Renormalization Group Flow and Fragmentation in the Self-Gravitating Thermal Gas

The self-gravitating thermal gas (non-relativistic particles of mass m at temperature T) is exactly equivalent to a field theory with a single scalar field phi(x) and exponential self-interaction. We build up perturbation theory around a space dependent stationary point phi_0(r) in a finite size domain delta \leq r \leq R ,(delta << R), which is relevant for astrophysical applica- tions (interstellar medium,galaxy distributions).We compute the correlations of the gravitational potential (phi) and of the density and find that they scale; the latter scales as 1/r^2. A rich structure emerges in the two-point correl- tors from the phi fluctuations around phi_0(r). The n-point correlators are explicitly computed to the one-loop level.The relevant effective coupling turns out to be lambda=4 pi G m^2 / (T R). The renormalization group equations (RGE) for the n-point correlator are derived and the RG flow for the effective coupling lambda(tau) [tau = ln(R/delta), explicitly obtained.A novel dependence on tau emerges here.lambda(tau) vanishes each time tau approaches discrete values tau=tau_n = 2 pi n/sqrt7-0, n=0,1,2, ...Such RG infrared stable behavior [lambda(tau) decreasing with increasing tau] is here connected with low density self-similar fractal structures fitting one into another.For scales smaller than the points tau_n, ultraviolet unstable behaviour appears which we connect to Jeans' unstable behaviour, growing density and fragmentation. Remarkably, we get a hierarchy of scales and Jeans lengths following the geometric progression R_n=R_0 e^{2 pi n /sqrt7} = R_0 [10.749087...]^n . A hierarchy of this type is expected for non-spherical geometries,with a rate different from e^{2 n/sqrt7}.Comment: LaTex, 31 pages, 11 .ps 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 $X^0 \to 0$ and $X^0 \to \infty$ and we plot the numerical solution for all times. Right after the big bang ($X^0 = 0$), the string energy decreasess as $R(X^0)^{-1}$ and the string size grows as $R(X^0)$ for $0 1$. Very soon [ $X^0 \sim 1$] , 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 A2A_2 spin chains combining different representations

A non homogeneous spin chain in the representations $\{3 \}$ and $\{3^*\}$ of $A_2$ 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.

The Effective Theory of Inflation and the Dark Matter Status in the Standard Model of the Universe

We present here the effective theory of inflation `a la Ginsburg-Landau in which the inflaton potential is a polynomial. The slow-roll expansion becomes a systematic 1/N expansion where N ~ 60. The spectral index and the ratio of tensor/scalar fluctuations are n_s - 1 = O(1/N), r = O(1/N) while the running turns to be d n_s/d \ln k = O(1/N^2) and can be neglected. The energy scale of inflation M ~ 0.7 10^{16} GeV is completely determined by the amplitude of the scalar adiabatic fluctuations. A complete analytic study plus the Monte Carlo Markov Chains (MCMC) analysis of the available CMB+LSS data showed: (a) the spontaneous breaking of the phi -> - phi symmetry of the inflaton potential. (b) a lower bound for r: r > 0.023 (95% CL) and r > 0.046 (68% CL). (c) The preferred inflation potential is a double well, even function of the field with a moderate quartic coupling yielding as most probable values: n_s = 0.964, r = 0.051. This value for r is within reach of forthcoming CMB observations. We investigate the DM properties using cosmological theory and the galaxy observations. Our DM analysis is independent of the particle physics model for DM and it is based on the DM phase-space density rho_{DM}/sigma^3_{DM}. We derive explicit formulas for the DM particle mass m and for the number of ultrarelativistic degrees of freedom g_d (hence the temperature) at decoupling. We find that m turns to be at the keV scale. The keV scale DM is non-relativistic during structure formation, reproduces the small and large scale structure but it cannot be responsible of the e^+ and pbar excess in cosmic rays which can be explained by astrophysical mechanisms (Abridged).Comment: 28 pages; to be published in the Lev Lipatov Festschrift on the occasion of Lev's 70th birthday, `Subtleties in Quantum Field Theories', D. Diakonov, Editor, Gatchina, Russia, 201