Chiral Four-Dimensional Heterotic String Vacua from by Florian Beye

By Florian Beye

This ebook is put on the interface among string thought and effortless particle physics and exhibits novel leads to the hunt for a heterotic string vacuum that reproduces these subject debris and interactions saw in our universe. the writer offers a scientific category of doubtless lifelike heterotic covariant lattice vacua, which own a decrease variety of moduli fields in comparison to traditional compactification equipment, by way of quantity theoretical equipment. those tools, whereas renowned to the maths group, haven't but came upon many purposes to physics. they're brought to the measure essential to comprehend the computations conducted all through this paintings. moreover, particular covariant lattice versions with rather attention-grabbing houses are analyzed intimately. eventually, new mild is shed at the relation among covariant lattice types and uneven orbifold compactifications, the outcome being a concrete correspondence among particular types of uneven orbifolds and people categorised covariant lattices.

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When we say that a lattice Λ is spanned (or generated) by a finite set {a1 , . . , aN } of vectors ai ∈ Λ, we mean that any x ∈ Λ can be written as a, not necessarily unique, integer linear combination of the ai . Now, one might hope that, for any such generating set, it is possible to choose a basis where all basis vectors bi belong to that generating set. 1 The Supercurrent Lattices 31 so for lattices (consider, for example, the lattice Z and the generating set {2, 3}). A counterexample that comes close to our situation has been found in [6].

Nucl. Phys. B 768, 135–156 (2007). 018 32. : Revisiting coupling selection rules in heterotic orbifold models. JHEP 1205, 008 (2012). 1007/JHEP05(2012)008 33. : Constructing 5-D orbifold grand unified theories from heterotic strings. Phys. Lett. B 593, 262–270 (2004). 058 34. : Searching for realistic 4d string models with a PatiSalam symmetry: orbifold grand unified theories from heterotic string compactification on a Z(6) orbifold. Nucl. Phys. B 704, 3–55 (2005). 035 35. : A Mini-landscape of exact MSSM spectra in heterotic orbifolds.

2 Right-Mover and Left-Mover Lattices We have now classified the possible supercurrent lattices Ξ that may appear in a chiral covariant lattice model. From these we can construct all possible right-mover lattices (Γ14 )R and discuss the associated left-mover lattices that are compatible with modular invariance. Before we are able to do this, we must briefly study some facts about discriminant forms and lattice genera. 1 Discriminant Forms and Lattice Genera Let us begin by introducing the concept of discriminant forms [11].

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