Dual dynamics of string theory

Before proceeding with the dual dynamics itself I would like to mention very good pedagogical reviews of the Double Field Theory appeared recently [1,2].

The so-called Duff's procedure implies a non-trivial feature of T-duality transformations: the hidden symmetry between equations of motion and Bianchi identities. It was suggested to understand left-moving and right-moving coordinates of a closed string as independent [1,2, for review of T-duality see 3]. And to collect them to a set of ordinary and dual coordinates. The so-called dual Lagrangian governs the dual dynamics. The key point is, equations of motion for the dual coordinates appear to be equivalent to Bianchi identities for the ordinary coordinates and vice versa. A relation between these coordinates leads to the notion of the generalised metric.

Facultimedia

"We focus on understanding the important and exciting outcomes of cutting edge research." This is written on the About page of facultimedia website.

This is a developing project of online video and articles repository. It is supposed, that people can use this site to share their projects, ideas, broaden their network.

The part, that I found the most interesting is the video repository. it seems, that it can become good online version of Scholarpedia (or wiki, if you want).

Finally, facultymedia.com were kind to record video of me talking about my research.

T-duality

The subject of dualities in physics has become a very popular topic these days. The examples that immediately come to mind are: AdS/CFT correspondence, AGT duality, mirror symmetry, non-perturbative dualities in string and M-theory. The latter are better known as T and U-dualities and are briefly reviewed in this post.

Gauged SUGRA

Lets continue with compactifications of maximal supergravities. As it is now clear from the previous post the Kaluza-Klein reduction leads to a theory whose vector multiplets are abelian. In other words the gauge group is $U(1)^{n_V}$ with $n_V$ as number of vector multiplets. And none of the matter fields is charged under the gauge group. At the same time both scalars and tensors transform non-trivially under the global duality group. Scalar are elements of the coset space (see the previous post) and vectors transform in some linear representation $\mathcal{R}_{n_V}$. This is what is called ungauged supergravity. 

Ungauged SUGRA

At the moment we have 5 different string theories that are connected to each other by duality transformations.

As it is shown on this picture low energy limits of IIA and Heterotic $E_8\times E_8$ string theories can be obtained by compactification of the 11D SUGRA on a circle $S^1$ and a line $I$ respectively.

What we know is that the $11$ dimensional supergravity is a low energy limit of the mysterious M-theory. Actually, this is more or less the only thing we know about M-theory. This means that it is worth understanding supergravity.

FQXi Essay Contest

The FQXi community closed its essay contest that started in spring. The topic is "Which of Our Basic Physical Assumptions Are Wrong?". 

Actually, there are a lot of these essays, and I read only one, written by Sabine Hossenfelder. She assumes in this essay that what we observe as a Planck constant is just a vacuum expectation value (VEV) of a scalar field. Thus, we see here a kind of spontaneous symmetry breaking.

Increasing temperature restores this symmetry and she assumes that the Planck constant goes top zero at high energies. That provides gravity decoupling from matter since newtons constant is proportional to Planck constant
\begin{equation}
G=\frac{\hbar c}{m_{Pl}^2}.
\end{equation}
This solves one of the problem — singularity of the initial state of the Universe. Since we have no interaction between matter and gravity at high temperatures then high densities do not form space-time singularities. Something similar happens inside black holes: as the process of a black hole formation is adiabatic (nothing escapes from it), then entropy is conserved and temperature grows while BH is collapsing.

The other problem arises when we are going to quantize gravity. It is known that gravity can be quantized perturbatively, but it is a non-renormalized theory. Setting $\hbar$ to go to zero as temperature increases solves this problem at high energies: gravity is just classical.

An interesting fact is that there disappears the notion of quantumness in this consideration. It appears as some kind of interaction of fields with VEV of a field of special type.

Official string theory site

Found very interesting "official" superstring theory website http://superstringtheory.com. One can read there about string theory on basic and advanced level. Actually, the advanced level is basic for a PhD student and very understandable.

Nice reading during breakfast or leasure time.