Anti-Quill Part 6: Type IIB and F-theory -I

 I genuinely forgot that I had a blog. Anyway, here is a short post on F-theory/M-theory duality. Inherently, type IIB superstring theory comes with a bundle of data like D-branes, O-planes and fluxes. I have mentioned how these play an important role in stabilising the moduli. We are yet to talk on the exact nature of these moduli stabilisations and especially in view of fluxes. But first, a short note on the axiodilaton, which is given by the RR field $C_{0}$ and string coupling $g_{s}$:

$$\tau = C_{0}+ig_{s}^{-1}\;.$$

This axiodilaton can be thought of as the modulus of elliptic fibration when KK-compactifying M-theory into type IIA theory, and performing a T-duality action on this type IIA theory gives you your type IIB theory back. That is, taking M-theory on $\mathbb{R}^{9}\times S^{1}\times S^{1}$ with some $R_{S^{1}}\to 0$, you obtain type IIA theory on $\mathbb{R}^{9}\times S^{1}$. Then, acting on this with T-duality gives us $\mathbb{R}^{9}\times \mathbf{S}^{1}$ type IIB theory, and in $\mathbf{R}_{S^{1}}\to \infty$ we get $\mathbb{R}^{10}$. The following tables are from nlab and the TASI lectures by Weigand respectively, which are helpful. 

I'll type more in a minute. Btw I saw Dune Part 2 yesterday from 1320 to 1620 hrs. After 114 viewings, it is more golden than before.