Your Week in Seminars Fermionic Edition

Good evening, and welcome to the second edition of YWiS. Last week I took in the full range of seminars, from colloquium to Friday lunch. I don't know if I can say I took in the full content of these talks as well, but let's see what I learned



On Monday we had Andrew Millis from Columbia University talk about Materials with Strong Electronic Correlations: The (Theoretical) End of the Beginning? (I think the subtitle wasn't actually there in the talk itself).

This was a condensed matter theory talk, and like all condensed matter talks it started off with the phase diagram for cuprates and a mention of the illustrious pseudogap, the Dark Energy of condensed matter. The pseudogap is a phase of cuprates - the materials that make high-temperature superconductors - that occurs at about the same concentration of defects as superconductivity but at a higher temperature. It is a little-understood phase that sits between two well-understood phases (antiferromagnetism and Fermi liquid) and perhaps holds some answers to the nature of high-temperature superconductivity.

Millis started with the pseudogap picture and a short overview of the current state of condensed matter theory. He claimed that perhaps some of the phases of matter in question have local, short-range ordering, but no overarching long-range order in the system, and that the investigation of these phases should take this into account.

At the end of this introduction he asked why we cannot easily solve the problems of condensed matter. The basic equations that govern the interactions in the field are known - the electromagnetic potential and Schrödinger's equation - and we should be able to just plug them into a computer and calculate away. The trouble, as Millis presented it, comes from the fermionic nature of the problem.

What we're trying to calculate, in metals, is the behavior of the electrons running through the bulk of the metal. Electrons are fermions, which means that no two can have the same quantum numbers, that is no two can be in the same place with the same momentum and spin. It turns out that the configurations with lowest energies tend to be symmetric, with many particles in the same position. Finding low-energy configurations that put every particle in a different place is much harder.

I didn't get a lot more from this talk. Millis went on to suggest a method that avoids tackling the problem directly, but rather solves an analogous one that we can translate to into a solution. I believe that there was some talk of a local, rather than global, solution, and of the Hubbard model, which is a popular approximation used in modeling electrons in a solid.

I phased in and out of this talk, but I'd peg my Understanding at 25 minutes, and my Interest at about 35 minutes.


The Wedenesday particle talk was by Jesse Thaler from MIT. He talked about Aspects of Goldstini.

Goldstini is the Italian plural form of goldstino, which is the fermionic version - we put "ino" at the end of fermionic particles, influenced by the neutrino - of the Goldstone boson. A Goldstone boson is a massless particle that we find in theories of spontaneous symmetry breaking.

Spontaneous symmetry breaking is a popular concept in particle physics, which springs from the concept of an unstable energy maximum. Imagine a pencil standing on its tip, a system which is symmetric in every direction. The pencil is unstable, though, and left by itself it would fall down in any one of the equivalent directions around it. Once it has fallen, it's broken the symmetry and created one preferred direction. Thus the symmetry of the system is broken when one direction is chosen spontaneously.

This sort of thing is at the bottom of our understanding the electroweak force, and pops up quite a bit in particle physics. When it does, we expect a Goldstone boson, a massless particle that roughly corresponds to spinning the fallen-down pencil around its tip. The goldstini is the fermionic version of that particle which springs from the breaking of supersymmetry - the symmetry that relates fermions and bosons.

The goldstino, then, is well known and accepted in common theories of supersymmetry. It breaks supersymmetry, and then interacts with the gravitino - another fermion, which mediates the force of gravity - to become massless. Thaler's work posits more than one goldstino, hence, goldstini.

How can we have more than one goldstino? By breaking supersymmetry more than once. We do this by imagining several "sectors" in our theory, different sets of fields (particles) that break supersymmetry but don't interact with each other significantly.

When you work through this model it turns out that you can have several goldstini. Also, as the original goldstini lost its mass by giving it to the gravitino, and the gravitino is now satisfied, the new goldstini get to keep their mass, which turns out to be exactly twice that of the (satisfied) gravitino.

Thaler then discussed three possible scenarios for this mass, and what we would expect to see at the LHC in each case. The important thing, it turns out, is how this mass compares with that of the lightest ordinary superpartner, the first supersymmetry-related particle we expect to see in the LHC.

If the mass of the goldstini is very small, they will not come into play as the LOSP will decay into particles we already know. If the mass of the goldstini is too large, then the LOSP cannot decay into it. But if the mass is in some goldstinilocks region in-between, things become interesting and we can expect to see evidence of the gravitino and the goldstini, and distinctly see one having double the mass of the other.

I followed a good portion of this talk, with Understanding of 30 minutes all in all, and perhaps 45 minutes of interest.


Finally, the Friday particle theory lunch had a talk by our own David Curtin, one of Csaba's grad students. He talked about Solving the gaugino mass problem in Direct Gauge Mediation.

I came into this one to follow more of it, on account of the speaker being a student, but ended up following very little as it was technical and above my level. It revolved, again, around supersymmetry breaking. David does model building, which means he starts out with some acceptable results, i.e. the universe as we know it, and tries to tinker up a combination of particles and interactions that would reproduce it, one portion at a time.

What he was trying to build this time was a metastable level in the broken supersymmetric potential. If we think back to our pencil, we had an unstable maximum, the pencil standing on its tip, and a minimum point, the pencil laying on the table, from which it cannot fall. But we can also imagine a midpoint - perhaps resting one side of the pencil on a book. It can't fall any further right away, but there is another, preferred position lying flat on the table. That's what we call a metastable energy level.

As it turns out, the metastable level has some desirable outcomes within the context of supersymmetry, and the talk revolved around the ways we have of getting the right energy structure to our system while avoiding things we don't want in our models - arbitrary particle masses, a large number of new particles, or anything blatantly unphysical.

My Understanding here was quite close to 0, as the technicalities were beyond me. (in fact, the pre-seminar discussion was about soccer, so one might say my understanding was negative). I probably kept trying to follow for about half the talk, or 30 minutes.


That's it for last week. This week we can expect gravity, (heavy!) Conformality Lost (literary!) and CFT/AdS (buzzwordy!). And hopefully less headscratching and more nodding in a agreement.