Matthew Lippert

Holographic nuclear physics

We analyze the phases of the Sakai-Sugimoto model at finite temperature and baryon chemical potential. Baryonic matter is represented either by 4-branes in the 8-branes or by strings stretched from the 8-branes to the horizon. We find the explicit configurations and use them to determine the phase diagram and equation of state of the model. The 4-brane configuration (nuclear matter) is always preferred to the string configuration (quark matter), and the latter is also unstable to density fluctuations. In the deconfined phase the phase diagram has three regions corresponding to the vacuum, quark-gluon plasma, and nuclear matter, with a first-order and a second-order phase transition separating the phases. We find that for a large baryon number density, and at low temperatures, the dominant phase has broken chiral symmetry. This is in qualitative agreement with studies of QCD at high density.

Quantum Hall effect in a holographic model

We consider a holographic description of a system of strongly coupled fermions in 2 + 1 dimensions based on a D7-brane probe in the background of D3-branes, and construct stable embeddings by turning on worldvolume fluxes. We study the system at finite temperature and charge density, and in the presence of a background magnetic field. We show that Minkowski-like embeddings that terminate above the horizon describe a family of quantum Hall states with filling fractions that are parameterized by a single discrete parameter. The quantization of the Hall conductivity is a direct consequence of the topological quantization of the fluxes. When the magnetic field is varied relative to the charge density away from these discrete filling fractions, the embeddings deform continuously into black-hole-like embeddings that enter the horizon and that describe metallic states. We also study the thermodynamics of this system and show that there is a first order phase transition at a critical temperature from the quantum Hall state to the metallic state.

Striped instability of a holographic Fermi-like liquid

We consider a holographic description of a system of strongly-coupled fermions in 2 + 1 dimensions based on a D7-brane probe in the background of D3-branes. The black hole embedding represents a Fermi-like liquid. We study the excitations of the Fermi liquid system. Above a critical density which depends on the temperature, the system becomes unstable towards an inhomogeneous modulated phase which is similar to a charge density and spin wave state. The essence of this instability can be effectively described by a Maxwell-axion theory with a background electric field. We also consider the fate of zero sound at non-zero temperature.

Response of Holographic QCD to Electric and Magnetic Fields

We study the response of the Sakai-Sugimoto holographic model of large Nc QCD at nonzero temperature to external electric and magnetic fields. In the electric case we find a first-order insulator-conductor transition in both the confining and deconfining phases of the model. In the deconfining phase the conductor is described by the parallel 8-brane-anti-8-brane embedding with a current of quarks and anti-quarks. We compute the conductivity and show that it agrees precisely with a computation using the Kubo formula. In the confining phase we propose a new kind of 8-brane embedding, corresponding to a baryonic conductor. In the magnetic field case we show that the critical temperature for chiral-symmetry restoration in the deconfined phase increases with the field and approaches a finite value in the limit of an infinite magnetic field. We also illustrate the nonlinear behavior of the electric and magnetic susceptibilities in the different phases.

Magnetic effects in a holographic Fermi-like liquid

A bstractWe explore the magnetic properties of the Fermi-like liquid represented by the D3-D7’ system. The system exhibits interesting magnetic properties such as ferro- magnetism and an anomalous Hall effect, which are due to the Chern-Simons term in the effective gravitational action. We investigate the spectrum of quasi-normal modes in the presence of a magnetic field and show that the magnetic field mitigates the instability to- wards a striped phase. In addition, we find a critical magnetic field above which the zero sound mode becomes massive.

A holographic quantum Hall model at integer filling

We construct a holographic model of a system of strongly-coupled fermions in 2 + 1 dimensions based on a D8-brane probe in the background of D2-branes. The Minkowski embeddings of the D8-brane represent gapped quantum Hall states with filling fraction one. By computing the conductivity and phase structure, we find results qualitatively similar to the experimental observations and also to the recent D3-D7’ model.

Evidence for a bound on the lifetime of de Sitter space

Recent work has suggested a surprising new upper bound on the lifetime of de Sitter vacua in string theory. The bound is parametrically longer than the Hubble time but parametrically shorter than the recurrence time. We investigate whether the bound is satisfied in a particular class of de Sitter solutions, the KKLT vacua. Despite the freedom to make the supersymmetry breaking scale exponentially small, which naively would lead to extremely stable vacua, we find that the lifetime is always less than about exp(1022) Hubble times, in agreement with the proposed bound. This result, however, is contingent on several estimates and assumptions; in particular, we rely on a conjectural upper bound on the Euler number of the Calabi-Yau fourfolds used in KKLT compactifications.

Magneto-roton excitation in a holographic quantum Hall fluid

We compute the neutral bosonic excitation spectra of the holographic quantum Hall fluid described by the D3-D7’ system. We find that the system is stable, gapped, and, in a range of parameters, exhibits a spectrum of low-lying excitations very similar to that of a fractional quantum Hall fluid, including a magneto-roton excitation.

Fluctuations and instabilities of a holographic metal

A bstractWe analyze the quasinormal modes of the D2-D8’ model of 2+1-dimensional, strongly-coupled, charged fermions in a background magnetic field and at non-zero density. The model is known to include a quantum Hall phase with integer filling fraction. As expected, we find a hydrodynamical diffusion mode at small momentum and the nonzero-temperature holographic zero sound, which becomes massive above a critical magnetic field. We confirm the previously-known thermodynamic instability. In addition, we discover an instability at low temperature, large mass, and in a charge density and magnetic field range near the quantum Hall phase to an inhomogeneous striped phase.

Holographic anyonic superfluidity

A bstractStarting with a holographic construction for a fractional quantum Hall state based on the D3-D7’ system, we explore alternative quantization conditions for the bulk gauge fields. This gives a description of a quantum Hall state with various filling fractions. For a particular alternative quantization of the bulk gauge fields, we obtain a holographic anyon fluid in a vanishing background magnetic field. We show that this system is a superfluid, exhibiting the relevant gapless excitation.