Emergent bubbling geometries in gauge theories with SU(2|4) symmetry

We study the gauge/gravity duality between bubbling geometries in type IIA supergravity and gauge theories with SU(2|4) symmetry, which consist of N=4 super Yang-Mills on $R\times S^3/Z_k$, N=8 super Yang-Mills on $R\times S^2$ and the plane wave matrix model. We show that the geometries are realized as field configurations in the strong coupling region of the gauge theories. On the gravity side, the bubbling geometries can be mapped to electrostatic systems with conducting disks. We derive integral equations which determine the charge densities on the disks. On the gauge theory side, we obtain a matrix integral by applying the localization to a 1/4-BPS sector of the gauge theories. The eigenvalue densities of the matrix integral turn out to satisfy the same integral equations as the charge densities on the gravity side. Thus we find that these two objects are equivalent.Comment: 29 pages, 3 figures; v2: typos corrected and a reference adde

Resonance states in a cylindrical quantum dot with an external magnetic field

Bound and resonance states of quantum dots play a significant role in photo-absorption processes. In this work, we analyze a cylindrical quantum dot, its spectrum and, in particular, the behaviour of the lowest resonance state when a magnetic field is applied along the symmetry axis of the cylinder. To obtain the energy and width of the resonance we use the complex rotation method. As it is expected the structure of the spectrum is strongly influenced by the Landau levels associated to the magnetic field. We show how this structure affects the behaviour of the resonance state and that the binding of the resonance has a clear interpretation in terms of the Landau levels and the probability of localization of the resonance state. The localization probability and the fidelity of the lowest energy state allows to identify two different physical regimes, a large field-small quantum dot radius regime and a small field-large quantum dot radius, where the binding of the resonance is dominated by the field strength or the potential well, respectively

Anderson localization through Polyakov loops: lattice evidence and Random matrix model

We investigate low-lying fermion modes in SU(2) gauge theory at temperatures above the phase transition. Both staggered and overlap spectra reveal transitions from chaotic (random matrix) to integrable (Poissonian) behavior accompanied by an increasing localization of the eigenmodes. We show that the latter are trapped by local Polyakov loop fluctuations. Islands of such "wrong" Polyakov loops can therefore be viewed as defects leading to Anderson localization in gauge theories. We find strong similarities in the spatial profile of these localized staggered and overlap eigenmodes. We discuss possible interpretations of this finding and present a sparse random matrix model that reproduces these features.Comment: 11 pages, 23 plots in 11 figures; some comments and references added, some axis labels corrected; journal versio

Diffusion on a hypercubic lattice with pinning potential: exact results for the error-catastrophe problem in biological evolution

In the theoretical biology framework one fundamental problem is the so-called error catastrophe in Darwinian evolution models. We reexamine Eigen's fundamental equations by mapping them into a polymer depinning transition problem in a ``genotype'' space represented by a unitary hypercubic lattice. The exact solution of the model shows that error catastrophe arises as a direct consequence of the equations involved and confirms some previous qualitative results. The physically relevant consequence is that such equations are not adequate to properly describe evolution of complex life on the Earth.Comment: 10 pages in LaTeX. Figures are available from the authors. [email protected] (e-mail address