Efficient classification of heterotic-string vacua

Student: Luke Detraux
Supervisors: Alon Farragi, Sven Schewe, Dominik Wojtczak (UoL)
Institution: University of Liverpool

The aim is to explore the existence of de Sitter vacua with stable moduli in heterotic--string compactifications. Dedicated computerised tools will be developed for efficient analysis of large spaces of models. In particular, we will develop the application of Satisfiability Modulo Theories (SMT) in the investigation of these spaces. The objectives are: 

1. Exploring the existence of De--Sitter string vacua with stable moduli.
2. Extend the classification methods to include further details of the models, such as Yukawa couplings and fermion mass matrices.

The motivation to study these spaces stems from their role in attempts to understand the synthesis of quantum mechanics and general relativity, which is still unknown. The process of seeking a unifying mathematical framework also produces important and novel results that are of interest and value from the experimental particle physics point of view. The prime example is the successful top quark mass prediction (A E Faraggi, Phys.Lett. B274 (1992) 47), which was obtained several years prior to the experimental observation. The classification of large spaces of these phenomenological string vacua has been ongoing since 2003 and led to important discoveries like spinor-vector duality and exophobic string vacua. The search for de Sitter string vacua occupies much of the contemporary research in string phenomenology. Toward that end we will extend the classification program to non-supersymmetric string models with asymmetric boundary conditions. You will develop the tools to extract tachyon free string vacua and to analyse the vacuum energy near the minimum of the potential. You will develop the tools to incorporate string vacua with asymmetric boundary conditions in which the untwisted moduli are stabilised.