Background needed for learning string theory.

[arroy_0205]

What type of background (both in Physics and mathematics) is needed for learning string/M-theory upto topics recently developed? I will appreciate detailed and specific answers.

 

[jtbell]

What physics and math do you know already?

 

[George Jones]

String Theory and M-Theory: A Modern Introduction by Katrin Becker, Melanie Becker, and John H. Schwarz,

https://www.amazon.com/dp/0521860695/?tag=pfamazon01-20,

is a grad level introduction to string theory.

From its preface: "The reader is assumed to have some familiarity with quantum field theory and general relativity. It is also very useful to a have broad mathematical background. Group theory is essential, and some knowledge of differential geometry and basic concepts of topology is very desirable."

 

[arroy_0205]

Thanks for the replies. I should have mentioned my background in maths and physics. In maths my backgound includes calculus with differential equations but no rigorous knowledge in analysis or differential geometry or topology. I also learned quantum field theory upto renormalization but do not have sound knowledge of renormalization group or advanced topics like instantons etc. Also my background in group theory is not that good. I have done masters in physics long ago but after that did not have touch with physics. Now I have become interested in string theory (quantum gravity in general) and trying to catch up myself. However it seems a huge background is needed in maths for string theory. People talk of very specialized topics like Atiyah-Singer index theorem etc. Unfortunately I am not getting precise information regarding this. There is huge material in maths but I need to choose exactly what I need in order to learn advanced topics in string theory. Hopefully this will explain my problem. Please give any suggestions you would like to make.

 

[phreak]

You need to know differential geometry to understand general relativity and string theory. To understand differential geometry, you will need some elementary topology. For that topology, you will need need to know the basics of analysis. My suggestion for someone at your level would be to pick up Munkres' Topology and read the entire thing (even the sections on algebraic topology), as it is quite elementary and you may not need too much analysis to work with it. If you have trouble with it, you could always consult Rudin's Principles of Mathematical Analysis. Then once you have mastered Munkres, pick up Lee's Introduction to Smooth Manifolds and master it. Then you should be mathematically ready for string theory.

The mentioned texts are probably the most popular for their respective areas. This is precisely because they are so elementary, and they avoid esoteric topics that other authors include in their textbooks.