The final session of the first day is back to technical subjects.
5:00 pm: "Currents in Supersymmetric Field Theories", J-P Derendinger
N=1, 4D SUSY. Not required that current be conserved; indeed, very interesting/useful when it is not.
Start with Poincare invariance. Standard, textbook. First extension to scale transformations and the dilatation current. Second extension to conformal transformations & current. In some though by no means all theories, scale invariance implies conformal symmetry; related to existence of CCJ tensor.
Okay, SUSY has been added and I just can't see what is the important point. Once again, I'd like to be able to scan the slides to come so I could put everything together. Instead, I'm going to follow the cricket instead.
5:30 pm: "Quantum Gravity and Dimensional Transmutation", Tim Jones
Okay, England are struggling to make a breakthrough so maybe this talk can prove interesting. This is apparently a 40 year old calculation applied to a simple quantum gravity system. Dimensional transmutation is, of course, the creation of a mass scale in a theory that did not have one by either non-perturbative or perturbative renormalisation effects.
The classic calculation is in massless φ4 theory, where we get a scale from one-loop effects. This is complicated by the fact that the simple one-loop calculation appears to give a VEV, but this is outside the domain of validity for perturbation theory. This problem can be avoided in e.g. scalar QED. In the SM, this ultimately fails thanks to the large top Yukawa (essentially, the instability that that generates).
Now consider quantum gravity, by which we mean the small-field expansion of the metric about some background. Usually, consider GR as leading term. However, consider scale-invariant theory (no Planck mass put in initially) and take R2 theory. (Issues with ghosts/unitarity...) Take massless φ4 with non-minimal scalar-metric coupling. Want the scalar to gain a VEV giving the Planck scale. Also want the theory to be UV-complete (asymptotically free or UV fixed points).
Good news: found UV fixed points and dimensional transmutation minima. Bad news: they don't overlap in parameter space. So good effort, but not there yet.
Extend to SO(10) with adjoint scalar. Allows two independent quartics. Turns out must have fermions to make beta function small in magnitude (asymptotically free, but as close to not being as possible). Yet to show that the UV fixed points here do (or do not) work. Also, must address a true naturalness issue between the transmutation scale and the EW scale.
Questions
Issues with ghosts (I missed exactly what): not considered the IR behaviour yet.
6:00 pm: "Off-trail SUSY", Karim Benakli
We finish the first day with a talk on... pushing the SUSY scale arbitrarily high, and breaking SUSY with neither F nor D terms (?!).
Question: what is the range of MSUSY? Lower bound from LHC of few TeV. What about upper bound? If can be GUT-scale, SUSY breaking can be tree level. However, in the MSSM the Higgs mass is computable. Split SUSY: you get a limit of 108 GeV. High-scale SUSY: 1011 GeV. The reason is due to renormalisation, monotonically increasing the Higgs quartic in the IR.
This leads to the solution: change the beta function. Which is done by adding lots of extra stuff. What was that about working with minimal particle content? The cricket has returned from tea, so you'll have to do better to keep my attention.
SUSY breaking with a fluid. This also breaks Lorentz invariance...
5:00 pm: "Currents in Supersymmetric Field Theories", J-P Derendinger
N=1, 4D SUSY. Not required that current be conserved; indeed, very interesting/useful when it is not.
Start with Poincare invariance. Standard, textbook. First extension to scale transformations and the dilatation current. Second extension to conformal transformations & current. In some though by no means all theories, scale invariance implies conformal symmetry; related to existence of CCJ tensor.
Okay, SUSY has been added and I just can't see what is the important point. Once again, I'd like to be able to scan the slides to come so I could put everything together. Instead, I'm going to follow the cricket instead.
5:30 pm: "Quantum Gravity and Dimensional Transmutation", Tim Jones
Okay, England are struggling to make a breakthrough so maybe this talk can prove interesting. This is apparently a 40 year old calculation applied to a simple quantum gravity system. Dimensional transmutation is, of course, the creation of a mass scale in a theory that did not have one by either non-perturbative or perturbative renormalisation effects.
The classic calculation is in massless φ4 theory, where we get a scale from one-loop effects. This is complicated by the fact that the simple one-loop calculation appears to give a VEV, but this is outside the domain of validity for perturbation theory. This problem can be avoided in e.g. scalar QED. In the SM, this ultimately fails thanks to the large top Yukawa (essentially, the instability that that generates).
Now consider quantum gravity, by which we mean the small-field expansion of the metric about some background. Usually, consider GR as leading term. However, consider scale-invariant theory (no Planck mass put in initially) and take R2 theory. (Issues with ghosts/unitarity...) Take massless φ4 with non-minimal scalar-metric coupling. Want the scalar to gain a VEV giving the Planck scale. Also want the theory to be UV-complete (asymptotically free or UV fixed points).
Good news: found UV fixed points and dimensional transmutation minima. Bad news: they don't overlap in parameter space. So good effort, but not there yet.
Extend to SO(10) with adjoint scalar. Allows two independent quartics. Turns out must have fermions to make beta function small in magnitude (asymptotically free, but as close to not being as possible). Yet to show that the UV fixed points here do (or do not) work. Also, must address a true naturalness issue between the transmutation scale and the EW scale.
Questions
Issues with ghosts (I missed exactly what): not considered the IR behaviour yet.
6:00 pm: "Off-trail SUSY", Karim Benakli
We finish the first day with a talk on... pushing the SUSY scale arbitrarily high, and breaking SUSY with neither F nor D terms (?!).
Question: what is the range of MSUSY? Lower bound from LHC of few TeV. What about upper bound? If can be GUT-scale, SUSY breaking can be tree level. However, in the MSSM the Higgs mass is computable. Split SUSY: you get a limit of 108 GeV. High-scale SUSY: 1011 GeV. The reason is due to renormalisation, monotonically increasing the Higgs quartic in the IR.
This leads to the solution: change the beta function. Which is done by adding lots of extra stuff. What was that about working with minimal particle content? The cricket has returned from tea, so you'll have to do better to keep my attention.
SUSY breaking with a fluid. This also breaks Lorentz invariance...
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