Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userSatisfiability Modulo Theories and Chiral Heterotic String Vacua with Positive Cosmological Constant
79
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We apply Boolean Satisfiability (SAT) and Satisfiability Modulo Theories (SMT) solvers in the context of finding chiral heterotic string models with positive cosmological constant from $mathbb{Z}_2times mathbb{Z}_2$ orbifolds. The power of using SAT/SMT solvers to sift large parameter spaces quickly to decide satisfiability, both to declare and prove unsatisfiability and to declare satisfiability, are demonstrated in this setting. These models are partly chosen to be small enough to plot the performance against exhaustive search, which takes around 2 hours 20 minutes to comb through the parameter space. We show that making use of SMT based techniques with integer encoding is rather simple and effective, while a more careful Boolean SAT encoding provides a significant speed-up -- determining satisfiability or unsatisfiability has, in our experiments varied between 0.03 and 0.06 seconds, while determining all models (where models exist) took 19 seconds for a constraint system that allows for 2048 models and 8.4 seconds for a constraint system that admits 640 models. We thus gain several orders of magnitude in speed, and this advantage is set to grow with a growing parameter space. This holds the promise that the method scales well beyond the initial problem we have used it for in this paper.
rate research
Read More
The heterotic--string models in the free fermionic formulation gave rise to some of the most realistic string models to date, which possess N=1 spacetime supersymmetry. Lack of evidence for supersymmetry at the LHC instigated recent interest in non-supersymmetric heterotic-string vacua. We explore what may be learned in this context from the quasi--realistic free fermionic models. We show that constructions with a low number of families give rise to proliferation of a priori tachyon producing sectors, compared to the non--realistic examples, which typically may contain only one such sector. The reason being that in the realistic cases the internal six dimensional space is fragmented into smaller units. We present one example of a quasi--realistic, non--supersymmetric, non--tachyonic, heterotic--string vacuum and compare the structure of its massless spectrum to the corresponding supersymmetric vacuum. While in some sectors supersymmetry is broken explicitly, i.e. the bosonic and fermionic sectors produce massless and massive states, other sectors, and in particular those leading to the chiral families, continue to exhibit fermi-bose degeneracy. In these sectors the massless spectrum, as compared to the supersymmetric cases, will only differ in some local or global U(1) charges. We discuss the conditions for obtaining $n_b=n_f$ at the massless level in these models. Our example model contains an anomalous U(1) symmetry, which generates a tadpole diagram at one loop-order in string perturbation theory. We speculate that this tadpole diagram may cancel the corresponding diagram generated by the one-loop non-vanishing vacuum energy and that in this respect the supersymmetric and non-supersymmetric vacua should be regarded on equal footing. Finally we discuss vacua that contain two supersymmetry generating sectors.
Classification of Left-Right Symmetric (LRS) heterotic-string vacua in the free fermionic formulation, using random generation of generalised GSO (GGSO) projection coefficients, produced phenomenologically viable models with probability $4times 10^{-11}$. Extracting substantial number of phenomenologically viable models requires modification of the classification method. This is achieved by identifying phenomenologically amenable conditions on the Generalised GSO projection coefficients that are randomly generated at the $SO(10)$ level. Around each of these fertile cores we perform a complete LRS classification, generating viable models with probabilility $1.4times 10^{-2}$, hence increasing the probability of generating phenomenologically viable models by nine orders of magnitude, and producing some $1.4times 10^5$ such models. In the process we identify a doublet-triplet selection mechanism that operates in twisted sectors of the string models that break the $SO(10)$ symmetry to the Pati-Salam subgroup. This mechanism therefore operates as well in free fermionic models with Pati-Salam and Standard-like Model $SO(10)$ subgroups.
Recently it was proposed that ten-dimensional tachyonic string vacua may serve as starting points for the construction of viable four dimensional phenomenological string models which are tachyon free. This is achieved by projecting out the tachyons in the four-dimensional models using projectors other than the projector which is utilised in the supersymmetric models and those of the $SO(16)times SO(16)$ heterotic string. We continue the exploration of this class of models by developing systematic computerised tools for their classification, the analysis of their tachyonic and massless spectra, as well as analysis of their partition functions and vacuum energy. We explore a randomly generated space of $2times10^9$ string vacua in this class and find that tachyon--free models occur with $sim 5times 10^{-3}$ probability, and of those, phenomenologically inclined $SO(10)$ vacua with $a_{00}=N_b^0-N_f^0=0$, i.e. equal number of fermionic and bosonic massless states, occur with frequency $sim 2times 10^{-6}$. Extracting larger numbers of phenomenological vacua therefore requires adaptation of fertility conditions that we discuss, and significantly increase the frequency of tachyon--free models. Our results suggest that spacetime supersymmetry may not be a necessary ingredient in phenomenological string models, even at the Planck scale.
Based on the studies in Type IIB string theory phenomenology, we conjecture that a good fraction of the meta-stable de Sitter vacua in the cosmic stringy landscape tend to have a very small cosmological constant $Lambda$ when compared to either the string scale $M_S$ or the Planck scale $M_P$, i.e., $Lambda ll M_S^4 ll M_P^4$. These low lying de Sitter vacua tend to be accompanied by very light scalar bosons/axions. Here we illustrate this phenomenon with the bosonic mass spectra in a set of Type IIB string theory flux compactification models. We conjecture that small $Lambda$ with light bosons is generic among de Sitter solutions in string theory; that is, the smallness of $Lambda$ and the existence of very light bosons (may be even the Higgs boson) are results of the statistical preference for such vacua in the landscape. We also discuss a scalar field $phi^3/phi^4$ model to illustrate how this statistical preference for a small $Lambda$ remains when quantum loop corrections are included, thus bypassing the radiative instability problem.
The three generation heterotic-string models in the free fermionic formulation are among the most realistic string vacua constructed to date, which motivated their detailed investigation. The classification of free fermion heterotic string vacua has revealed a duality under the exchange of spinor and vector representations of the SO(10) GUT symmetry over the space of models. We demonstrate the existence of the spinor-vector duality using orbifold techniques, and elaborate on the relation of these vacua to free fermionic models.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
