90 research outputs found
Large-Spin and Large-Winding Expansions of Giant Magnons and Single Spikes
We generalize the method of our recent paper on the large-spin expansions of
Gubser-Klebanov-Polyakov (GKP) strings to the large-spin and large-winding
expansions of finite-size giant magnons and finite-size single spikes. By
expressing the energies of long open strings in RxS2 in terms of Lambert's
W-function, we compute the leading, subleading and next-to-subleading series of
classical exponential corrections to the dispersion relations of
Hofman-Maldacena giant magnons and infinite-winding single spikes. We also
compute the corresponding expansions in the doubled regions of giant magnons
and single spikes that are respectively obtained when their angular and linear
velocities become smaller or greater than unity.Comment: 43 pages, 13 figures; Matches published version. Rewritten appendix
On the Octonionic Self Duality equations of 3-brane Instantons
We study the octonionic selfduality equations for -branes in the light
cone gauge and we construct explicitly, instanton solutions for spherical and
toroidal topologies in various flat spacetime dimensions ,
extending previous results for membranes. Assuming factorization of time
we reduce the self-duality equations to integrable systems and we determine
explicitly periodic, in Euclidean time, solutions in terms of the elliptic
functions. These solutions describe 4d associative and non-associative
calibrations in dimensions. It turns out that for spherical topology
the calibration is non compact while for the toroidal topology is compact. We
discuss possible applications of our results to the problem of 3-brane topology
change and its implications for a non-perturbative definition of the 3-brane
interactions.Comment: 15 pages, 4 figure
Large-Spin Expansions of GKP Strings
We demonstrate that the large-spin expansion of the energy of
Gubser-Klebanov-Polyakov (GKP) strings that rotate in RxS2 and AdS3 can be
expressed in terms of Lambert's W-function. We compute the leading, subleading
and next-to-subleading series of exponential corrections to the infinite-volume
dispersion relation of GKP strings that rotate in RxS2. These strings are dual
to certain long operators of N=4 SYM theory and provide their scaling
dimensions at strong coupling. We also show that the strings obey a short-long
(strings) duality. For the folded GKP strings that spin inside AdS3 and are
dual to twist-2 operators, we confirm the known formulas for the leading and
next-to-leading coefficients of their anomalous dimensions and derive the
corresponding expressions for the next-to-next-to-leading coefficients.Comment: 46 pages, 8 figures; Matches published version; Contains equation
(7.3) that gives the finite-size corrections to the dispersion relation of
giant magnons at strong couplin
Chaotic Information Processing by Extremal Black Holes
We review an explicit regularization of the AdS/CFT correspondence,
that preserves all isometries of bulk and boundary degrees of freedom. This
scheme is useful to characterize the space of the unitary evolution operators
that describe the dynamics of the microstates of extremal black holes in four
spacetime dimensions. Using techniques from algebraic number theory to evaluate
the transition amplitudes, we remark that the regularization scheme expresses
the fast quantum computation capability of black holes as well as its chaotic
nature.Comment: 8 pages, 2 JPEG figues. Contribution to the VII Black Holes Workshop,
Aveiro PT, Decemeber 201
The quantum cat map on the modular discretization of extremal black hole horizons
Based on our recent work on the discretization of the radial AdS geometry
of extremal BH horizons,we present a toy model for the chaotic unitary
evolution of infalling single particle wave packets.
We construct explicitly the eigenstates and eigenvalues for the single
particle dynamics for an observer falling into the BH horizon, with time
evolution operator the quantum Arnol'd cat map (QACM).
Using these results we investigate the validity of the eigenstate
thermalization hypothesis (ETH), as well as that of the fast scrambling time
bound (STB).
We find that the QACM, while possessing a linear spectrum, has eigenstates,
which are random and satisfy the assumptions of the ETH.
We also find that the thermalization of infalling wave packets in this
particular model is exponentially fast, thereby saturating the STB, under the
constraint that the finite dimension of the single--particle Hilbert space
takes values in the set of Fibonacci integers.Comment: 28 pages LaTeX2e, 8 jpeg figures. Clarified certain issues pertaining
to the relation between mixing time and scrambling time; enhanced discussion
of the Eigenstate Thermalization Hypothesis; revised figures and updated
references. Typos correcte
The Omega-Infinity Limit of Single Spikes
A new infinite-size limit of strings in RxS2 is presented. The limit is
obtained from single spike strings by letting by letting the angular velocity
parameter omega become infinite. We derive the energy-momenta relation of
omega-infinity single spikes as their linear velocity v-->1 and their angular
momentum J-->1. Generally, the v-->1, J-->1 limit of single spikes is singular
and has to be excluded from the spectrum and be studied separately. We discover
that the dispersion relation of omega-infinity single spikes contains
logarithms in the limit J-->1. This result is somewhat surprising, since the
logarithmic behavior in the string spectra is typically associated with their
motion in non-compact spaces such as AdS. Omega-infinity single spikes seem to
completely cover the surface of the 2-sphere they occupy, so that they may
essentially be viewed as some sort of "brany strings". A proof of the
sphere-filling property of omega-infinity single spikes is given in the
appendix.Comment: 35 pages, 14 figures. Matches published version; Contains equation
(4.21) that gives the first few finite-size corrections to the energy of
omega-infinity single spike
M2-brane Dynamics in the Classical Limit of the BMN Matrix Model
We investigate the large-N limit of the BMN matrix model by analyzing the
dynamics of ellipsoidal M2-branes that spin in the 11-dimensional maximally
supersymmetric SO(3)xSO(6) plane-wave background. We identify finite-energy
solutions by specifying the local minima of the corresponding energy
functional. These configurations are static in SO(3) due to the Myers effect
and rotate in SO(6) with an angular momentum that is bounded from above. As a
first step towards studying their chaotic properties, we evaluate the Lyapunov
exponents of their radial fluctuations.Comment: 7 pages, 8 figure
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