35 research outputs found
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 , N=8 super Yang-Mills on
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
Melnikov's method in String Theory
Melnikov's method is an analytical way to show the existence of classical
chaos generated by a Smale horseshoe. It is a powerful technique, though its
applicability is somewhat limited. In this paper, we present a solution of type
IIB supergravity to which Melnikov's method is applicable. This is a brane-wave
type deformation of the AdSS background. By employing two
reduction ans\"atze, we study two types of coupled pendulum-oscillator systems.
Then the Melnikov function is computed for each of the systems by following the
standard way of Holmes and Marsden and the existence of chaos is shown
analytically.Comment: 37 pages, 5 figure
Chaos in the BMN matrix model
We study classical chaotic motions in the Berenstein-Maldacena-Nastase (BMN)
matrix model. For this purpose, it is convenient to focus upon a reduced system
composed of two-coupled anharmonic oscillators by supposing an ansatz. We
examine three ans\"atze: 1) two pulsating fuzzy spheres, 2) a single
Coulomb-type potential, and 3) integrable fuzzy spheres. For the first two
cases, we show the existence of chaos by computing Poincar\'e sections and a
Lyapunov spectrum. The third case leads to an integrable system. As a result,
the BMN matrix model is not integrable in the sense of Liouville, though there
may be some integrable subsectors.Comment: 23 pages, 15 figures, v2: further clarifications and references adde
Emergent bubbling geometries in the plane wave matrix model
The gravity dual geometry of the plane wave matrix model is given by the
bubbling geometry in the type IIA supergravity, which is described by an
axially symmetric electrostatic system. We study a quarter BPS sector of the
plane wave matrix model in terms of the localization method and show that this
sector can be mapped to a one-dimensional interacting Fermi gas system. We find
that the mean-field density of the Fermi gas can be identified with the charge
density in the electrostatic system in the gravity side. We also find that the
scaling limits in which the dual geometry reduces to the D2-brane or NS5-brane
geometry are given as the free limit or the strongly coupled limit of the Fermi
gas system, respectively. We reproduce the radii of 's in these geometries
by solving the Fermi gas model in the corresponding limits.Comment: 34 pages, 3 figures; typos correcte
A Computer Test of Holographic Flavour Dynamics II
We study the second derivative of the free energy with respect to the
fundamental mass (the mass susceptibility) for the Berkooz-Douglas model as a
function of temperature and at zero mass. The model is believed to be
holographically dual to a D0/D4 intersection. We perform a lattice simulation
of the system at finite temperature and find excellent agreement with
predictions from the gravity dual.Comment: typos fixed, acknowledgements update
Chaotic strings in a near Penrose limit of AdS
We study chaotic motions of a classical string in a near Penrose limit of
AdS. It is known that chaotic solutions appear on , depending on initial conditions. It may be interesting to ask whether
the chaos persists even in Penrose limits or not. In this paper, we show that
sub-leading corrections in a Penrose limit provide an unstable separatrix, so
that chaotic motions are generated as a consequence of collapsed
Kolmogorov-Arnold-Moser (KAM) tori. Our analysis is based on deriving a reduced
system composed of two degrees of freedom by supposing a winding string ansatz.
Then, we provide support for the existence of chaos by computing Poincare
sections. In comparison to the AdS case, we argue that no
chaos lives in a near Penrose limit of AdSS, as expected from the
classical integrability of the parent system.Comment: 19 pages, 9 figures, LaTeX, v2: typos corrected and some
clarifications adde
The Flavoured BFSS Model at High Temperature
We study the high temperature series expansion of the Berkooz-Douglas matrix
model which describes the D0/D4--brane system. At high temperature the model is
weakly coupled and we develop the series to second order. We check our results
against the high temperature regime of the bosonic model (without fermions) and
find excellent agreement. We track the temperature dependence of the bosonic
model and find backreaction of the fundamental fields lifts the zero
temperature adjoint mass degeneracy. In the low temperature phase the system is
well described by a gaussian model with three masses ,
and , the adjoint longitudional
and transverse masses and the mass of the fundamental fields respectively.Comment: 36 pages 11 figures and tables; v2: major revision for clarification,
numerical results updated and typos correcte