arXiv subjects

Stefan Mendez-Diez

Publications and source records attributed to Stefan Mendez-Diez.

6 recordsLinked to original sources

arXiv2025

Orientifolds for F-theory on K3 Surfaces

We study F-theory orientifolds, starting with products of two elliptic curves, but focusing mostly on a family of K3 surfaces, lattice polarized by the rank-17 lattice $\langle 8 \rangle \oplus 2D_8(-1)$, generalizing the family (to which it degenerates) of Kummer surfaces of products of two non-isogenous elliptic curves. After a thorough study of the complex geometry of this family and its elliptic fibrations, we proceed to study real structures on the K3 surfaces in the family which are equivariant with respect to an elliptic fibration. We also study the physics of the associated F-theory orientifolds with a particular focus on the impact of the real structure on the charge spectrum. We also study how these orientifolds degenerate to the case of isotrivial Kummer surface fibrations.

hep-th↗

arXiv2019

Geometrization of N-Extended 1-Dimensional Supersymmetry Algebras

The problem of classifying off-shell representations of the $N$-extended one-dimensional super Poincaré algebra is closely related to the study of a class of decorated $N$-regular, $N$-edge colored bipartite graphs known as {\em Adinkras}. In this paper we {\em canonically} realize these graphs as Grothendieck ``dessins d'enfants,'' or Belyi curves uniformized by certain normal torsion-free subgroups of the $(N,N,2)$-triangle group. We exhibit an explicit algebraic model over $\mathbb{Q}(ζ_{2N})$, as a complete intersection of quadrics in projective space, and use Galois descent to prove that the curves are, in fact, definable over $\mathbb{Q}$ itself. The stage is thereby set for the geometric interpretation of the remaining Adinkra decorations in Part II.

hep-th↗

arXiv2016

N=4 and N=8 SUSY Quantum Mechanics and Klein's Vierergruppe

Sets of signed permutation matrices satisfying the GR(4,4) algebra are shown to be, up to sign, left cosets of Klein's famous Vierergruppe. In this way we verify the count done by computer in 2012, and set it in a more significant mathematical context. A similar analysis works for GR(1,1), GR(2,2) and GR(8,8).

hep-th↗

arXiv2014

String theory on elliptic curve orientifolds and KR-theory

We analyze the brane content and charges in all of the orientifold string theories on space-times of the form E x R^8, where E is an elliptic curve with holomorphic or anti-holomorphic involution. Many of these theories involve "twistings" coming from the B-field and/or sign choices on the orientifold planes. A description of these theories from the point of view of algebraic geometry, using the Legendre normal form, naturally divides them into three groupings. The physical theories within each grouping are related to one another via sequences of T-dualities. Our approach agrees with both previous topological calculations of twisted KR-theory and known physics arguments, and explains how the twistings originate from both a mathematical and a physical perspective.

hep-th↗

arXiv2014

T-duality For Orientifolds and Twisted KR-theory

D-brane charges in orientifold string theories are classified by the KR-theory of Atiyah. However, this is assuming that all O-planes have the same sign. When there are O-planes of different signs, physics demands a "KR-theory with a sign choice" which up until now has not been studied by mathematicians (with the unique exception of Moutuou, who didn't have a specific application in mind). We give a definition of this theory and compute it for orientifold theories compactified on a circle and 2-torus. We also explain how and why additional "twisting" is implemented. We show that our results satisfy all possible T-duality relationships for orientifold string theories on elliptic curves, which will be studied further in subsequent work.

hep-th↗

arXiv2011

K-theoretic matching of brane charges in S- and U-duality

We discuss K-theoretic matching of D-brane charges in the string duality between type I on the 4-torus and type IIA on a K3 surface. This case is more complex than the familiar case of IIA/IIB duality, which is already well understood, but it turns out that replacing K3 by its orbifold blow-down seems largely to resolve the apparent problems with the theory. In particular, this allows for precise matching of 2-torsion brane charges.

hep-th↗