scholarly journals Adiabatic limits, vanishing theorems and the noncommutative residue

2009 ◽  
Vol 52 (12) ◽  
pp. 2699-2713 ◽  
Author(s):  
KeFeng Liu ◽  
Yong Wang
Keyword(s):  
Vanishing Theorems ◽  
Adiabatic Limits ◽  
Noncommutative Residue

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.

Relative vanishing theorems in analytic spaces

1985 ◽  
Vol 52 (1) ◽  
pp. 273-279 ◽  
Author(s):  
Kensho Takegoshi
Keyword(s):  
Vanishing Theorems

scholarly journals Adiabatic limits of Ricci-flat Kähler metrics

2010 ◽  
Vol 84 (2) ◽  
pp. 427-453 ◽  
Author(s):  
Valentino Tosatti
Keyword(s):  
Kähler Metrics ◽  
Kahler Metrics ◽  
Adiabatic Limits ◽  
Ricci Flat

scholarly journals Vanishing theorems for perverse sheaves on abelian varieties, revisited

2017 ◽  
Vol 24 (1) ◽  
pp. 63-84 ◽  
Author(s):  
Bhargav Bhatt ◽  
Christian Schnell ◽  
Peter Scholze
Keyword(s):  
Abelian Varieties ◽  
Vanishing Theorems ◽  
Perverse Sheaves

scholarly journals Differential forms and the noncommutative residue

2008 ◽  
Vol 58 (12) ◽  
pp. 1739-1751 ◽  
Author(s):  
William J. Ugalde
Keyword(s):  
Differential Forms ◽  
Noncommutative Residue

Kodaira-Nakano Vanishing Theorems

1985 ◽  
pp. 26-49
Author(s):  
Bernard Shiffman ◽  
Andrew John Sommese
Keyword(s):  
Vanishing Theorems

scholarly journals Corrigendum: Gromov-Witten invariants of symplectic quotients and adiabatic limits

2009 ◽  
Vol 7 (3) ◽  
pp. 377-379
Author(s):  
A. Rita Gaio ◽  
A. Rita Gaio ◽  
Dietmar A. Salamon ◽  
Dietmar A. Salamon
Keyword(s):  
Adiabatic Limits ◽  
Symplectic Quotients
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