**1:30 pm: Do interacting UV fixed points exist, and if so, what can we do with them?**

*Daniel Litim***I was talking to Daniel's student earlier, so I know what this talk is about: gravity. Specifically, asymptotic safety: the possibility that GR runs to a UV interacting fixed point. This resolves the issue of quantum gravity in an interesting way.**

The title is a question, but the answer is apparently yes!

Issue goes beyond gravity, to all theories with a sickness in the UV: in particular, the Higgs and abelian gauge theories.

Fixed points: classical example is non-interacting point. In perturbation theory, sign of beta-function encodes whether this fixed point lives in the UV or the IR. In either case, the theory is only predictive to some point in the other regime.

*e.g.*QCD has UV non-interacting fixed point (is arbitrarily predictive in the UV) but not in the IR (is predictive only to around Λ

_{QCD}~ GeV).

Interacting fixed points: arise from non-trivial zeroes in the (full) beta function. Simple example: naively non-renormalisable coupling, has linear term in beta function with positive coefficient. If coupling has negative coefficient for quadratic term (as for QCD) then UV interacting fixed point. Obviously, for this to make sense, need to still be in domain of perturbation theory. Points to either small dimensionality of coupling or large number of fields.

Examples in practice:

- Gravity in 2 + ε dimensions.
- Four-fermion couplings in 2 + ε dimensions.
- Gluons in 4 + ε dimensions.

All need ε very small.

New example: Strictly 4D gauge theory. Start with

*walking*quasi-fixed point, where beta function is very small so coupling evolves very slowly. Take a large

*Nc*, fixed

*g*limit. Now look for cancellation between quadratic and cubic terms in beta function.

^{2}NcWithout Yukawa couplings, this is impossible: sign of cubic term is wrong. A simple choice, with single matrix Higgs coupling to fermions and self, seems to work. Model has one-dimension fixed point,

*i.e.*to reach UV interacting fixed point must constrain three couplings in theory in terms of one of them.

*e.g.*Write Yukawa, Higgs quartic couplings in terms of gauge couplings.

Proof: UV fixed points do exist in 4D. Can we find one for gravity? Looking for one based on large anomalous dimension of the graviton, close to 2 so linear term in beta function becomes small. This forces us to consider strong coupling, unlike the previous perturbative possibility.

Evidence that it might, in a power series expansion of the Ricci scalar (a simplified gravity model).

**2:20 pm: From neutrino data to mass models (and back) with leptogenesis,**

*Pasquale Di Bari***Don't be too ambitious: focus on a single cosmological problem, the matter-antimatter asymmetry.**

BICEP2 may point towards interesting new era, when after inflation the temperature is so high that QCD has frozen out.

It always bothers me when speakers don't seem to realise they have a microphone. Feedback and distortion make it harder to follow you! Seriously, I'm losing interest already.

Cosmological limits (Planck)

*nearly*rule out the degenerate neutrino spectrum.

Once again,

*there is no need to shout.*

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