Related papers: A note on modular invariant species scale and pote…
Compactification of the heterotic string on toroidal orbifolds is a promising set-up for the construction of realistic unified models of particle physics. The target space dynamics of such models, however, drives them slightly away from the…
The EFT coefficients in any gapped, scalar, Lorentz invariant field theory must satisfy positivity requirements if there is to exist a local, analytic Wilsonian UV completion. We apply these bounds to the tree level scattering amplitudes…
We derive the scalar mass matrices in effective supergravity models augmented by a $U(1)_F$ family symmetry. Simple relations between $U(1)_F$ charges and modular weights of the superfields are derived and used to express the matrices with…
In a thermal field theory, the cumulants of the momentum distribution can be extracted from the dependence of the Euclidean path integral on a shift in the fields built into the temporal boundary condition. When combined with the Ward…
Many N=(2,2) two-dimensional nonlinear sigma models with Calabi-Yau target spaces admit ultraviolet descriptions as N=(2,2) gauge theories (gauged linear sigma models). We conjecture that the two-sphere partition function of such…
This is the author's PhD thesis. Two main sections address various aspects of mirror symmetry for compact Calabi-Yau threefolds and the roles that classically modular varieties play in string theory compactifications. The main results…
We derive the action for a massive tensor multiplet coupled to chiral and vector multiplets as it can appear in orientifold compactifications of type IIB string theory.We compute the potential of the theory and show its consistency with the…
We describe an application of tropical moduli spaces to complex dynamics. A post-critically finite branched covering $\varphi$ of $S^2$ induces a pullback map on the Teichm\"uller space of complex structures of $S^2$; this descends to an…
In this article we study invariance properties of shift-invariant spaces in higher dimensions. We state and prove several necessary and sufficient conditions for a shift-invariant space to be invariant under a given closed subgroup of…
We find de Sitter and flat space solutions with all moduli stabilized in four dimensional supergravity theories derived from the heterotic and type II string theories, and explain how all the previously known obstacles to finding such…
We generalize the known equivalence between higher order gravity theories and scalar tensor theories to a new class of theories. Specifically, in the context of a first order or Palatini variational principle where the metric and connection…
By identifying the moduli space of coupling constants in the SYM description of toroidal compactifications of M(atrix)-Theory, we construct the M(atrix) description of the moduli spaces of Type IIA string theory compactified on T^n.…
We show that in supersymmetry one can obtain inflationary potentials in the observable sector that are sufficiently flat at sub-Planckian field values. Structure of the supersymmetric scalar potential along a flat direction combined with…
The Swampland Distance Conjecture claims that effective theories derived from a consistent theory of quantum gravity only have a finite range of validity. This will imply drastic consequences for string theory model building. The refined…
Several arguments are given for the summability of the superstring perturbation series. Whereas the Schottky group coordinatization of moduli space may be used to provide refined estimates of large-order bosonic string amplitudes, the…
Much recent attention has focused on theories with large extra compactified dimensions. However, while the phenomenological implications of the volume moduli associated with such compactifications are well understood, relatively little…
We show that the higher homotopy groups of the moduli space of torus-invariant positive scalar curvature metrics on certain quasitoric manifolds are non-trivial.
It is a well established fact, that any projective algebraic variety is a moduli space of representations over some finite dimensional algebra. This algebra can be chosen in several ways. The counterpart in algebraic geometry is…
We discuss the period geometry and the topological string amplitudes on elliptically fibered Calabi-Yau fourfolds in toric ambient spaces. In particular, we describe a general procedure to fix integral periods. Using some elementary facts…
We extend the framework of modular invariant supersymmetric theories to encompass invariance under more general discrete groups $\Gamma$, that allow the presence of several moduli and make connection with the theory of automorphic forms.…