اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدKahler-Einstein and Kahler scalar flat supermanifolds
67
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Two results regarding Kahler supermanifolds with potential $K=A+Cthetabartheta$ are shown. First, if the supermanifold is Kahler-Einstein, then its base (the supermanifold of one lower fermionic dimension and with Kahler potential $A$) has constant scalar curvature. As a corollary, every constant scalar curvature Kahler supermanifold has a unique superextension to a Kahler-Einstein supermanifold of one higher fermionic dimension. Second, if the supermanifold is itself scalar flat, then its base satisfies the equation $$ phi^{bar ji}phi_{ibar j}=2Delta_0 S_0 + R_0^{bar ji}R_{0ibar j} - S_0^2, $$ where $Delta_0$ is the Laplace operator, $S_0$ is the scalar curvature, and $R_{0ibar j}$ is the Ricci tensor of the base, and $phi$ is some harmonic section on the base. Remarkably, precisely this equation arises in the construction of certain supergravity compactifications. Examples of bosonic manifolds satisfying the equation above are discussed.
قيم البحث
اقرأ أيضاً
Let $mathcal{K}(n, V)$ be the set of $n$-dimensional compact Kahler-Einstein manifolds $(X, g)$ satisfying $Ric(g)= - g$ with volume bounded above by $V$. We prove that after passing to a subsequence, any sequence ${ (X_j, g_j)}_{j=1}^infty$ in $math
cal{K}(n, V)$ converges, in the pointed Gromov-Hausdorff topology, to a finite union of complete Kahler-Einstein metric spaces without loss of volume. The convergence is smooth off a closed singular set of Hausdorff dimension no greater than $2n-4$, and the limiting metric space is biholomorphic to an $n$-dimensional semi-log canonical model with its non log terminal locus of complex dimension no greater than $n-1$ removed. We also show that the Weil-Petersson metric extends uniquely to a Kahler current with bounded local potentials on the KSBA compactification of the moduli space of canonically polarized manifolds. In particular, the coarse KSBA moduli space has finite volume with respect to the Weil-Petersson metric. Our results are a high dimensional generalization of the well known compactness results for hyperbolic metrics on compact Riemann surfaces of fixed genus greater than one.
We introduce and study the notion of a biholomorphic gerbe with connection. The biholomorphic gerbe provides a natural geometrical framework for generalized Kahler geometry in a manner analogous to the way a holomorphic line bundle is related to Kahl
er geometry. The relation between the gerbe and the generalized Kahler potential is discussed.
Let $G$ be a simply-connected semisimple compact Lie group, $X$ a compact Kahler manifold homogeneous under $G$, and $L$ a negative $G$-equivariant holomorphic line bundle over $X$. We prove that all $G$-invariant Kahler metrics on the total space of
$L$ arise from the Calabi ansatz. Using this, we then show that there exists a unique $G$-invariant scalar-flat Kahler metric in each Kahler class of $L$.
We use newly discovered N = (2, 2) vector multiplets to clarify T-dualities for generalized Kahler geometries. Following the usual procedure, we gauge isometries of nonlinear sigma-models and introduce Lagrange multipliers that constrain the field-st
rengths of the gauge fields to vanish. Integrating out the Lagrange multipliers leads to the original action, whereas integrating out the vector multiplets gives the dual action. The description is given both in N = (2, 2) and N = (1, 1) superspace.
It is presented a method of construction of sigma-models with target space geometries different from conformally flat ones. The method is based on a treating of a constancy of a coupling constant as a dynamical constraint following as an equation of
motion. In this way we build N=4 and N=8 supersymmetric four-dimensional sigma-models in d=1 with hyper-Kahler target space possessing one isometry, which commutes with supersymmetry.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
