Flux and Freund-Rubin Superpotentials in M-theory

We discuss the effective action for weak G_2 compactifications of M-theory. The presence of fluxes acts as a source for the the axions and drives the Freund-Rubin parameter to zero. The result is a stable non-supersymmetric vacuum with a negative cosmological constant. We also give the superpotential which generates the effective potential and discuss a simple model which aims to incorporate the effects of supersymmetry breaking by the gauge sector.Comment: Discussion of KK-scale and cosmological scales revise

VOA[MM_4]

We take a peek at a general program that associates vertex (or, chiral) algebras to smooth 4-manifolds in such a way that operations on algebras mirror gluing operations on 4-manifolds and, furthermore, equivalent constructions of 4-manifolds give rise to equivalences (dualities) of the corresponding algebras

Remark on integrating out heavy moduli in flux compactification

We study two steps of moduli stabilization in type IIB flux compactification with gaugino condensations. We consider the condition that one can integrate out heavy moduli first with light moduli remaining. We give appendix, where detail study is carried out for potential minima of the model with a six dimensional compact space with $h_{1,1}=h_{2,1}=1$, including the model, whose respective moduli with $h_{1,1}, h_{2,1} \neq 1$ are identified.Comment: 16 pages, late

Rigid surface operators and S-duality: some proposals

We study surface operators in the N=4 supersymmetric Yang-Mills theories with gauge groups SO(n) and Sp(2n). As recently shown by Gukov and Witten these theories have a class of rigid surface operators which are expected to be related by S-duality. The rigid surface operators are of two types, unipotent and semisimple. We make explicit proposals for how the S-duality map should act on unipotent surface operators. We also discuss semisimple surface operators and make some proposals for certain subclasses of such operators.Comment: 27 pages. v2: minor changes, added referenc