Any reading suggestions for someone who wants to understand this and has a very strong math background but no physics background beyond basic second-year QM?
It's hard to gauge (pardon the pun) where to start you based on that.
I'll guess that you're keen on understanding the General Relativity part in detail.
Carroll and ‘t Hooft have kindly put up lecture notes that might be a good starting place. Stefan Waner has made available good lecture notes on differential geometry in the GR context.
If you can wrap your head around those you could proceed to any of the standard grad texts on GR (MTW, Wald, Weinberg mainly). Weinberg is popular with people who like concise maths.
If it's all too novel, then Hartle, Schutz and Carroll all have excellent introductory texts aimed at grad students.
Once you understand how General Relativity works as a general background to any field theory -- classical or quantum -- then you'd be ready for semiclassical gravity or various quantizations of GR.
An alternative approach might be to aim you instead towards QFTs via group theory, Lie groups, Yang-Mills theory, renormalization, renormalization group flow, and so forth.
Eventually you hit on gauge/group correspondence arguments in general, which will equip you to understand the attractions of AdS/CFT in moving the tedious calculations from one setting to another setting in which they're a lot less tedious, and hopefully not fall too hard for the idea that AdS/CFT automatically helps us with gravity and matter theories in our universe.
There is certainly ample scope for talented mathematicians to test the correspondence argument (and especially whether AdS/CFT specifically or gauge/gravity generally really is a duality) rigourously.
I think that'd cover all the ideas touched on in comment you replied to.
PS: Sorry I meant to list off some QFT resources for you but I have run out of time today. :(
I think that as you have some rough exposure to relativity already, you could first absorb the idea that Minkowski (flat) spacetime is a theory where at every point the Poincaré group is the isometry group. That's a good way to hit on representation theory.
However, Lancaster and Blundell's book has some reviews suggesting that someone good at math should be able to work through it without the background needed by textbooks like Srednicki's https://www.dur.ac.uk/physics/qftgabook/ (I have not read it though).
Thanks again. Your suggestions led me to scan the QC174.45 shelves at a nearby university library. I settled on Maggiore's A Modern Introduction to Quantum Field Theory, which seems to be almost all Math.
