We study a racetrack model in the presence of the leading alpha-correction in flux compactification in Type IIB string theory, for the purpose of getting conceivable de-Sitter vacua in the large compactified volume approximation. Unlike the Kahler Up
lift model studied previously, the alpha-correction is more controllable for the meta-stable de-Sitter vacua in the racetrack case since the constraint on the compactified volume size is very much relaxed. We find that the vacuum energy density Lambda for de-Sitter vacua approaches zero exponentially as the volume grows. We also analyze properties of the probability distribution of Lambda in this class of models. As in other cases studied earlier, the probability distribution again peaks sharply at Lambda=0. We also study the Racetrack Kahler Uplift model in the Swiss-Cheese type model.
We study the probability distribution P(Lambda) of the cosmological constant Lambda in a specific set of KKLT type models of supersymmetric IIB vacua. We show that, as we sweep through the quantized flux values in this flux compactification, P(Lambda
) behaves divergent at Lambda =0^- and the median magnitude of Lambda drops exponentially as the number of complex structure moduli h^{2,1} increases. Also, owing to the hierarchical and approximate no-scale structure, the probability of having a positive Hessian (mass squared matrix) approaches unity as h^{2,1} increases.
Based on the properties of probability distributions of functions of random variables, we proposed earlier a simple stringy mechanism that prefers the meta-stable vacua with a small cosmological constant Lambda. As an illustration of this approach, w
e study in this paper particularly simple but non-trivial models of the Kahler uplift in the large volume flux compactification scenario in Type IIB string theory, where all parameters introduced in the model are treated either as fixed constants motivated by physics, or as random variables with some given uniform probability distributions. We determine the value w_0 of the superpotential W_0 at the supersymmetric minima, and find that the resulting probability distribution P(w_0) peaks at w_0=0; furthermore, this peaking behavior strengthens as the number of complex structure moduli increases. The resulting probability distribution P(Lambda) for meta-stable vacua also peaks as Lambda -> 0, for both positive and negative Lambda. This peaking/divergent behavior of P(Lambda) strengthens as the number of moduli increases. In some scenarios for Lambda > 0, the likely value of Lambda decreases exponentially as the number of moduli increases. The light cosmological moduli issue accompanying a very small Lambda is also mentioned.
Based on the probability distributions of products of random variables, we propose a simple stringy mechanism that prefers the meta-stable vacua with a small cosmological constant. We state some relevant properties of the probability distributions of
functions of random variables. We then illustrate the mechanism within the flux compactification models in Type IIB string theory. As a result of the stringy dynamics, we argue that the generic probability distribution for the meta-stable vacua typically peaks with a divergent behavior at the zero value of the cosmological constant. However, its suppression in the single modulus model studied here is modest.
The search for classically stable Type IIA de-Sitter vacua typically starts with an ansatz that gives Anti-de-Sitter supersymmetric vacua and then raises the cosmological constant by modifying the compactification. As one raises the cosmological cons
tant, the couplings typically destabilize the classically stable vacuum, so the probability that this approach will lead to a classically stable de-Sitter vacuum is Gaussianly suppressed. This suggests that classically stable de-Sitter vacua in string theory (at least in the Type IIA region), especially those with relatively high cosmological constants, are very rare. The probability that a typical de-Sitter extremum is classically stable (i.e., tachyon-free) is argued to be Gaussianly suppressed as a function of the number of moduli.
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 th
e 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.
We construct a model of quintessence in string theory based on the idea of axion monodromy as discussed by McAllister, Silverstein and Westphal arXiv:0808.0706. In the model, the quintessence field is an axion whose shift symmetry is broken by the pr
esence of 5-branes which are placed in highly warped throats. This gives rise to a potential for the axion field which is slowly varying, even after incorporating the effects of moduli stabilization and supersymmetry breaking. We find that the resulting time dependence in the equation of state of Dark Energy is potentially detectable, depending on the initial conditions. The model has many very light extra particles which live in the highly warped throats, but these are hard to detect. A signal in the rotation of the CMB polarization can also possibly arise.
We show that the N=8 superconformal Bagger-Lambert theory based on the Lorentzian 3-algebra can be derived by taking a certain scaling limit of the recently proposed N=6 superconformal U(N)xU(N) Chern-Simons-matter theories at level (k, -k). The scal
ing limit (and Inonu-Wigner contraction) is to scale the trace part of the bifundamental fields as X_0 -> lambda^{-1} X_0 and an axial combination of the two gauge fields as B_{mu} -> lambda B_mu. Simultaneously we scale the level as k -> lambda^{-1} k and then take lambda -> 0 limit. Interestingly the same constraint equation partial^2 X_0=0 is derived by imposing finiteness of the action. In this scaling limit, M2-branes are located far from the origin of C^4/Z_k compared to their fluctuations and Z_k identification becomes a circle identification. Hence the scaled theory describes N=8 supersymmetric theory of 2-branes with dynamical coupling. The coupling constant is promoted to a space-time dependent SO(8) vector X_0^I and we show that the scaled theory has a generalized conformal symmetry as well as manifest SO(8) with the transformation of the background fields X_0^I.
Based on the recent proposal of N=8 superconformal gauge theories of the multiple M2 branes, we derive (2+1)-dimensional supersymmetric Janus field theories with a space-time dependent coupling constant. From the original Bagger-Lambert model, we get
a supersymmetric field theory with a similar action to the N D2 branes, but the coupling varies with the space-time as a function of the light-cone coordinate, g(t+x). Half of the supersymmetries can be preserved. We further investigate the M2 brane action deformed by mass and Myers-like terms. In this case, the final YM action is deformed by mass and Myers terms and the coupling behaves as exp(mu x) where mu is a constant mass parameter. Weak coupling gauge theory is continuously changed to strong coupling in the large x region.
