From Random Matrices to Stochastic Operators

We propose that classical random matrix models are properly viewed as finite difference schemes for stochastic differential operators. Three particular stochastic operators commonly arise, each associated with a familiar class of local eigenvalue behavior. The stochastic Airy operator displays soft edge behavior, associated with the Airy kernel. The stochastic Bessel operator displays hard edge behavior, associated with the Bessel kernel. The article concludes with suggestions for a stochastic sine operator, which would display bulk behavior, associated with the sine kernel.Comment: 41 pages, 5 figures. Submitted to Journal of Statistical Physics. Changes in this revision: recomputed Monte Carlo simulations, added reference [19], fit into margins, performed minor editin

Competition of ferromagnetic and antiferromagnetic spin ordering in nuclear matter

In the framework of a Fermi liquid theory it is considered the possibility of ferromagnetic and antiferromagnetic phase transitions in symmetric nuclear matter with Skyrme effective interaction. The zero temperature dependence of ferromagnetic and antiferromagnetic spin polarization parameters as functions of density is found for SkM$^*$, SGII effective forces. It is shown that in the density domain, where both type of solutions of self--consistent equations exist, ferromagnetic spin state is more preferable than antiferromagnetic one.Comment: 9p., 3 figure

Statistical Mechanics of Three-dimensional Kerr-de Sitter Space

The statistical computation of the (2+1)-dimensional Kerr-de Sitter space in the context of the {\it classical} Virasoro algebra for an asymptotic isometry group has been a mystery since first, the degeneracy of the states has the right value only at the infinite boundary which is casually disconnected from our universe, second, the analyses were based on the unproven Cardy's formula for complex central charge and conformal weight. In this paper, I consider the entropy in Carlip's "would-be gauge" degrees of freedom approach instead. I find that it agree with the Bekenstein-Hawking entropy but there are no the above problems. Implications to the dS/CFT are noted.Comment: Added comments about diffeomorphism generators and Wheeler-de Witt equation; Added references; Accpected in CQ

Equation of state and magnetic susceptibility of spin polarized isospin asymmetric nuclear matter

Properties of spin polarized isospin asymmetric nuclear matter are studied within the framework of the Brueckner--Hartree--Fock formalism. The single-particle potentials of neutrons and protons with spin up and down are determined for several values of the neutron and proton spin polarizations and the asymmetry parameter. It is found an almost linear and symmetric variation of the single-particle potentials as increasing these parameters. An analytic parametrization of the total energy per particle as a function of the asymmetry and spin polarizations is constructed. This parametrization is employed to compute the magnetic susceptibility of nuclear matter for several values of the asymmetry from neutron to symmetric matter. The results show no indication of a ferromagnetic transition at any density for any asymmetry of nuclear matter.Comment: 23 pages, 8 figures, 2 tables (submitted to Phys. Rev. C

Warped Spectroscopy: Localization of Frozen Bulk Modes

We study the 10D equation of motion of dilaton-axion fluctuations in type IIB string compactifications with three-form flux, taking warping into account. Using simplified models with physics comparable to actual compactifications, we argue that the lightest mode localizes in long warped throats and takes a mass of order the warped string scale. Also, Gukov-Vafa-Witten superpotential is valid for the lightest mass mode; however, the mass is similar to the Kaluza-Klein scale, so the dilaton-axion should be integrated out of the effective theory in this long throat regime (leaving a constant superpotential). On the other hand, there is a large hierarchy between flux-induced and KK mass scales for moderate or weak warping. This hierarchy agrees with arguments given for trivial warping. Along the way, we also estimate the effect of the other 10D supergravity equations of motion on the dilaton-axion fluctuation, since these equations act as constraints. We argue that they give negligible corrections to the simplest approximation.Comment: 24pp + appendices, 6 figs, JHEP3 class; v2. corrected reference; v3. added clarifications; v4. corrected typo

An Inflaton Mass Problem in String Inflation from Threshold Corrections to Volume Stabilization

Inflationary models whose vacuum energy arises from a D-term are believed not to suffer from the supergravity eta problem of F-term inflation. That is, D-term models have the desirable property that the inflaton mass can naturally remain much smaller than the Hubble scale. We observe that this advantage is lost in models based on string compactifications whose volume is stabilized by a nonperturbative superpotential: the F-term energy associated with volume stabilization causes the eta problem to reappear. Moreover, any shift symmetries introduced to protect the inflaton mass will typically be lifted by threshold corrections to the volume-stabilizing superpotential. Using threshold corrections computed by Berg, Haack, and Kors, we illustrate this point in the example of the D3-D7 inflationary model, and conclude that inflation is possible, but only for fine-tuned values of the stabilized moduli. More generally, we conclude that inflationary models in stable string compactifications, even D-term models with shift symmetries, will require a certain amount of fine-tuning to avoid this new contribution to the eta problem.Comment: 25 page

Orientifolds, RG Flows, and Closed String Tachyons

We discuss the fate of certain tachyonic closed string theories from two perspectives. In both cases our approach involves studying directly configurations with finite negative tree-level cosmological constant. Closed string analogues of orientifolds, which carry negative tension, are argued to represent the minima of the tachyon potential in some cases. In other cases, we make use of the fact, noted in the early string theory literature, that strings can propagate on spaces of subcritical dimension at the expense of introducing a tree-level cosmological constant. The form of the tachyon vertex operator in these cases makes it clear that a subcritical-dimension theory results from tachyon condensation. Using results of Kutasov, we argue that in some Scherk-Schwarz models, for finely-tuned tachyon condensates, a minimal model CFT times a subcritical dimension theory results. In some instances, these two sets of ideas may be related by duality.Comment: 15 pages, 2 figures, uses harvmac; v2: references adde

Phase transition to the state with nonzero average helicity in dense neutron matter

The possibility of the appearance of the states with a nonzero average helicity in neutron matter is studied in the model with the Skyrme effective interaction. By providing the analysis of the self-consistent equations at zero temperature, it is shown that neutron matter with the Skyrme BSk18 effective force undergoes at high densities a phase transition to the state in which the degeneracy with respect to helicity of neutrons is spontaneously removed.Comment: 4 pages, 3 figures; v2: journal versio

Stability Constraints on Classical de Sitter Vacua

We present further no-go theorems for classical de Sitter vacua in Type II string theory, i.e., de Sitter constructions that do not invoke non-perturbative effects or explicit supersymmetry breaking localized sources. By analyzing the stability of the 4D potential arising from compactification on manfiolds with curvature, fluxes, and orientifold planes, we found that additional ingredients, beyond the minimal ones presented so far, are necessary to avoid the presence of unstable modes. We enumerate the minimal setups for (meta)stable de Sitter vacua to arise in this context.Comment: 18 pages; v2: argument improved, references adde