Quantum cosmology at finite temperature in superstring theory
We study cosmology induced by an ideal superstring gas at finite temperature. The thermal/quantum effects of the string gas generate a nontrivial effective potential at one-loop level. At certain points in the moduli space where generically massive states become massless, the effective potential develops local minima. The latter serve as moduli attractors, which induce time-dependent scalar masses decreasing in cosmological time. As a result, the coherent scalar oscillations dilute before nucleosynthesis, and the cosmological moduli problem is avoided. In particular, we study moduli stabilization in the cases of cosmology induced by i) a maximally supersymmetric heterotic string gas; ii) a gas of type II string compactified on Calabi-Yau three-folds. In case i), the local minima of the potential arise at enhanced gauge symmetry points, which can stabilize all moduli but the dilaton. In case ii), local minima of the effective potential are reached at the loci where 2-spheres or 3-spheres in the Calabi-Yau space shrink to zero size, giving rise to either conifold transitions or non Abelian gauge symmetries. Extra massless states are induced by D-brane wrapping the shrinking spheres, and the stabilized moduli are those controlling the volume of those spheres. In addition, in the two cases we also study respectively the type I dual theory which is maximally supersymmetric and the heterotic dual theory compactified on K3xT2. We show that dual moduli can be stabilized by novel non-perturbative effects implied by duality maps.

title: Moduli stabilization in type II Calabi-Yau compactifications at finite temperature
abstract: A bstractWe consider the type II superstring compactified on Calabi-Yau threefolds, at finite temperature. The latter is implemented at the string level by a free action on the Euclidean time circle. We show that all Kähler and complex structure moduli involved in the gauge theories geometrically engineered in the vicinity of singular loci are lifted by the stringy thermal effective potential. The analysis is based on the effective gauged super-gravity at low energy, without integrating out the non-perturbative BPS states becoming massless at the singular loci. The universal form of the action in the weak coupling regime and at low enough temperature is determined in two cases. Namely, the conifold locus, as well as a locus where the internal space develops a genus-g curve of AN −1 singularities, thus realizing an SU(N ) gauge theory coupled to g hypermultiplets in the adjoint. In general, we argue that the favored points of stabilization sit at the intersection of several such loci. As a result, the entire vector multiplet moduli space is expected to be lifted, together with hypermultiplet moduli. The scalars are dynamically stabilized during the cosmological evolution induced by the back-reaction of the thermal effective potential on the originally static background. When the universe expands and the temperature T drops, the scalars converge to minima, with damped oscillations. Moreover, they store an energy density that scales as T4, which never dominates over radiation. The reason for this is that the mass they acquire at one-loop is of order the temperature scale, which is time-dependent rather than constant. As an example, we analyze the type IIA compactification on a hy-persurface $$ \mathbb{P}_{{\left(  \right)}}^4 $$ [12], with Hodge numbers h11 = 2 and h12 = 128. In this case, both Kähler moduli are stabilized at a point, where the internal space develops a node and an enhanced SU(2) gauge theory coupled to 2 adjoint hypermultiplets. This shows that in the dual thermal heterotic picture on K3 × T2, the torus modulus and the axio-dilaton are stabilized, though in a strong coupling heterotic regime.

title: Massless D-strings and moduli stabilization in type I cosmology
abstract: We consider the cosmological evolution induced by the free energy F of a gas of maximally supersymmetric heterotic strings at finite temperature and weak coupling in dimension D ≥ 4. We show that F, which plays the role of an effective potential, has minima associated to enhanced gauge symmetries, where all internal moduli can be attracted and dynamically stabilized. Using the fact that the heterotic/type I S-duality remains valid at finite temperature and can be applied at each instant of a quasi-static evolution, we find in the dual type I cosmology that all internal NS-NS and RR moduli in the closed string sector and the Wilson lines in the open string sector can be stabilized. For the special case of D = 6, the internal volume modulus remains a flat direction, while the dilaton is stabilized. An essential role is played by light D-string modes wrapping the internal manifold and whose contribution to the free energy cannot be omitted, even when the type I string is at weak coupling. As a result, the order of magnitude of the internal radii expectation values on the type I side is $ \sqrt {{{\lambda_{\text{I}}}{\alpha^{\prime}}}} $, where λI is the ten-dimensional string coupling. The non-perturbative corrections to the type I free energy can alternatively be described as effects of “thermal E1-instantons”, whose worldsheets wrap the compact Euclidean time cycle.

title: Lecture notes on thermodynamics of ideal string gases and its application in cosmology
abstract: In these lecture notes I give a pedagogical introduction to the thermodynamics of ideal string gases. The computation of thermodynamic quantities in the canonical ensemble formalism will be shown in detail with explicit examples. Attention will be given mainly to the thermodynamical consequences of string degrees of freedom, where I will especially address i) the Hagedorn temperature, a critical temperature above which the canonical ensemble description breaks down, which can be the onset point of some instability of the string gas; ii) the phase structure arising from compactification, embodied in the moduli-dependence of the Helmholtz free energy, which corrects the tree-level vacuum and can provide mechanism for moduli stabilization. Then I will briefly explain the implementation of string gas thermodynamics in cosmology, showing a simple example which gives rise to a radiation-dominated early universe. Further phenomenological issues and open questions will be discussed qualitatively with references indicated, including the Hagedorn instability in the resolution of the initial singularity, moduli stabilization, generation of hierarchy, radiative symmetry breaking and primordial cosmological fluctuations.

title: Moduli stabilisation in early superstring cosmology
abstract: We study the cosmological evolution induced by the free energy of a string gas at finite temperature. We first consider the maximally supersymmetric heterotic string in the weak coupling regime in dimension D ≥ 4. The free energy develops local minima associated to some gauge symmetry enhancement induced by perturbative states. This can stabilize all heterotic moduli except the dilaton. By string-string S-dualities, it follows that the dual type I moduli can be stabilized by either non perturbative D-string states or perturbative open string states. We next consider the type II string compactified on Calabi-Yau three-folds, which has = 2 supersymmetry in D = 4. The moduli space has singular loci where the Calabi-Yau space undergoes extremal transitions, accompanied with either conifold transitions or certain gauge symmetry enhancement. Also the free energy reaches local minima due to the emergence of extra non perturbative massless modes. Consequently, the type II moduli are attracted to these singular loci. Using the type II/heterotic string duality, we can stabilize the dual heterotic moduli, and in particular it is possible to stabilize the heterotic dilaton.

title: Holographic renormalization in no-boundary quantum cosmology
abstract: Recent results of Hartle-Hawking wave functions on asymptotic dS boundaries show non-normalizability, while the bulk origin is not clear. This paper attempts to addresse this problem by studying (Kerr-)dS_3 cosmology in Einstein gravity deformed by a minimally coupled scalar field. Various saddle-point contributions exp[i(saddle-point action)] to the Hartle-Hawking wave functions are computed with mini-superspace formalism. The saddle-point actions are first obtained in the spacetime bulks by direct computation, then on the asymptotic dS boundary by holographic renormalization. It is found that the imaginary part of the saddle-point actions, as functions of scalar field deformation, are generally bounded in the bulk, but can diverge to -infty on the boundary. This can probably be a source of the scalar field-related non-normalizability of the boundary Hartle-Hawking wave functions. For Kerr-dS_3 cosmology, some saddle-point actions have imaginary parts diverging to -infty both in the bulk and on the boundary, when the boundary T^2 is stretched to infinitely long. This can be an origin of non-normalizability of the boundary Hartle-Hawking wave functions related to temperature divergence. Finally the holographic renormalization is extended to scalar-deformed dS_{d+1} (d>= 3) cosmologies for the imaginary part of the saddle-point actions. The result is tested on a 5d example, and saddle points leading to divergent contribution to the boundary Hartle-Hawking wave function are shown to exist.

title: Centrality Dependence of Charged Particle Production at Large Transverse Momentum in Pb--Pb Collisions at $\sqrt{s_{\rm{NN}}} = 2.76$ TeV
abstract: The inclusive transverse momentum ($p_{\rm T}$) distributions of primary charged particles are measured in the pseudo-rapidity range $|\eta|<0.8$ as a function of event centrality in Pb--Pb collisions at $\sqrt{s_{\rm{NN}}}=2.76$ TeV with ALICE at the LHC. The data are presented in the $p_{\rm T}$ range $0.1530$ GeV/$c$. In peripheral collisions (70--80%), the suppression is weaker with $R_{\rm{AA}} \approx 0.7$ almost independently of $p_{\rm T}$. The measured nuclear modification factors are compared to other measurements and model calculations.

title: Spontaneous Broken Local Conformal Symmetry and Dark Energy
abstract: The local conformal symmetry is spontaneously broken down to the Local Lorentz invariance symmetry through the approach of nonlinear realization. The resulting effective Lagrangian, in the unitary gauge, describes a cosmological vector field non-minimally coupling to the gravitational field. As a result of the Higgs mechanism, the vector field absorbs the dilaton and becomes massive, but with an independent energy scale. The Proca type vector field can be modelled as dark energy candidate. The possibility that it further triggers Lorentz symmetry violation is also pointed out.

title: Could the Gravitons Have Rest Masses
abstract: If the cosmological constant $\Lambda $ can not be neglected, we will show in this short report, that graviton should have a rest mass $m_g=\sqrt{2\Lambda }=\sqrt{2\Lambda}\hbar c^{-1}$ different from zero.

title: Scaling of Yukawa Couplings and Quark Flavor Mixings in the UED Model
abstract: The evolution properties of Yukawa couplings and quark mixings are performed for the one-loop renormalization group equations in the Universal Extra Dimension (UED) model. It is found that the UED model has a substantial effect on the scaling of the fermion masses, including both quark and lepton sectors, whilst the radiative effects on the unitarity triangle is not a sensitive test in this model. Also, for this model, the renormalization invariants $R_{13}$ and $R_{23}$ describe the correlation between the mixing angles and mass ratios to a good approximation, with a variation of the order of $\lambda^4$ and $\lambda^5$ under energy scaling respectively.

title: String dynamics, spontaneous breaking of supersymmetry, and dual scalar field theory
abstract: The dynamics of a vortex string, which describes the Nambu-Goldstone modes of the spontaneous breakdown of the target space $D=4$, $N=1$ supersymmetry and internal $U(1{)}_{R}$ symmetry to the world sheet $\mathrm{ISO}(1,1)$ symmetry, is constructed by using the approach of nonlinear realization. The resulting action describing the low energy oscillations of the string into the covolume (super)space is found to have an invariant synthesis form of the Akulov-Volkov and Nambu-Goto actions. Its dual scalar field action is obtained by means of introducing two vectorial Lagrangian multipliers into the action of the string.