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I've been looking for sources about conformal field theory (CFT) applications in condensed matter theory (CMT) like bosonization, critical phenomena, and QFT anomalies. I have studied CFT from Blumenhagen and several other review papers, and I have looking for its applications in CMT. I have tried to read Tsvelik's "Bosonization and Strongly Correlated Systems" for bosonization, but I think it is not an easygoing book for the subject. For critical phenomena, I've looked to Nishimori's "Elements of Phase Transitions and Critical Phenomena". I think it is a good book, but it uses CFT less than I thought, the Ising model specifically. Are there any sources (books,papers, etc.) for studying bosonization and critical phenomena with CFT methods, i.e. CFT applications in CMT? I'll appreciate for any source recommendations.

Mauricio
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Abdülcanbaz
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1 Answers1

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The canonical reference is the Big Yellow Book by Di Francesco, Mathieu, and Sénéchal. It may be hard to read like the other references, however.

If, like me, you're averse to spending money, I particularly recommend various lecture notes from John McGreevy, and specifically the QFT sequence 215A-C, and especially the third installment, which has a lot of CFT (OPEs etc.), and Where do QFTs come from?, which also has some CFT in a very condensed-matter-y setting. There is some mention of CFTs in the courses on Renormalization Group and Quantum Phases of Matter as well. I find McGreevy's writing to be extremely user friendly, and if you start with 215A, you shouldn't need to know much beyond basic QM. If you have some familiarity with QFT, you can probably dive in anywhere.

There's also David Tong's notes. I usually find his notes useful, but you may need to "back track" a bit to get up to speed with the starting point of that paper.

For just bosonization, I recommend von Delft and Schöller's Bosonization for beginners, refermionization for experts, which is where I learned it. It gives a careful derivation of the Luttinger liquid and bosonization map and also has plenty of formulas on vertex operators and such. This reference requires minimal prior knowledge.

For further references, I would strongly suggest looking for lecture notes and even recordings of lectures from various summer schools, including the Boulder Condensed Matter Summer School and TASI (also at Boulder). I assume CFTs have come up a few times in these contexts. The recordings are on YouTube and the topics are on the websites for the two schools.

just a phase
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