409 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 $\omega_n=
\sqrt{n^2+m^2\alpha'^2H^2}$ 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 $D=25,$ as in de Sitter space. A cosmological constant
$\Lambda\neq 0$ (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 $\Lambda\sim \mid\Lambda\mid N^2,$ {\it
independent} of $\alpha',$ and the level spacing {\it grows} with the
eigenvalue of the number operator, $N.$ The density of states $\rho(m)$ 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 $P=(\gamma-1)E,$ with
the pressure and energy expressed closely and completely in terms of elliptic
functions, the instantaneous coefficient $\gamma$ depending on the elliptic
modulus. We semi-classically quantize the oscillating circular strings. The
string mass is $m=\sqrt{C}/(\pi H\alpha'),\;C$ being the Casimir operator,
$C=-L_{\mu\nu}L^{\mu\nu},$ of the $O(3,1)$-dS [$O(2,2)$-AdS] group, and $H$ 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 $n\in N_0$) and
N_{\mbox{AdS}}=\infty in anti de Sitter spacetime. The level spacing grows
with $n$ 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

### Exact String Solutions in 2+1-Dimensional De Sitter Spacetime

Exact and explicit string solutions in de Sitter spacetime are found. (Here,
the string equations reduce to a sinh-Gordon model). A new feature without flat
spacetime analogy appears: starting with a single world-sheet, several (here
two) strings emerge. One string is stable and the other (unstable) grows as the
universe grows. Their invariant size and energy either grow as the expansion
factor or tend to constant. Moreover, strings can expand (contract) for large
(small) universe radius with a different rate than the universe.Comment: 11 pages, Phyzzx macropackage used, PAR-LPTHE 92/32. Revised version
with a new understanding of the previous result

### 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

### Folded Strings Falling into a Black Hole

We find all the classical solutions (minimal surfaces) of open or closed
strings in {\it any} two dimensional curved spacetime. As examples we consider
the SL(2,R)/R two dimensional black hole, and any 4D black hole in the
Schwarzschild family, provided the motion is restricted to the time-radial
components. The solutions, which describe longitudinaly oscillating folded
strings (radial oscillations in 4D), must be given in lattice-like patches of
the worldsheet, and a transfer operation analogous to a transfer matrix
determines the future evolution. Then the swallowing of a string by a black
hole is analyzed. We find several new features that are not shared by particle
motions. The most surprizing effect is the tunneling of the string into the
bare singularity region that lies beyond the black hole that is classically
forbidden to particles.Comment: 28 pages plus 4 figures, LaTeX, USC-94/HEP-B

### The Statistical Mechanics of the Self-Gravitating Gas: Equation of State and Fractal Dimension

We provide a complete picture of the self-gravitating non-relativistic gas at
thermal equilibrium using Monte Carlo simulations (MC), analytic mean field
methods (MF) and low density expansions. The system is shown to possess an
infinite volume limit, both in the canonical (CE) and in the microcanonical
ensemble (MCE) when N, V \to \infty, keeping N/ V^{1/3} fixed. We {\bf compute}
the equation of state (we do not assume it as is customary), the entropy, the
free energy, the chemical potential, the specific heats, the compressibilities,
the speed of sound and analyze their properties, signs and singularities. The
MF equation of state obeys a {\bf first order} non-linear differential equation
of Abel type. The MF gives an accurate picture in agreement with the MC
simulations both in the CE and MCE. The inhomogeneous particle distribution in
the ground state suggest a fractal distribution with Haussdorf dimension D with
D slowly decreasing with increasing density, 1 \lesssim D < 3.Comment: LaTex, 7 pages, 2 .ps figures, minor improvements, to appear in
Physics Letters

### Infinitely Many Strings in De Sitter Spacetime: Expanding and Oscillating Elliptic Function Solutions

The exact general evolution of circular strings in $2+1$ dimensional de
Sitter spacetime is described closely and completely in terms of elliptic
functions. The evolution depends on a constant parameter $b$, related to the
string energy, and falls into three classes depending on whether $b<1/4$
(oscillatory motion), $b=1/4$ (degenerated, hyperbolic motion) or $b>1/4$
(unbounded motion). The novel feature here is that one single world-sheet
generically describes {\it infinitely many} (different and independent)
strings. The world-sheet time $\tau$ is an infinite-valued function of the
string physical time, each branch yields a different string. This has no
analogue in flat spacetime. We compute the string energy $E$ as a function of
the string proper size $S$, and analyze it for the expanding and oscillating
strings. For expanding strings $(\dot{S}>0)$: $E\neq 0$ even at $S=0$, $E$
decreases for small $S$ and increases $\propto\hspace*{-1mm}S$ for large $S$.
For an oscillating string $(0\leq S\leq S_{max})$, the average energy $$
over one oscillation period is expressed as a function of $S_{max}$ as a
complete elliptic integral of the third kind.Comment: 32 pages, Latex file, figures available from the authors under
request. LPTHE-PAR 93-5

### Statistical Mechanics of the Self-gravitating gas with two or more kinds of Particles

We study the statistical mechanics of the self-gravitating gas at thermal
equilibrium with two kinds of particles. We start from the partition function
in the canonical ensemble which we express as a functional integral over the
densities of the two kinds of particles for a large number of particles. The
system is shown to possess an infinite volume limit when (N_1,N_2,V)->infty,
keeping N_1/V^{1/3} and N_2/V^{1/3} fixed. The saddle point approximation
becomes here exact for (N_1,N_2,V)->infty.It provides a nonlinear differential
equation on the particle densities. For the spherically symmetric case, we
compute the densities as functions of two dimensionless physical parameters:
eta_1=G m_1^2 N_1/[V^{1/3} T] and eta_2=G m_2^2 N_2/[V^{1/3} T] (where G is
Newton's constant, m_1 and m_2 the masses of the two kinds of particles and T
the temperature). According to the values of eta_1 and eta_2 the system can be
either in a gaseous phase or in a highly condensed phase.The gaseous phase is
stable for eta_1 and eta_2 between the origin and their collapse values. The
gas is inhomogeneous and the mass M(R) inside a sphere of radius R scales with
R as M(R) propto R^d suggesting a fractal structure. The value of d depends in
general on eta_1 and eta_2 except on the critical line for the canonical ensem-
ble where it takes the universal value d simeq 1.6 for all values of N_1/N_2.
The equation of state is computed.It is found to be locally a perfect gas
equation of state. Thermodynamic functions are computed as functions of eta_1
and eta_2. They exhibit a square root Riemann sheet with the branch points on
the critical canonical line. This treatment is further generalized to the
self-gravitating gas with n-types of particles.Comment: LaTex, 29 pages, 11 .ps figures, expanded version to appear in Phys.
Rev.

### Exact solution of the $SU_{q}(n)$ invariant quantum spin chains

The Nested Bethe Ansatz is generalized to open boundary conditions. This is
used to find the exact eigenvectors and eigenvalues of the $A_{n-1}$ vertex
model with fixed open boundary conditions and the corresponding $SU_{q}(n)$
invariant hamiltonian.
The Bethe Ansatz equations obtained are solved in the thermodynamic limit
giving the vertex model free energy and the hamiltonian ground state energy
including the corresponding boundary contributions.Comment: 29 page

### New vortex solution in SU(3) gauge-Higgs theory

Following a brief review of known vortex solutions in SU(N) gauge-adjoint
Higgs theories we show the existence of a new ``minimal'' vortex solution in
SU(3) gauge theory with two adjoint Higgs bosons. At a critical coupling the
vortex decouples into two abelian vortices, satisfying Bogomol'nyi type, first
order, field equations. The exact value of the vortex energy (per unit length)
is found in terms of the topological charge that equals to the N=2
supersymmetric charge, at the critical coupling. The critical coupling signals
the increase of the underlying supersymmetry.Comment: 15 page

- …