9,072 research outputs found
Mass Spectrum of Strings in Anti de Sitter Spacetime
We perform string quantization in anti de Sitter (AdS) spacetime. The string
motion is stable, oscillatory in time with real frequencies and the string size and energy are bounded. The
string fluctuations around the center of mass are well behaved. We find the
mass formula which is also well behaved in all regimes. There is an {\it
infinite} number of states with arbitrarily high mass in AdS (in de Sitter (dS)
there is a {\it finite} number of states only). The critical dimension at which
the graviton appears is as in de Sitter space. A cosmological constant
(whatever its sign) introduces a {\it fine structure} effect
(splitting of levels) in the mass spectrum at all states beyond the graviton.
The high mass spectrum changes drastically with respect to flat Minkowski
spacetime. For {\it
independent} of and the level spacing {\it grows} with the
eigenvalue of the number operator, The density of states grows
like \mbox{Exp}[(m/\sqrt{\mid\Lambda\mid}\;)^{1/2}] (instead of
\rho(m)\sim\mbox{Exp}[m\sqrt{\alpha'}] as in Minkowski space), thus {\it
discarding} the existence of a critical string temperature.
For the sake of completeness, we also study the quantum strings in the black
string background, where strings behave, in many respects, as in the ordinary
black hole backgrounds. The mass spectrum is equal to the mass spectrum in flat
Minkowski space.Comment: 31 pages, Latex, DEMIRM-Paris-9404
Semi-Classical Quantization of Circular Strings in De Sitter and Anti De Sitter Spacetimes
We compute the {\it exact} equation of state of circular strings in the (2+1)
dimensional de Sitter (dS) and anti de Sitter (AdS) spacetimes, and analyze its
properties for the different (oscillating, contracting and expanding) strings.
The string equation of state has the perfect fluid form with
the pressure and energy expressed closely and completely in terms of elliptic
functions, the instantaneous coefficient depending on the elliptic
modulus. We semi-classically quantize the oscillating circular strings. The
string mass is being the Casimir operator,
of the -dS [-AdS] group, and is
the Hubble constant. We find \alpha'm^2_{\mbox{dS}}\approx 5.9n,\;(n\in N_0),
and a {\it finite} number of states N_{\mbox{dS}}\approx 0.17/(H^2\alpha') in
de Sitter spacetime; m^2_{\mbox{AdS}}\approx 4H^2n^2 (large ) and
N_{\mbox{AdS}}=\infty in anti de Sitter spacetime. The level spacing grows
with in AdS spacetime, while is approximately constant (although larger
than in Minkowski spacetime) in dS spacetime. The massive states in dS
spacetime decay through tunnel effect and the semi-classical decay probability
is computed. The semi-classical quantization of {\it exact} (circular) strings
and the canonical quantization of generic string perturbations around the
string center of mass strongly agree.Comment: Latex, 26 pages + 2 tables and 5 figures that can be obtained from
the authors on request. DEMIRM-Obs de Paris-9404
String Driven Cosmology and its Predictions
We present a minimal model for the Universe evolution fully extracted from
effective String Theory. This model is by its construction close to the
standard cosmological evolution, and it is driven selfconsistently by the
evolution of the string equation of state itself. The inflationary String
Driven stage is able to reach enough inflation, describing a Big Bang like
evolution for the metric. By linking this model to a minimal but well
established observational information, (the transition times of the different
cosmological epochs), we prove that it gives realistic predictions on early and
current energy density and its results are compatible with General Relativity.
Interestingly enough, the predicted current energy density is found Omega = 1
and a lower limit Omega \geq 4/9 is also found. The energy density at the exit
of the inflationary stage also gives | Omega |_{inf}=1. This result shows an
agreement with General Relativity (spatially flat metric gives critical energy
density) within an inequivalent Non-Einstenian context (string low energy
effective equations). The order of magnitude of the energy density-dilaton
coupled term at the beginning of the radiation dominated stage agrees with the
GUT scale. The predicted graviton spectrum is computed and analyzed without any
free parameters. Peaks and asymptotic behaviours of the spectrum are a direct
consequence of the dilaton involved and not only of the scale factor evolution.
Drastic changes are found at high frequencies: the dilaton produces an
increasing spectrum (in no string cosmologies the spectrum is decreasing).
Without solving the known problems about higher order corrections and graceful
exit of inflation, we find this model closer to the observational Universe than
the current available string cosmology scenarii.Comment: LaTex, 22 pages, Lectures delivered at the Chalonge School, Nato ASI:
Phase Transitions in the Early Universe: Theory and Observations. To appear
in the Proceedings, Editors H. J. de Vega, I. Khalatnikov, N. Sanchez.
(Kluwer Pub
String dynamics in cosmological and black hole backgrounds: The null string expansion
We study the classical dynamics of a bosonic string in the --dimensional
flat Friedmann--Robertson--Walker and Schwarzschild backgrounds. We make a
perturbative development in the string coordinates around a {\it null} string
configuration; the background geometry is taken into account exactly. In the
cosmological case we uncouple and solve the first order fluctuations; the
string time evolution with the conformal gauge world-sheet --coordinate
is given by , where
are given by Eqs.\ (3.15), and is the exponent of the conformal factor
in the Friedmann--Robertson--Walker metric, i.e. . The string
proper size, at first order in the fluctuations, grows like the conformal
factor and the string energy--momentum tensor corresponds to that of
a null fluid. For a string in the black hole background, we study the planar
case, but keep the dimensionality of the spacetime generic. In the null
string expansion, the radial, azimuthal, and time coordinates are
and The first terms of the series represent a
{\it generic} approach to the Schwarzschild singularity at . First and
higher order string perturbations contribute with higher powers of . The
integrated string energy-momentum tensor corresponds to that of a null fluid in
dimensions. As the string approaches the singularity its proper
size grows indefinitely like . We end the paper
giving three particular exact string solutions inside the black hole.Comment: 17 pages, REVTEX, no figure
Strings in Cosmological and Black Hole Backgrounds: Ring Solutions
The string equations of motion and constraints are solved for a ring shaped
Ansatz in cosmological and black hole spacetimes. In FRW universes with
arbitrary power behavior [R(X^0) = a\;|X^0|^{\a}\, ], the asymptotic form of
the solution is found for both and and we plot the
numerical solution for all times. Right after the big bang (), the
string energy decreasess as and the string size grows as for . Very
soon [ ] , the ring reaches its oscillatory regime with frequency
equal to the winding and constant size and energy. This picture holds for all
values of \a including string vacua (for which, asymptotically, \a = 1).
In addition, an exact non-oscillatory ring solution is found. For black hole
spacetimes (Schwarzschild, Reissner-Nordstr\oo m and stringy), we solve for
ring strings moving towards the center. Depending on their initial conditions
(essentially the oscillation phase), they are are absorbed or not by
Schwarzschild black holes. The phenomenon of particle transmutation is
explicitly observed (for rings not swallowed by the hole). An effective horizon
is noticed for the rings. Exact and explicit ring solutions inside the
horizon(s) are found. They may be interpreted as strings propagating between
the different universes described by the full black hole manifold.Comment: Paris preprint PAR-LPTHE-93/43. Uses phyzzx. Includes figures. Text
and figures compressed using uufile
A method for solve integrable spin chains combining different representations
A non homogeneous spin chain in the representations and
of is analyzed. We find that the naive nested Bethe ansatz is not
applicable to this case. A method inspired in the nested Bethe ansatz, that can
be applied to more general cases, is developed for that chain. The solution for
the eigenvalues of the trace of the monodromy matrix is given as two coupled
Bethe equations different from that for a homogeneous chain. A conjecture about
the form of the solutions for more general chains is presented.
PACS: 75.10.Jm, 05.50+q 02.20 SvComment: PlainTeX, harvmac, 13 pages, 3 figures, to appear in Phys. Rev.
QFT, String Temperature and the String Phase of De Sitter Space-time
The density of mass levels \rho(m) and the critical temperature for strings
in de Sitter space-time are found. QFT and string theory in de Sitter space are
compared. A `Dual'-transform is introduced which relates classical to quantum
string lengths, and more generally, QFT and string domains. Interestingly, the
string temperature in De Sitter space turns out to be the Dual transform of the
QFT-Hawking-Gibbons temperature. The back reaction problem for strings in de
Sitter space is addressed selfconsistently in the framework of the `string
analogue' model (or thermodynamical approach), which is well suited to combine
QFT and string study.We find de Sitter space-time is a self-consistent solution
of the semiclassical Einstein equations in this framework. Two branches for the
scalar curvature R(\pm) show up: a classical, low curvature solution (-), and a
quantum high curvature solution (+), enterely sustained by the strings. There
is a maximal value for the curvature R_{\max} due to the string back reaction.
Interestingly, our Dual relation manifests itself in the back reaction
solutions: the (-) branch is a classical phase for the geometry with intrinsic
temperature given by the QFT-Hawking-Gibbons temperature.The (+) is a stringy
phase for the geometry with temperature given by the intrinsic string de Sitter
temperature. 2 + 1 dimensions are considered, but conclusions hold generically
in D dimensions.Comment: LaTex, 24 pages, no figure
Multi-String Solutions by Soliton Methods in De Sitter Spacetime
{\bf Exact} solutions of the string equations of motion and constraints are
{\bf systematically} constructed in de Sitter spacetime using the dressing
method of soliton theory. The string dynamics in de Sitter spacetime is
integrable due to the associated linear system. We start from an exact string
solution and the associated solution of the linear system , and we construct a new solution differing from
by a rational matrix in with at least four
poles . The periodi-
city condition for closed strings restrict to discrete values
expressed in terms of Pythagorean numbers. Here we explicitly construct solu-
tions depending on -spacetime coordinates, two arbitrary complex numbers
(the 'polarization vector') and two integers which determine the string
windings in the space. The solutions are depicted in the hyperboloid coor-
dinates and in comoving coordinates with the cosmic time . Despite of
the fact that we have a single world sheet, our solutions describe {\bf multi-
ple}(here five) different and independent strings; the world sheet time
turns to be a multivalued function of .(This has no analogue in flat space-
time).One string is stable (its proper size tends to a constant for , and its comoving size contracts); the other strings are unstable (their
proper sizes blow up for , while their comoving sizes tend to cons-
tants). These solutions (even the stable strings) do not oscillate in time. The
interpretation of these solutions and their dynamics in terms of the sinh-
Gordon model is particularly enlighting.Comment: 25 pages, latex. LPTHE 93-44. Figures available from the auhors under
reques
Planetoid strings : solutions and perturbations
A novel ansatz for solving the string equations of motion and constraints in
generic curved backgrounds, namely the planetoid ansatz, was proposed recently
by some authors. We construct several specific examples of planetoid strings in
curved backgrounds which include Lorentzian wormholes, spherical Rindler
spacetime and the 2+1 dimensional black hole. A semiclassical quantisation is
performed and the Regge relations for the planetoids are obtained. The general
equations for the study of small perturbations about these solutions are
written down using the standard, manifestly covariant formalism. Applications
to special cases such as those of planetoid strings in Minkowski and spherical
Rindler spacetimes are also presented.Comment: 24 pages (including two figures), RevTex, expanded and figures adde
Integrable Generalized Thirring Model
We derive the conditions that the coupling constants of the Generalized
Thirring Model have to satisfy in order for the model to admit an infinite
number of commuting classical conserved quantities. Our treatment uses the
bosonized version of the model, with periodic boundary conditions imposed on
the space coordinate. Some explicit examples that satisfy these conditions are
discussed. We show that, with a different set of boundary conditions, there
exist additional conserved quantities, and we find the Poisson Bracket algebra
satisfied by them.Comment: Final version to be published in Nucl.Phys.B. Only minor changes. An
equation was deleted and a conclusion revised, and a few comments were added.
Harvmac, 15 pages. Full postscript available from
http://theor1.lbl.gov/www/theorgroup/papers/39040.p
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