arXiv subjects

C. Herbert Clemens

Publications and source records attributed to C. Herbert Clemens.

4 recordsLinked to original sources

arXiv2021

Relative Scales of the GUT and Twin Sectors in an F-theory model

In this letter we analyze the relative scales for the GUT and twin sectors in the F-theory model discussed in Ref. \cite{Clemens-3}. There are a number of volume moduli in the model. The volume of the GUT surface in the visible sector {[}sector(1){]} (with the Wilson line GUT breaking) defines the GUT scale $M_{GUT}\sim2\times10^{16}~GeV$ as the unification scale with precise gauge coupling unification of $SU(3)\times SU(2)\times U(1)_{Y}$. We choose $α_{GUT}^{-1}\sim24$. We are then free to choose the ratio $α_{G}(2)/α_{G}(1)=m_{1}/m_{2}$ with $m(1)$ and $m(2)$ independent volume moduli associated with the directions perpendicular to the two GUT surfaces. We then analyze the effective field theory of the twin sector(2), which may lead to a SUSY breaking gaugino condensate. Of course, all these results are subject to the self-consistent stabilization of the moduli.

hep-th↗

arXiv2020

Right-handed neutrinos and $U\left(1\right)_{X}$ symmetry-breaking

The authors have proposed a global model for Heterotic $F$-theory duality with Wilson line symmetry-breaking and a $4+1$ split of the $F$-theory spectral divisor. Goals of this note are to treat the existence of right-handed neutrinos in our $F$-theory model, show that the $\mathbb{Z}_{2}$-action in our model breaks the $U\left(1\right)_{X}$-symmetry associated to the $4+1$ split to $\mathbb{Z}_{2}$-matter parity, and to identify Yukawa couplings for the MSSM matter fields.

hep-th↗

arXiv2013

Incidence and Abel-Jacobi equivalence

For an algebraic (n-1)-cycle Z on a complex projective (2n-1)-manifold X, P. Griffiths conjectured that, if Z is algebraically equivalent to zero and if the incidence divisor of Z on every family of (n-1)-cycles is principal, then the Abel-Jacobi image of Z in the intermediate Jacobian J(X) of X is a point of finite order. Using a recent generalization of the classical height pairing, we give a proof of a stronger statement, namely that the Abel-Jacobi image of Z is zero.

math.AG↗

arXiv2010

Intersection numbers for normal functions

We expand the notion of a normal function for a Hodge class on an even-dimensional complex projective manifold to the notion of a 'topological normal function' associated to any primitive integral cohomology class. The definition of the intersection number of two topological normal functions is the analogue of that given by Griffiths and Green for classical normal functions. We give a simple proof that the intersection number of the normal functions is the same as the intersection number of their corresponding cohomology classes.

math.AG↗