I didn’t know much supersymmetry a couple of weeks ago - only as far as supermultiplets and superfields. In particular, I didn’t know how to construct supersymmetric gauge theories and the like, so that was my starting point. Also, I’ve found the new exotic territory (that I describe in this post) extremely appealing: I love the way that SUSY gauge theories can be lifted to string theory, the way that statistical field theoretic notions like phase transitions and superconductors are found in high-energy QCD.
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High-energy particle physics models - It might sound odd, but this is one of the areas adjoint to raw supersymmetry that I’m not as interested in currently! Nonetheless the immediate extensions of the Standard Model and gauge/gravity-mediated SUSY breaking are incredibly important tools which were appealing to me.
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Supersymmetric solitons - David Tong’s TASI notes, and the Shifman compendium are the go-to sources on these. When they’re powered (that is, constrained) by SUSY, solitons become really powerful, while still maintaining their elegant geometrical nature
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Supersymmetric moduli/pseudomoduli spaces - especially that of supersymmetric quantum chromodynamics, which displays a wide array of intriguing phenomena (gaugino condensation, phase transitions, etc.)
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Even phases of regular ol’ gauge theories are super interesting (so many cool analogies with the ‘t Hooft model and superconductors!), but the one thing that SQCD really has going for it is Seiberg duality, which is simply fantastic (and, not to mention, completely unexpected!). Matt Strassler has some great lectures on the full-fledged duality cascade (passing D3 branes on conifolds (!) along the way)
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Supersymmetric sigma models (particularly for $\mathcal N = 2$, you get to see hyperKähler and special Kähler manifolds in the wild) - I find these incredibly elegant: you get to encode the low-energy spectrum of an extremely complex supersymmetric gauge theory geometrically as a manifold with a lot of structure on it!
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Non-renormalization theorems, holomorphy, instantons - very pragmatic tools, it goes without saying.
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Cosmology - I don’t know much beyond the basic equations of $\Lambda$CDM, so I’m going to be reading about some more advanced things like inflation, early-universe matter generation and cosmological perturbation theory
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Statistical field theory - the most underrated topic in physics in my opinion. As I mention in my quantum field theory guide, you should learn graduate-level statistical field theory before starting quantum field theory (I didn’t, and I wish I did). The analogies between the two are vast, but the intuition that statistical field theory provides is far greater, since it’s “closer to Earth” (and Ken Wilson). I was learning about domain walls, RG flows, non-trivial fixed points, sigma models, and a smörgåsbord of dualities. But that’s not all! There’s universal criticality, minimal models, WZW models (I’m learning from the Yellow book of course) that can manifest before your eyes in a condensed matter lab.
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Superfluidity and superconductivity: Finally getting to bring my basic solid-state QM knowledge into a more advanced context! Plus it’s nice seeing a quantum field theory that’s outside of HEP. Superconductivity is the correct classical analogy of the Higgs mechanism, interestingly enough.
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Holographic descriptions of quark-gluon plasma: The ultimate “real-life” application of string theory! You use the AdS/CFT correspondence to link SYM (and even SQCD, if you’re feeling brave) to a 5D black hole and its perturbations. The classical description of QGP is also a nice foray into condensed matter physics. On that note, something that I want to learn about is holographic descriptions of hadron and glueball spectra.
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Sphalerons - introducing the instantons’ wilder cousin. They trigger B and L violation in the Standard Model, nonperturbatively.
I might conclude with the fact that I no longer do much string theory - not because of some misplaced disillusionment, but because supersymmetry on its own is just way too cool. I still find the S-matrix properties of string theory extremely alluring, but perhaps I’m going to learn about something like “practical” AdS/CFT, non-commutative geometry or “lifting” QFTs to string theory rather than, say, superstrings.