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I want to start looking at the conformal bootstrap. I've heard very interesting things about it but would like to clear some things up first.

I taken QFT at the level of Peskin & Schroeder, written a bachelors thesis on quantum integrability, know complex analysis up to things like mobius transformations and conformal mappings, functional analysis and algebraic topology. Then stuff like EM with Jackson and QM with Merzbacher's books etc.

What resources are best for working up to the conformal bootstrap?

From what I've seen the bootstrap seems to be heavily numerical. I'm extremely used to exact analytical expressions so would like to know the use of the bootstrap, particularly in relation to N=4 SYM (recently looked through a paper on this topic but it was above my level) or even general QFT.

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  • $\begingroup$ The TASI lectures by David Simmons Duffin on this topic are really good. $\endgroup$ – Prahar Aug 14 '16 at 12:37
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Recently David Simmons-Duffin's published his TASI lecture notes on conformal bootstrap. These are a nice complement to Slava Rychkov's lectures (which by the way are now available on arxiv).

I don't think I agree that 1+1 dimensional bootstrap is a good place to start, or at least you need a rather special exposition. Usually 1+1 CFT texts rush into Virasoro algebra very quickly, and rely heavily on holomorphic language, none of which are central in higher dimensions (although both play their role in some special situations). A lot of problems present in higher dimensions are not present or central in 2d : correlation functions of operators with spin or conserved currents, numerics of conformal blocks, conformal blocks for spinning operators, etc.

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If you have not seen it yet, conformal bootstrap in $1+1$ is extremely powerful, and in many cases essentially determine the whole theory. Everything is done analytically. Recent works of higher-dimensional generalizations share many basic features with the $1+1$ version, so it seems not a bad idea to start from there.

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  • $\begingroup$ Actually higher dimensional bootstrap is often easier than its two dimensional one (since Virasoro modules are more complicated that higher dimensional conformal modules). I would not suggest studying the two dimensional case as an introduction. $\endgroup$ – Prahar Aug 14 '16 at 12:39
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Start with the lecture notes at the top of Slava Rychkov's blog, http://sites.google.com/site/slavarychkov/home

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