We present a new way to construct de Sitter vacua in type IIB flux compactifications, in which moduli stabilization and D-term uplifting can be combined in a manner consistent with the supergravity constraints. Here, the closed string fluxes fix the dilaton and the complex structure moduli while perturbative quantum corrections to the Kähler potential stabilize the volume Kähler modulus in an A...

We compute the moduli Kähler potential for M-theory on a compact manifold of G2 holonomy in a large radius approximation. Our method relies on an explicit G2 structure with small torsion, its periods and the calculation of the approximate volume of the manifold. As a verification of our result, some of the components of the Kähler metric are computed directly by integration over harmonic forms....

This paper pursues the study of the Calabi–Yau equation on certain sym-plectic non-Kähler 4-manifolds, building on a key example of Tosatti–Weinkove [24] in which more general theory had proved less effective. Symplectic 4-manifolds admitting a 2-torus fibration over a 2-torus base T 2 are modelled on one of three solvable Lie groups. Having assigned an invariant almost-Kähler structure and a v...

We give a classification of toric anti-self-dual conformal structures on compact 4-orbifolds with positive Euler characteristic. Our proof is twistor theoretic: the interaction between the complex torus orbits in the twistor space and the twistor lines induces meromorphic data, which we use to recover the conformal structure. A compact anti-self-dual orbifold can also be constructed by adding a...

We present a new way to construct de Sitter vacua in type IIB flux compactifications, in which the interplay of the leading perturbative and non-perturbative effects stabilize all moduli in dS vacua at parametrically large volume. Here, the closed string fluxes fix the dilaton and the complex structure moduli while the universal leading perturbative quantum correction to the Kähler potential to...

This paper pursues the study of the Calabi–Yau equation on certain symplectic non-Kähler 4-manifolds, building on a key example of Tosatti and Weinkove in which more general theory had proved less effective. Symplectic 4-manifolds admitting a 2-torus fibration over a 2-torus base T2 are modelled on one of three solvable Lie groups. Having assigned an invariant almost-Kähler structure and a volu...

The problem of finding Kähler-Einstein metrics on a compact Kähler manifold has been the subject of intense study over the last few decades. In his solution to Calabi’s conjecture, Yau [Ya1] proved the existence of a Kähler-Einstein metric on compact Kähler manifolds with vanishing or negative first Chern class. An alternative proof of Yau’s theorem is given by Cao [Ca] using the Kähler-Ricci f...

A realization of coherent state Lie algebras by first-order differential operators with holomorphic polynomial coefficients on Kähler coherent state orbits is presented. Explicit formulas involving the Bernoulli numbers and the structure constants for the semisimple Lie groups are proved.

There are two basic approaches to quantum TGD. The first approach, which is discussed in this article, is a generalization of Einstein’s geometrization program of physics to an infinitedimensional context. Second approach is based on the identification of physics as a generalized number theory. The first approach relies on the vision of quantum physics as infinite-dimensional Kähler geometry fo...

The corresponding Kähler form ω = √ −1gij̄dz ∧ dz̄j is a closed (1, 1) form. So a Kähler class [ω] defines a nontrivial cohomology class. For simplicity, we use both g and ω to denote the same Kähler metric. For any Kähler metric ωφ in the same Kähler class [ω], we can write ωφ = ω + √ −1∂∂̄φ, where φ is a real valued function and it is called a Kähler potential. The Calabi flow is defined by ∂φ ∂...