The theory of superstring with flux on non-Kähler manifolds and the complex Monge-Ampère equation

By Jixiang Fu, Shing-Tung Yau. 2006

338 citations recorded by the source corpus.

The purpose of this paper is to solve a problem posed by Strominger in constructing smooth models of superstring theory with flux. These are given by non-Kahler manifolds with torsion.

Subfields: Applied Mathematics, Geometry and Topology, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/2b760e340f56040bb1d3def1ce6d76542a80a7a8

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In Applied Mathematics

In Geometry and Topology

In Nuclear and High Energy Physics

Citations in the corpus

Anomaly cancellation and smooth non-Kähler solutions in heterotic string theory (2006, methodology): “The existence of a smooth solution of this equation has recently been proven in [ 15 ].”
$$C^{2,\alpha }$$C2,α estimates for nonlinear elliptic equations in complex and almost complex geometry (2014, methodology): “This was introduced and investigated by Fu–Wang–Wu [25,26], motivated by some questions related to mathematical physics (see [27,41], for example).”
On Curvature Tensors of Hermitian Manifolds (2016, background): “In a larger context, recall that balanced metrics play an important role in the Strominger system ([21], [15], [5]).”
Fully non-linear parabolic equations on compact Hermitian manifolds (2017, background): “A recent example of particular interest is the Fu-Yau equation [14, 15, 32, 35] and its corresponding geometric flows [36].”
A second order estimate for general complex Hessian equations (2015, background): “An important case corresponding to k = n = 2, so that it is actually a Monge-Ampère equation in two dimensions, is central to the solution by Fu and Yau [5, 6] of a Strominger system on a toric fibration over a K3 surface.”
Semilinear equations, the $\gamma_k$ function, and generalized Gauduchon metrics (2010, background): “[10, 12]), we can define a complex structure on S5×S1 such that π is a holomorphic map.”
Strominger connection and pluriclosed metrics (2019, methodology): “We refer the readers to the papers [8], [13], [14], [16], [26], [39] for study involving Hull-Strominger system, which uses Bismut-Strominger connection in an essential way, and to the papers [33], [34], [35] where the study of Hermitian curvature flow involving the connection were initiated which h”
Non-Kähler Calabi-Yau manifolds (2014, background): “hard to construct, see [30, 49, 61, 78] and references therein for more about this system.”
Non-K\"ahler Calabi-Yau manifolds (2014, background): “hard to construct, see [30, 49, 61, 78] and references therein for more about this system.”
The Monge-Ampère equation for (n − 1)-plurisubharmonic functions on a compact Kähler manifold (2013, methodology): “Nontrivial solutions of the Strominger system were first constructed by Li-Yau [35] on some Kähler manifolds, and by Fu-Yau [19] on certain non-Kähler manifolds.”
Geometric flows and Strominger systems (2015, methodology): “Furthermore, the convergence of the Anomaly flow on Goldstein-Prokushkin fibrations has been established in [27], for both α > 0 and α < 0, thus unifying the results of Fu and Yau [14, 15].”
Ricci Curvatures on Hermitian manifolds (2014, background): “For more works on Hermitian manifolds with specials metrics, we refer the reader to [1, 2, 4, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 27, 21, 36, 39, 38, 41, 49, 42, 43, 44] and the references therein.”