__10:45am: David Shih, "An Overview of Models for A-Terms and the Higgs"__

__A nice conventional topic: SUSY Higgses.__

Two points of view on the Higgs discovery and results. To experimentalists it is a veritable buffet of potential work, with 125GeV pretty much the ideal mass in terms of things to measure. For theorists, it is a barren desert of no new physics.

David Shih: Too early to panic. We've only scratched the surface in what the LHC can do. Also, 125GeV is intriguing for SUSY; heavy but not morbidely obese.

In minimal SUSY, we need either large A-terms or (very) heavy stops. Beyond that, we have NMSSM-type models, extra vector-like generations, non-decoupling D-terms or other possibilities. In many of these scenarios, even in the least fine-tuned scenarios, a 125 GeV Higgs implies

*we should not have seen superpartners yet*.

Large A-terms is attractive as least possible fine-tuned case within MSSM, as it contributes polynomially to the Higgs mass rather than through a log. It is also surprisingly under-explored. Of course, the reason for that is that it is hard to generate large A-terms with the most popular methods of SUSY-breaking,

*e.g.*(minimal) GMSB or AMSB.

Where can A-terms come from?

- Planck-scale; SUSY flavour problem.
- RGEs; only option in GMSB; not easy.
- Messenger-scale; requires messenger-matter interactions; currently popular because the alternatives are hard.

RGEs tell us about the gluino mass/messenger scale. In particular, for a messenger scale below the the Planck scale, we need at least 2.5TeV gluino. There are also possible interesting cosmological constraints from tachyonic stops at high scales.

Messenger-matter couplings generate the A-terms through Kahler potential couplings of the form

*e.g.*XQQ, with X the SUSY-breaking spurion. There are three contributions to the A-terms that give the same result, two couplings to squarks and one to the Higgs. The last is MFV-safe, the former two are not.
There's also an analogy to the µ/Bµ problem, where the soft squark masses come from XXQQ, which we expect to be generated with a similar dimensionless coefficient. Then we expect soft masses much larger than the A-terms,

*i.e.*maximal mixing is impossible.
Amusingly, the only weakly-coupled way to get one-loop soft masses in a weakly coupled theory is if we have the messengers of minimal gauge mediation! 31 possible single-coupling models, all of which would have unaccessible superpartners at the 7/8 TeV LHC. Flavour, CP constraints a work in progress.

Alternative: a strongly-coupled hidden sector, but weakly-coupled messenger sector. This amounts to looking for hidden sector sequestration. Ideas long-standing as part of work on the µ-Bµ problem. If the ideas work there, they should also work here. It looks like they do, and indeed we can generalise beyond full sequestration (Bµ = 0) to partial.

Question: Messenger scale? For weak coupling, order 10 to 100 TeV; for strong coupling, higher. What about renormalisation effects? Leads to additional fine tuning.

Question: Messenger scale? For weak coupling, order 10 to 100 TeV; for strong coupling, higher. What about renormalisation effects? Leads to additional fine tuning.

__11:20am: Asimina Arvanitaki, "Physics beyond colliding particles"__

__A gravity wave talk? LIGO will turn on soon, should observe gravitational waves for the first time. Also a talk on other high-precision tests of__

*e.g.*EDMs, equivalence principle, atom neutrality, short-distance gravity.

No, these were examples. Actual focus is related but different new class of experiments based on optically-levitated objects, with a number of possible applications. Okay, the talk

*is*about using this to search for GWs. I have to give the organisers credit, I was not expecting a talk like this.

Idea is to use lasers to trap dielectrics. This isolates them from their environment with quality factors of at least 10

^{12}even at room temperature. The trapped object can be a number of possible different objects; if it is an atom, we are dealing with atomic interferometry, a field that has won four Nobels in fifteen years.

Optical cooling uses tricks so that atoms/etc absorb laser photons of one energy, and emit another at higher frequency, thereby losing energy.

Gravity wave detection uses cavities of 10-100m and trapped silica spheres or disks of ~100nm. A gravity wave will change the length of the cavity and the position of the trapped probe relative to the ends. Sensitivity depends on both of these things, obviously, but also the resonant frequency of the sensor; so by changing the laser frequency we have a tunable GW detector. Projected sensitivity is comparable with LIGO; better at high frequencies away from LIGO resonances. Main noise is thermal fluctuations in sensor position, hence the benefits of optical cooling.

Interestingly, the highest frequency sources of gravitational waves come from BSM physics; radiation from small black holes that can trap clouds of massive bosons in their ergosphere. In particular, the QCD axion can easily play this role, affecting the black hole by sucking energy out of it. The axion forms a bound state with black hole. Axion self-interactions raise the possibility of axion annihilations to a single gravity wave of monochromatic energy. These can be looked for by this type of experiment, but not LIGO.

Interesting side-effect; measurements of BH mass and spin based on axion-BH bound states already rules out an axion scale above ~ 10

^{17}GeV, in particular the Planck scale is ruled out. Sadly, the planned experiment will not yet probe a GUT-scale QCD axion.

Very interesting prospect: using this cooling technology to create quantum superpositions of

*macroscopic*objects, the "Schrodinger cat state".

__11:55am: Mariana Grana, "Generalizing the Geometry of Space-Time: from Gravity to Supergravity and beyond...?__

__Needs shorter title.__

Einstein: gravity = geometry.

Add SUSY: supergravity = generalised geometry.

Supergravity: extension of Einstein gravity to include supersymmetry. Unique in 11 dimensions, two possibilities in 10. Three relevant bosonic fields; the metric, antisymmetric two-form and dilaton. These are the massless modes on a closed string, hence our interest in 10D.

Einstein deals with point particles, which have momentum. Strings also have a winding charge. To deal with this it is "convenient" to work on a double-tangent space,

*i.e.*in 20D. We can think of doubling as momentum + winding; or left-moving + right-moving. Generalised geometry helps to think about metric + B-field.

The metric has diffeomorphism invariance, described by a vector in the tangent space; the B-field also has a gauge symmetry, defined by a covector in the cotangent space. Hence we don't really double the tangent space, but work in the combined tangent + cotangent space. This space has a natural inner product combining the vector coordinates with the covector coordinates. This generates a generalised Lie algebra and generalised Lie derivative.

We have a generalised metric, combining the metric (in the natural way) and the B-field. This defines a natural torsion-free generalised connection, though sadly it is not unique. Guess what, this defines a generalised curvature in the obvious way but this is not a tensor. To get a tensor object you must extend the definition, but this is still not unique. However, the (relevant components of the) Ricci tensor

*is*unique.

Doing

*all of this*, we get an action for the graviton and partners that is

*exactly analogous to*those of Einstein gravity. The action is the Einstein action with the generalised scalar curvature, and in the vacuum the equation of motion is simply that the generalised Ricci tensor vanishes. This is a purely

*geometrical*description of supergravity.

We can even generalise this idea further. Instead of just doubling the tangent space, double the actual geometry subject to an appropriate constraint (to reduce back to the correct number of degrees of freedom). This ends up being related to T-duality; indeed, the identification of the physical degrees of freedom can vary with position so we go from one set of coordinates to its T-dual as we move in spacetime. This could be a purely

*geometrical*description of string theory.

This was possibly the best talk of the morning session, in that I was able to follow it and understand the conclusions and (somewhat) where they came from. Usually in this type of string theory talk, I give up after ten minutes or so.

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