy of the dual gauge matter before and during the thermalization.Comment: 39 pages, 14 figures, 1 table, comments and references added, to appear in JHE

Thermalization from gauge/gravity duality: Evolution of singularities in unequal time correlators

We consider a gauge/gravity dual model of thermalization which consists of a collapsing thin matter shell in asymptotically Anti-de Sitter space. A central aspect of our model is to consider a shell moving at finite velocity as determined by its equation of motion, rather than a quasi-static approximation as considered previously in the literature. By applying a divergence matching method, we obtain the evolution of singularities in the retarded unequal time correlator $G^R(t,t')$, which probes different stages of the thermalization. We find that the number of singularities decreases from a finite number to zero as the gauge theory thermalizes. This may be interpreted as a sign of decoherence. Moreover, in a second part of the paper, we show explicitly that the thermal correlator is characterized by the existence of singularities in the complex time plane. By studying a quasi-static state, we show the singularities at real times originate from contributions of normal modes. We also investigate the possibility of obtaining complex singularities from contributions of quasi-normal modes.Comment: 35 pages, 4 figure

A soliton menagerie in AdS

We explore the behaviour of charged scalar solitons in asymptotically global AdS4 spacetimes. This is motivated in part by attempting to identify under what circumstances such objects can become large relative to the AdS length scale. We demonstrate that such solitons generically do get large and in fact in the planar limit smoothly connect up with the zero temperature limit of planar scalar hair black holes. In particular, for given Lagrangian parameters we encounter multiple branches of solitons: some which are perturbatively connected to the AdS vacuum and surprisingly, some which are not. We explore the phase space of solutions by tuning the charge of the scalar field and changing scalar boundary conditions at AdS asymptopia, finding intriguing critical behaviour as a function of these parameters. We demonstrate these features not only for phenomenologically motivated gravitational Abelian-Higgs models, but also for models that can be consistently embedded into eleven dimensional supergravity.Comment: 62 pages, 21 figures. v2: added refs and comments and updated appendice

Stellar spectroscopy: Fermions and holographic Lifshitz criticality

Electron stars are fluids of charged fermions in Anti-de Sitter spacetime. They are candidate holographic duals for gauge theories at finite charge density and exhibit emergent Lifshitz scaling at low energies. This paper computes in detail the field theory Green's function G^R(w,k) of the gauge-invariant fermionic operators making up the star. The Green's function contains a large number of closely spaced Fermi surfaces, the volumes of which add up to the total charge density in accordance with the Luttinger count. Excitations of the Fermi surfaces are long lived for w <~ k^z. Beyond w ~ k^z the fermionic quasiparticles dissipate strongly into the critical Lifshitz sector. Fermions near this critical dispersion relation give interesting contributions to the optical conductivity.Comment: 38 pages + appendices. 9 figure

Refined Chern-Simons theory and (q, t)-deformed Yang-Mills theory : Semi-classical expansion and planar limit

We study the relationship between refined Chern-Simons theory on lens spaces S-3/Z(p) and (q, t)-deformed Yang-Mills theory on the sphere S-2. We derive the instanton partition function of (q, t)-deformed U(N) Yang-Mills theory and describe it explicitly as an analytical continuation of the semi-classical expansion of refined Chern-Simons theory. The derivations are based on a generalization of the Weyl character formula to Macdonald polynomials. The expansion is used to formulate q-generalizations of beta-deformed matrix models for refined Chern-Simons theory, as well as conjectural formulas for the chi(y)-genus of the moduli space of U(N) instantons on the surface O(-p) -> P-1 for all p >= 1 which enumerate black hole microstates in refined topological string theory. We study the large N phase structures of the refined gauge theories, and match them with refined topological string theory on the resolved conifold

Holographic Fermi and Non-Fermi Liquids with Transitions in Dilaton Gravity

We study the two-point function for fermionic operators in a class of strongly coupled systems using the gauge-gravity correspondence. The gravity description includes a gauge field and a dilaton which determines the gauge coupling and the potential energy. Extremal black brane solutions in this system typically have vanishing entropy. By analyzing a charged fermion in these extremal black brane backgrounds we calculate the two-point function of the corresponding boundary fermionic operator. We find that in some region of parameter space it is of Fermi liquid type. Outside this region no well-defined quasi-particles exist, with the excitations acquiring a non-vanishing width at zero frequency. At the transition, the two-point function can exhibit non-Fermi liquid behaviour.Comment: 52 pages, 6 figures. v3: Appendix F added showing numerical interpolation between the near-horizon region and AdS4. Additional minor comments also adde

QCD with Chemical Potential in a Small Hyperspherical Box

To leading order in perturbation theory, we solve QCD, defined on a small three sphere in the large N and Nf limit, at finite chemical potential and map out the phase diagram in the (mu,T) plane. The action of QCD is complex in the presence of a non-zero quark chemical potential which results in the sign problem for lattice simulations. In the large N theory, which at low temperatures becomes a conventional unitary matrix model with a complex action, we find that the dominant contribution to the functional integral comes from complexified gauge field configurations. For this reason the eigenvalues of the Polyakov line lie off the unit circle on a contour in the complex plane. We find at low temperatures that as mu passes one of the quark energy levels there is a third-order Gross-Witten transition from a confined to a deconfined phase and back again giving rise to a rich phase structure. We compare a range of physical observables in the large N theory to those calculated numerically in the theory with N=3. In the latter case there are no genuine phase transitions in a finite volume but nevertheless the observables are remarkably similar to the large N theory.Comment: 44 pages, 18 figures, jhep3 format. Small corrections and clarifications added in v3. Conclusions cleaned up. Published versio

Quasilocal formalism and thermodynamics of asymptotically flat black objects

We study the properties of 5-dimensional black objects by using the renormalized boundary stress-tensor for locally asymptotically flat spacetimes. This provides a more refined form of the quasilocal formalism which is useful for a holographic interpretation of asymptotically flat gravity. We apply this technique to examine the thermodynamic properties of black holes, black rings, and black strings. The advantage of using this method is that we can go beyond the `thin ring' approximation and compute the boundary stress tensor for any general (thin or fat) black ring solution. We argue that the boundary stress tensor encodes the necessarily information to distinguish between black objects with different horizon topologies in the bulk. We also study in detail the susy black ring and clarify the relation between the asymptotic charges and the charges defined at the horizon. Furthermore, we obtain the balance condition for `thin' dipole black rings.Comment: v2 clarifications on the advantage of using quasilocal formalism for black rings added, CQG versio

Semi-local quantum liquids

Gauge/gravity duality applied to strongly interacting systems at finite density predicts a universal intermediate energy phase to which we refer as a semi-local quantum liquid. Such a phase is characterized by a finite spatial correlation length, but an infinite correlation time and associated nontrivial scaling behavior in the time direction, as well as a nonzero entropy density. For a holographic system at a nonzero chemical potential, this unstable phase sets in at an energy scale of order of the chemical potential, and orders at lower energies into other phases; examples include superconductors and antiferromagnetic-type states. In this paper we give examples in which it also orders into Fermi liquids of "heavy" fermions. While the precise nature of the lower energy state depends on the specific dynamics of the individual system, we argue that the semi-local quantum liquid emerges universally at intermediate energies through deconfinement (or equivalently fractionalization). We also discuss the possible relevance of such a semi-local quantum liquid to heavy electron systems and the strange metal phase of high temperature cuprate superconductors.Comment: 31 pages, 7 figure