Six string pheno papers

It's the first of May: time to read the Czech children's most memorized poem, Karel Hynek Mácha's romantic 1836 poem "Máj". Try the translation by Edith Pargeter or James Naughton or the translation to some other languages (including some audios).

May Day turned out to be a busy day on the arXiv, especially when it comes to papers on string (and string-inspired) phenomenology. I will briefly mention six papers, including three articles on string inflation.

First, Savas Dimopoulos, Kiel Howe, and John March-Russell of Stanford-Oxford (a perfect rhyme, indeed) wrote about

Maximally Natural Supersymmetry

which argues that models involving both SUSY and one large, multi-\({\rm TeV}\) dimension are realistic. Somewhat similarly to Hořava-Witten heterotic M-theory models, there is a \(S^1/\ZZ_2\times \ZZ_2\) compactification. The two \(\ZZ_2\) groups break the theory from \(\NNN=2\) to \(\NNN=1\) SUSY in two different, mutually incompatible ways, so that no SUSY is left in the effective theory. Alternatively, you may say that there's no good \(\NNN=1\) 4D effective field theory because the Kaluza-Klein scale coincides with the SUSY breaking scale: the breaking is effectively of the Scherk-Schwarz type, by antiperiodic boundary conditions for the fermions.

The model proposes light \(650\GeV\) top squarks, \(2\TeV\) gluinos, and a new massive \(U(1)'\) gauge boson \(Z'\) – all of these should be accessible to the LHC13 or LHC14 run that will begin next year. Despite the large fifth dimension, they say that they produce strong enough gravitational waves for BICEP2 if the dimension is small during inflation. I have a problem with the sudden growth of the dimensions (i.e. with the usage of different sizes of extra dimensions for different epochs) but maybe it is just a psychological prejudice.




Nana Cabo Bizet, Albrecht Klemm, and Daniel Vieira Lopes show that they are hardcore string algebraic geometers. In their 150-page-long paper

Landscaping with fluxes and the \(E_8\) Yukawa Point in F-theory,

they study F-theory models with the \(E_8\) extended gauge symmetry point living at one "Hawaiian" fiber of the base. Recall that this paper by Heckman, Tavanfar, and Vafa managed to obtain a realistic mass matrix for the neutrinos – one that was soon confirmed by experiments. In the new Bizet et al. paper, they exploit some advanced mathematical tools and determine some superpotential for the first time.




The third non-inflation paper I want to mention is

New String Theories And Their Generation Number

by Arel Genish and Doron Gepner. Gepner is known for his "Gepner models", clever combinations of minimal model CFTs into realistic "string-sized" compactifications of extra dimensions in perturbative, especially heterotic string theory. Here they are doing something similar. Aside from the minimal models, they are adding a nonstandard parafermion SCFT by Babichenko and Gepner (2012).

Surprisingly for me, they may generate infinitely (countably) many new \(D=4\) heterotic string theories belonging to five infinite classes – where elements are labeled by one or two positive integers. For example, the elements in the first class are denoted \(\{N_1\}\) where \(N_1\in\ZZ^+\) is a positive integer. You could think that the search through the infinite zoo of new theories could be hard and time-consuming. After all, some of the stupid people think that even the search through as little as \(10^{500}\) vacua is hard. How many good candidates to describe our Universe are there in the Genish-Gepner list?

It turns out that they have some wonderful news: there is only one viable candidate in the set, namely the theory \(\{6\}(13,18)\), which is the only one that has three families of quarks and leptons. Wow, quite a candidate for a theory of everything. ;-) They're far from confirming that the theory has everything it needs to be realistic. For example, it yields an \(E_8\times E_6\) gauge group and it is not clear whether the \(E_6\) may be broken down to the Standard Model with the available field content. It would also be interesting to know what is the corresponding Calabi-Yau manifold.

Now, the three string inflation papers

All of the three papers sort of focus on the need to get trans-Planckian changes of the inflaton field, as Liam McAllister was emphasizing in his guest blog.

First, Ido Ben-Dayan, Francisco Gil Pedro, and Alexander Westphal talk about the

Hierarchical Axion Inflation

which shows that one may get very natural inflation – compatible with BICEP2 – using two axions with very different (hierarchically separated) decay constants. Be ready for some nice pictures of potentials \(V(\phi_1,\phi_2)\) for these two fields – which mostly look like waves in one of the two directions. Non-perturbative effects are enough to produce a slow-roll inflation with the trans-Planckian shift of the inflaton field.

They briefly discuss the embedding of this paradigm within type IIB string theory on a Calabi-Yau manifold (with a 3-form flux) where the two fields come from the axion-dilaton field \(\tau\).

Finally, there are two inflation papers co-written by Liam McAllister. In the first one,

A New Angle on Chaotic Inflation

written together with Thomas C. Bachlechner, Mafalda Dias, and Jonathan Frazer, they show that the mixing of the several axions' kinetic terms – the "kinetic alignment" – actually makes the effective decay constant larger than previously thought. If the decay constants are \(f_1,f_2,\dots , f_N\), you would expect the overall effective decay constant to be the Pythagorean hypotenuse \(f_{Py}=\sqrt{N}f_{RMS}\) where \(f_{RMS}\) is the root mean square of the decay constants.

However, due to the kinetic alignment, you actually get \(\sqrt{N}f_{N}\) instead – the average one is replaced by the largest one. It's a technical observation but if correct, it shifts the people's expectation about how hard it is to get the high effective decay constant in \(N\)-flation. The order-of-magnitude estimates were not quite enough. So if the paper is right, it's much easier to get the right numbers in stringy \(N\)-flation.

This new alignment of theirs doesn't need fine-tuning as the alignment by Kim, Nilles, and Peloso.

In the second, related new paper

Aligned Natural Inflation in String Theory

written with Cody Long and Paul McGuirk, Liam returns to the original Kim-Nilles-Peloso picture and presents a more specific example of how type IIB string theory with two axions manages to produce a large effective decay constant. Magnetized or multiply-wrapped D7-branes are needed (pretty pictures of ropes wound around a doughnut are included). They contain gauginos that undergo condensation which destroys the discrete shift symmetry of some fields while preserving others.