Sphere Partition Functions and the Kähler Metric on the Conformal Manifold

2016 ◽  
pp. 101-110
Author(s):  
Efrat Gerchkovitz ◽  
Zohar Komargodski
Keyword(s):  
Partition Functions ◽  
Kähler Metric ◽  
Kahler Metric

scholarly journals Hierarchical structure of physical Yukawa couplings from matter field Kähler metric

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Keiya Ishiguro ◽  
Tatsuo Kobayashi ◽  
Hajime Otsuka
Keyword(s):  
String Theory ◽  
Hierarchical Structure ◽  
Matter Field ◽  
Heterotic String ◽  
Heterotic String Theory ◽  
Kähler Metric ◽  
Yukawa Couplings ◽  
String Compactifications ◽  
Kahler Metric ◽  
Matter Fields

Abstract We study the impacts of matter field Kähler metric on physical Yukawa couplings in string compactifications. Since the Kähler metric is non-trivial in general, the kinetic mixing of matter fields opens a new avenue for realizing a hierarchical structure of physical Yukawa couplings, even when holomorphic Yukawa couplings have the trivial structure. The hierarchical Yukawa couplings are demonstrated by couplings of pure untwisted modes on toroidal orbifolds and their resolutions in the context of heterotic string theory with standard embedding. Also, we study the hierarchical couplings among untwisted and twisted modes on resolved orbifolds.

scholarly journals Quaternionic contact 4n + 3-manifolds and their 4n-quotients

2021 ◽  
Author(s):  
Yoshinobu Kamishima
Keyword(s):  
Scalar Curvature ◽  
Lie Group ◽  
Contact Structure ◽  
Einstein Manifolds ◽  
Hermitian Metrics ◽  
Kähler Metric ◽  
Formula One ◽  
Quaternion Space ◽  
Kahler Metric ◽  
Do So

AbstractWe study some types of qc-Einstein manifolds with zero qc-scalar curvature introduced by S. Ivanov and D. Vassilev. Secondly, we shall construct a family of quaternionic Hermitian metrics $$(g_a,\{J_\alpha \}_{\alpha =1}^3)$$ ( g a , { J α } α = 1 3 ) on the domain Y of the standard quaternion space $${\mathbb {H}}^n$$ H n one of which, say $$(g_a,J_1)$$ ( g a , J 1 ) is a Bochner flat Kähler metric. To do so, we deform conformally the standard quaternionic contact structure on the domain X of the quaternionic Heisenberg Lie group$${{\mathcal {M}}}$$ M to obtain quaternionic Hermitian metrics on the quotient Y of X by $${\mathbb {R}}^3$$ R 3 .

scholarly journals TWISTING OF N=1 SUSY GAUGE THEORIES AND HETEROTIC TOPOLOGICAL THEORIES

1995 ◽  
Vol 10 (30) ◽  
pp. 4325-4357 ◽  
Author(s):  
A. JOHANSEN
Keyword(s):  
Complex Structure ◽  
Kähler Manifold ◽  
Dolbeault Cohomology ◽  
Kähler Metric ◽  
Yang Mills ◽  
Kahler Manifold ◽  
Brst Charge ◽  
Kahler Metric ◽  
Compact Kähler Manifold ◽  
Topological Theories

It is shown that D=4N=1 SUSY Yang-Mills theory with an appropriate supermultiplet of matter can be twisted on a compact Kähler manifold. The conditions for cancellation of anomalies of BRST charge are found. The twisted theory has an appropriate BRST charge. We find a nontrivial set of physical operators defined as classes of the cohomology of this BRST operator. We prove that the physical correlators are independent of the external Kähler metric up to a power of a ratio of two Ray-Singer torsions for the Dolbeault cohomology complex on a Kähler manifold. The correlators of local physical operators turn out to be independent of antiholomorphic coordinates defined with a complex structure on the Kähler manifold. However, a dependence of the correlators on holomorphic coordinates can still remain. For a hyper-Kähler metric the physical correlators turn out to be independent of all coordinates of insertions of local physical operators.

scholarly journals Lagrangian foliations and Anosov symplectomorphisms on Kähler manifolds

2020 ◽  
pp. 1-11
Author(s):  
M. J. D. HAMILTON ◽  
D. KOTSCHICK
Keyword(s):  
The Other ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Kähler Metric ◽  
Other Hand ◽  
Kähler Form ◽  
Lagrangian Foliation ◽  
The One ◽  
Kahler Metric

Abstract We investigate parallel Lagrangian foliations on Kähler manifolds. On the one hand, we show that a Kähler metric admitting a parallel Lagrangian foliation must be flat. On the other hand, we give many examples of parallel Lagrangian foliations on closed flat Kähler manifolds which are not tori. These examples arise from Anosov automorphisms preserving a Kähler form.

scholarly journals Curvature and the c-projective mobility of Kähler metrics with hamiltonian 2-forms

2016 ◽  
Vol 152 (8) ◽  
pp. 1555-1575 ◽  
Author(s):  
David M. J. Calderbank ◽  
Vladimir S. Matveev ◽  
Stefan Rosemann
Keyword(s):  
Necessary Conditions ◽  
Kähler Metrics ◽  
Kähler Metric ◽  
Kahler Metrics ◽  
Local Classification ◽  
Complex Cone ◽  
Kahler Metric ◽  
Cone Metric

The mobility of a Kähler metric is the dimension of the space of metrics with which it is c-projectively equivalent. The mobility is at least two if and only if the Kähler metric admits a nontrivial hamiltonian 2-form. After summarizing this relationship, we present necessary conditions for a Kähler metric to have mobility at least three: its curvature must have nontrivial nullity at every point. Using the local classification of Kähler metrics with hamiltonian 2-forms, we describe explicitly the Kähler metrics with mobility at least three and hence show that the nullity condition on the curvature is also sufficient, up to some degenerate exceptions. In an appendix, we explain how the classification may be related, generically, to the holonomy of a complex cone metric.

Conformally Kähler manifolds

1954 ◽  
Vol 50 (1) ◽  
pp. 16-19 ◽  
Author(s):  
W. J. Westlake
Keyword(s):  
Conformal Geometry ◽  
Kähler Manifold ◽  
Hermitian Manifold ◽  
Necessary And Sufficient Condition ◽  
Kähler Metric ◽  
Kahler Manifold ◽  
Hermitian Space ◽  
Necessary And Sufficient ◽  
Simply Connected ◽  
Kahler Metric

Introduction. The present paper is concerned with the conformal geometry of Hermitian spaces. In the first part we find a necessary and sufficient condition for a Hermitian space to be conformally Kähler, that is, conformal to some Kähler space. The condition is that a certain conformal tensor, , vanishes identically. Then, defining a Hermitian manifold as in Hodge (3), we consider such a manifold where the restriction is made that at every point the tensor is zero. This will be called a conformally Kähler manifold, and conditions under which it may be given a Kähler metric are obtained. It is found that any conformally Kähler manifold may be given a Kähler metric provided it is simply-connected or that its fundamental group is of finite order.

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