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In the covariant lattice formalism, chiral four-dimensional heterotic string vacua are obtained from certain even self-dual lattices which completely decompose into a left-mover and a right-mover lattice. The main purpose of this work is to classify all right-mover lattices that can appear in such a chiral model, and to study the corresponding left-mover lattices using the theory of lattice genera. In particular, the Smith-Minkowski-Siegel mass formula is employed to calculate a lower bound on the number of left-mover lattices. Also, the known relationship between asymmetric orbifolds and covariant lattices is considered in the context of our classification.
Three-dimensional string models with half-maximal supersymmetry are believed to be invariant under a large U-duality group which unifies the S and T dualities in four dimensions. We propose an exact, U-duality invariant formula for four-derivative sc
We construct a Lorentz and generally covariant, polynomial action for free chiral $p-$forms, classically equivalent to the Pasti-Sorokin-Tonin (PST) formulation. The minimal set up requires introducing an auxiliary $p-$form on top of the physical gau
We derive the chiral kinetic equation in 8 dimensional phase space in non-Abelian $SU(N)$ gauge field within the Wigner function formalism. By using the covariant gradient expansion, we disentangle the Wigner equations in four-vector space up to the
We discuss type I -- heterotic duality in four-dimensional models obtained as a Coulomb phase of the six-dimensional U(16) orientifold model compactified on T^2 with arbitrary SU(16) Wilson lines. We show that Kahler potentials, gauge threshold corre
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/