**11:00 am: Minimal Models for Inflation from Minimal Supergravity,**

*Sergio Ferrara***Planck and BICEP2 seem to favour single-field inflation. The tension between the two models over the tensor-to-scalar ratio**

*r*point to different types of inflationary potentials; exponential from Planck or polynomial (quadratic) from BICEP. This talk embeds both models into supergravity.

There are no graphs, pictures or anything in these slides. They are just pages of hand-written text with occasional equations in red.

**11:30 am: Naturalness without prejudice Beyond the Standard Theory,**

*Ignatios Antoniadis***First part of talk: review that we have found a Higgs. Second part of talk: possible future colliders. I've written about many talks on these topics, so I say no more.**

Third part of talk (into second half now by number of slides): SUSY. Three methods to reduce fine tuning: low messenger scale, extend MSSM (raise tree level bound) or low-scale SUSY breaking (include effects of goldstino).

The obvious way to think about extensions of theories is with EFTs. Why not do that with SUSY? Dimension 5 and 6 operators in superpotential. First sub-leading terms in Higgs bilinears increase mass (lie along D-flat directions). Though I worry about the corresponding terms in the fermion sector, which don't seem to be discussed here. Also, Higgs mass still looks too low.

Non-linear MSSM (with goldstino). Non-linear implementation of SUSY. Goldstino couplings modify Higgs potential. I'm glad I recently read a paper on this, else I'd be completely lost instead of only partly lost. At least this time we can unambiguously get the Higgs mass, provided SUSY scale is not too large (less that 2 to 3 TeV).

We used fine tuning measures earlier, but only now define them.

Alternative: extra dimensions/low scale strings or gravity. Claim can probe string scales up to 40 TeV or so...

Question: squark/gluino limits approaching scale used in non-linear SUSY. Is this an issue? Yes? Maybe?

**12:00 pm: The Higgs and Naturalness,**

*Tony Gherghetta***Core question: how natural are SUSY and composite Higgs models post-LHC1?**

For a change, we start with composite theories, specifically where Higgs is pNGB. Tuning is the ratio between confining scale

*f*and EW scale

*v*. Partial compositeness needs light top partners, whose mass can be related to the Higgs mass. However, we also expect gluon partners (

*e.g.*KK gluon in RS models) which have a

*negative*contribution to the Higgs mass. This eases the tuning, by making heavier

*f*and top partners more compatible with observation. Top partner masses of about a TeV are fine.

We then have a reference to the work Tony did with Tirtha Sankar Ray and James Barnard on a UV completion of these models in 4D without elementary scalars. I attended Tirtha's talk on this on Tuesday.

Next we move on to SUSY models. We know that naturalness needs "natural SUSY" with light stops (among other things). But then you need additional contributions to the Higgs quartic to get a large enough Higgs mass. One way to do this is through the NMSSM, which leads on to what Tony did with Michael Schmidt, Anibal Medina and Benedict von Harling on the tuning in the MSSM. Michael talked about this last year at Planck, and I attended that talk too. The end result is that the tuning is down to worse than 10% even in natural SUSY.

The general issue with these analyses is that they are bottom-up. They might miss some details associated with SUSY breaking. So we have a 5D SUSY model that generates the SUSY spectrum through sfermion localisation. This shows still ~5% fine tuning.

Tuning from Higgs couplings important. In MSSM

*e.g.*tuning goes like |

*r*- 1|

^{-1}where

*r*are the Higgs coupling strengths; this diverges as

*r*goes to 1.

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