scholarly journals Generalized vanishing theorems for Yukawa couplings in heterotic compactifications

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Lara B. Anderson ◽  
James Gray ◽  
Magdalena Larfors ◽  
Matthew Magill ◽  
Robin Schneider
Keyword(s):  
Vector Bundles ◽  
Geometric Approach ◽  
Low Energy ◽  
Geometric Features ◽  
Vanishing Theorems ◽  
Vanishing Theorem ◽  
Alternative Derivation ◽  
Yukawa Couplings ◽  
Geometric Methods ◽  
Higher Dimensional

Abstract Heterotic compactifications on Calabi-Yau threefolds frequently exhibit textures of vanishing Yukawa couplings in their low energy description. The vanishing of these couplings is often not enforced by any obvious symmetry and appears to be topological in nature. Recent results used differential geometric methods to explain the origin of some of this structure [1, 2]. A vanishing theorem was given which showed that the effect could be attributed, in part, to the embedding of the Calabi-Yau manifolds of interest inside higher dimensional ambient spaces, if the gauge bundles involved descended from vector bundles on those larger manifolds. In this paper, we utilize an algebro-geometric approach to provide an alternative derivation of some of these results, and are thus able to generalize them to a much wider arena than has been considered before. For example, we consider cases where the vector bundles of interest do not descend from bundles on the ambient space. In such a manner we are able to highlight the ubiquity with which textures of vanishing Yukawa couplings can be expected to arise in heterotic compactifications, with multiple different constraints arising from a plethora of different geometric features associated to the gauge bundle.

scholarly journals ON THE STABILITY OF SYZYGY BUNDLES

2011 ◽  
Vol 22 (04) ◽  
pp. 515-534 ◽  
Author(s):  
IUSTIN COANDĂ
Keyword(s):  
Projective Space ◽  
Complete Intersection ◽  
Vector Bundles ◽  
Elementary Proof ◽  
Base Point ◽  
Vector Spaces ◽  
Similar Argument ◽  
Vanishing Theorem ◽  
The Stability ◽  
Koszul Cohomology

We are concerned with the problem of the stability of the syzygy bundles associated to base-point-free vector spaces of forms of the same degree d on the projective space of dimension n. We deduce directly, from M. Green's vanishing theorem for Koszul cohomology, that any such bundle is stable if its rank is sufficiently high. With a similar argument, we prove the semistability of a certain syzygy bundle on a general complete intersection of hypersurfaces of degree d in the projective space. This answers a question of H. Flenner [Comment. Math. Helv.59 (1984) 635–650]. We then give an elementary proof of H. Brenner's criterion of stability for monomial syzygy bundles, avoiding the use of Klyachko's results on toric vector bundles. We finally prove the existence of stable syzygy bundles defined by monomials of the same degree d, of any possible rank, for n at least 3. This extends the similar result proved, for n = 2, by L. Costa, P. Macias Marques and R. M. Miro-Roig [J. Pure Appl. Algebra214 (2010) 1241–1262]. The extension to the case n at least 3 has been also, independently, obtained by P. Macias Marques in his thesis [arXiv:0909.4646/math.AG (2009)].

scholarly journals Moduli spaces of vector bundles on higher dimensional varieties

2001 ◽  
Vol 49 (3) ◽  
pp. 605-620 ◽  
Author(s):  
Laura Costa ◽  
Rosa M. Miró-Roig
Keyword(s):  
Moduli Spaces ◽  
Vector Bundles ◽  
Higher Dimensional

scholarly journals Positivity and vanishing theorems for ample vector bundles

2012 ◽  
Vol 22 (2) ◽  
pp. 303-331 ◽  
Author(s):  
Kefeng Liu ◽  
Xiaofeng Sun ◽  
Xiaokui Yang
Keyword(s):  
Vector Bundles ◽  
Vanishing Theorems

scholarly journals A generalization of Kita and Noumi’s vanishing theorems of cohomology groups of local system

1997 ◽  
Vol 147 ◽  
pp. 63-69 ◽  
Author(s):  
Koji Cho
Keyword(s):  
Algebraic Geometry ◽  
Spectral Sequence ◽  
Local System ◽  
Vanishing Theorems ◽  
Vanishing Theorem ◽  
Cohomology Groups ◽  
De Rham

AbstractWe prove vanishing theorems of cohomology groups of local system, which generalize Kita and Noumi’s result and partially Aomoto’s result. Main ingredients of our proof are the Hodge to de Rham spectral sequence and Serre’s vanishing theorem in algebraic geometry.

scholarly journals A KIND OF PREDICTION FROM STRING PHENOMENOLOGY: EXTRA MATTER AT LOW ENERGY

2007 ◽  
Vol 22 (14) ◽  
pp. 989-1003 ◽  
Author(s):  
CARLOS MUÑOZ
Keyword(s):  
Potential Problem ◽  
Low Energy ◽  
Mixing Angles ◽  
Yukawa Couplings ◽  
Problem Finding ◽  
String Phenomenology ◽  
Fermion Masses ◽  
Interesting Pattern ◽  
Low Energies ◽  
Crucial Ingredient

We review the possibility that the Supersymmetric Standard Model arises from orbifold constructions of the E8×E8 Heterotic Superstring, and the phenomenological properties that such a model should have. In particular, trying to solve the discrepancy between the unification scale predicted by the Heterotic Superstring (≈g GUT × 5.27 × 1017 GeV ) and the value deduced from LEP experiments (≈2 × 1016 GeV ), we will predict the presence at low energies of three families of Higgses and vector-like colour triplets. Our approach relies on the Fayet–Iliopoulos breaking, and this is also a crucial ingredient, together with having three Higgs families, to obtain in these models an interesting pattern of fermion masses and mixing angles at the renormalizable level. Namely, after the gauge breaking some physical particles appear combined with other states, and the Yukawa couplings are modified in a well-controlled way. On the other hand, dangerous flavour-changing neutral currents may appear when fermions of a given charge receive their mass through couplings with several Higgs doublets. We will address this potential problem, finding that viable scenarios can be obtained for a reasonable light Higgs spectrum.

Hodge and Vanishing Theorems on Complex Finsler Vector Bundles

2019 ◽  
Author(s):  
Jinling Li ◽  
Chunhui Qiu ◽  
Tongde Zhong
Keyword(s):  
Vector Bundles ◽  
Vanishing Theorems

scholarly journals Vanishing Theorems on Compact Hyper-kähler Manifolds

Geometry ◽  
2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Qilin Yang
Keyword(s):  
Line Bundle ◽  
Nonnegative Integer ◽  
Kähler Manifold ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Holomorphic Line Bundle ◽  
Vanishing Theorems ◽  
Vanishing Theorem ◽  
Positive Holomorphic Line Bundle ◽  
Special Case

We prove that if B is a k-positive holomorphic line bundle on a compact hyper-kähler manifold M, then HpM,Ωq⊗B=0 for P>n+[k/2] with q a nonnegative integer. In a special case, k=0 and q=0, we recover a vanishing theorem of Verbitsky’s with a little stronger assumption.

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