50 research outputs found
The Exact MSSM Spectrum from String Theory
We show the existence of realistic vacua in string theory whose observable
sector has exactly the matter content of the MSSM. This is achieved by
compactifying the E_8 x E_8 heterotic superstring on a smooth Calabi-Yau
threefold with an SU(4) gauge instanton and a Z_3 x Z_3 Wilson line.
Specifically, the observable sector is N=1 supersymmetric with gauge group
SU(3)_C x SU(2)_L x U(1)_Y x U(1)_{B-L}, three families of quarks and leptons,
each family with a right-handed neutrino, and one Higgs-Higgs conjugate pair.
Importantly, there are no extra vector-like pairs and no exotic matter in the
zero mode spectrum. There are, in addition, 6 geometric moduli and 13 gauge
instanton moduli in the observable sector. The holomorphic SU(4) vector bundle
of the observable sector is slope-stable.Comment: 15 pages, LaTeX; v2: Hidden sector is unstable, symbol typesetting
error corrected, clarifications and references added; v3: New discussion of
hidden secto
Elliptic Calabi-Yau Threefolds with Z_3 x Z_3 Wilson Lines
A torus fibered Calabi-Yau threefold with first homotopy group Z_3 x Z_3 is
constructed as a free quotient of a fiber product of two dP_9 surfaces.
Calabi-Yau threefolds of this type admit Z_3 x Z_3 Wilson lines. In conjunction
with SU(4) holomorphic vector bundles, such vacua lead to anomaly free, three
generation models of particle physics with a right handed neutrino and a
U(1)_{B-L} gauge factor, in addition to the SU(3)_C x SU(2)_L x U(1)_Y standard
model gauge group. This factor helps to naturally suppress nucleon decay. The
moduli space and Dolbeault cohomology of the threefold is also discussed.Comment: 51 pages, 13 figures; v2: references adde
The Moduli of Reducible Vector Bundles
A procedure for computing the dimensions of the moduli spaces of reducible,
holomorphic vector bundles on elliptically fibered Calabi-Yau threefolds X is
presented. This procedure is applied to poly-stable rank n+m bundles of the
form V + pi* M, where V is a stable vector bundle with structure group SU(n) on
X and M is a stable vector bundle with structure group SU(m) on the base
surface B of X. Such bundles arise from small instanton transitions involving
five-branes wrapped on fibers of the elliptic fibration. The structure and
physical meaning of these transitions are discussed.Comment: 33+1 page
Hermitian Yang-Mills instantons on Calabi-Yau cones
We study and construct non-abelian hermitian Yang-Mills (HYM) instantons on
Calabi-Yau cones. By means of a particular isometry preserving ansatz, the HYM
equations are reduced to a novel Higgs-Yang-Mills flow on the Einstein-Kahler
base. For any 2d-dimensional Calabi-Yau cone, we find explicit solutions of the
flow equations that correspond to non-trivial SU(d) HYM instantons. These can
be regarded as deformations of the spin connection of the Calabi-Yau cone.Comment: 17 page
The Spectra of Heterotic Standard Model Vacua
A formalism for determining the massless spectrum of a class of realistic
heterotic string vacua is presented. These vacua, which consist of SU(5)
holomorphic bundles on torus-fibered Calabi-Yau threefolds with fundamental
group Z_2, lead to low energy theories with standard model gauge group (SU(3)_C
x SU(2)_L x U(1)_Y)/Z_6 and three families of quarks and leptons. A methodology
for determining the sheaf cohomology of these bundles and the representation of
Z_2 on each cohomology group is given. Combining these results with the action
of a Z_2 Wilson line, we compute, tabulate and discuss the massless spectrum.Comment: 41+1pp, 2 fig
The Particle Spectrum of Heterotic Compactifications
Techniques are presented for computing the cohomology of stable, holomorphic
vector bundles over elliptically fibered Calabi-Yau threefolds. These
cohomology groups explicitly determine the spectrum of the low energy,
four-dimensional theory. Generic points in vector bundle moduli space manifest
an identical spectrum. However, it is shown that on subsets of moduli space of
co-dimension one or higher, the spectrum can abruptly jump to many different
values. Both analytic and numerical data illustrating this phenomenon are
presented. This result opens the possibility of tunneling or phase transitions
between different particle spectra in the same heterotic compactification. In
the course of this discussion, a classification of SU(5) GUT theories within a
specific context is presented.Comment: 77 pages, 3 figure
Heterotic Standard Model Moduli
In previous papers, we introduced a heterotic standard model and discussed
its basic properties. The Calabi-Yau threefold has, generically, three Kahler
and three complex structure moduli. The observable sector of this vacuum has
the spectrum of the MSSM with one additional pair of Higgs-Higgs conjugate
fields. The hidden sector has no charged matter in the strongly coupled string
and only minimal matter for weak coupling. Additionally, the spectrum of both
sectors will contain vector bundle moduli. The exact number of such moduli was
conjectured to be small, but was not explicitly computed. In this paper, we
rectify this and present a formalism for computing the number of vector bundle
moduli. Using this formalism, the number of moduli in both the observable and
strongly coupled hidden sectors is explicitly calculated.Comment: 28 pages, LaTeX; v2: typos corrected, references added; v3:
clarifications, references adde
World-sheet Instanton Superpotentials in Heterotic String theory and their Moduli Dependence
To understand in detail the contribution of a world-sheet instanton to the
superpotential in a heterotic string compactification, one has to understand
the moduli dependence (bundle and complex structure moduli) of the one-loop
determinants from the fluctuations, which accompany the classical exponential
contribution (involving K\"ahler moduli) when evaluating the world-volume
partition function. Here we use techniques to describe geometrically these
Pfaffians for spectral bundles over rational base curves in elliptically
fibered Calabi-Yau threefolds, and provide a (partially exhaustive) list of
cases involving {\em factorising} (or vanishing) superpotential. This gives a
conceptual explanation and generalisation of the few previously known cases
which were obtained just experimentally by a numerical computation.Comment: 57 pages; minor changes, discussion section 1.3 adde
A Two-Form Formulation of the Vector-Tensor Multiplet in Central Charge Superspace
A two-form formulation for the N=2 vector-tensor multiplet is constructed
using superfield methods in central charge superspace. The N=2 non-Abelian
standard supergauge multiplet in central charge superspace is also discussed,
as is with the associated Chern-Simons form. We give the constraints, solve the
Bianchi identities and present the action for a theory of the vector-tensor
multiplet coupled to the non-Abelian supergauge multiplet via the Chern-Simons
form.Comment: 16 pages, LaTeX2e with AMS-LaTe
Moduli Dependent mu-Terms in a Heterotic Standard Model
In this paper, we present a formalism for computing the non-vanishing Higgs
mu-terms in a heterotic standard model. This is accomplished by calculating the
cubic product of the cohomology groups associated with the vector bundle moduli
(phi), Higgs (H) and Higgs conjugate (Hbar) superfields. This leads to terms
proportional to phi H Hbar in the low energy superpotential which, for non-zero
moduli expectation values, generate moduli dependent mu-terms of the form
H Hbar. It is found that these interactions are subject to two very restrictive
selection rules, each arising from a Leray spectral sequence, which greatly
reduce the number of moduli that can couple to Higgs-Higgs conjugate fields. We
apply our formalism to a specific heterotic standard model vacuum. The
non-vanishing cubic interactions phi H Hbar are explicitly computed in this
context and shown to contain only four of the nineteen vector bundle moduli.Comment: 23 pages, LaTe