String theory (and indeed AdS/CFT) in itself is a huge vortex that one gets sucked into, so I am cautious about spending too much time there - besides, there is something entirely unsatisfying about learning something at the pinnacle of physics research as AdS/CFT from distilled lecture notes without a sufficiently strong background in strings, and indeed, an appreciation of other fields of HEP. That said, I am very fond of D-brane dynamics.
- Gauge theories: both from the point of view of constrained dynamics à la Henneaux and Teitelboim as well as phenomenological aspects. The former is elegant and powerful, the latter is so far-reaching it’s ridiculous. This is supplemented bvy Tong’s TASI Lectures on Solitons which are possibly my favourite lectures of all time - wonderfully and cleanly presented, with applications in string theory. I now love D3 brane stacks and want to explore D-brane bound states (I am of course defaulting to the D-brane bible by Clifford Johnson) as well as D-brane wrapping and (choral sounds) K-theoretic classification of RR charges on D-branes.
- Anomalies: lots of modern viewpoints here - the Atiyah-Singer index theorem, the Dai-Freed theorem, descent equations, Green-Schwarz anomaly cancellation. Four references in particular stood out: Dai-Freed Anomalies in Particle Physics (with spectral sequences and homology!), TASI Lectures on Anomalies, a lightning review culminating in M-theory anomalies, Anomalies in Quantum Field Theory by Serone (which had a nice review of SQM and the descent equations) and Lectures on Anomalies by Bilal (the Weinberg of sorts)
- AdS3/CFT2: rather than jumping straight to 5 dimensions, I thought I would dip my toes in its (much more concrete) 3-dimensional cousin. Naturally, this led to the conformal bootstrap, minimal models and Verma modules. Something which I would really like to know about is the CS/WZW correspondence, but the only good source is currently nLab, I am yet to picture what a “circle 3-bundle” is. I am also delving into the renormalisation group properly: statements like “a QFT is just an effective field theory on an RG flow between two CFTs in the IR and the UV” are super-intriguing
- Like I said - rather than learning string theory proper, I have lately preferred to learn about ideas that are perhaps better grounded in string theory, but have wide implications in ordinary super-Yang Mills, for example: Montonen-Olive duality, as well as compactifications. To anyone learning string theory: I suggest you drop Becker, Becker, Schwarz now. It’s downright impossible to learn any actual string theory properly from it, save for the big picture. It seems like it would probably be the best “summary” book as a reference to people who are already experts, but I would not recommend learning from it for the first time.
- In mathematics (if you don’t count most of the previous stuff as mathematics), I’ve really just been reading up on physics-motivated algebraic geometry and algebraic topology (AT II on MIT CourseWare is very well written), index theorems for elliptical operators and the McKay correspondence, for fun.