Reference request: Supermanifolds with open charts approach

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SUMMARY

The discussion centers on the need for accessible resources on supermanifolds for an undergraduate thesis in supersymmetry. The user has a foundational understanding of differentiable manifolds but lacks knowledge in sheaves and schemes, which are critical in the book "Quantum Fields and Strings: A Course for Mathematicians" by Witten and Deligne. Recommendations include exploring arXiv papers, specifically "1209.2199" for supermanifolds and "hep-ph/9709356" for supersymmetric quantum field theories, which do not require advanced algebraic geometry knowledge.

PREREQUISITES
  • Understanding of differentiable manifolds
  • Basic knowledge of real analysis
  • Familiarity with module theory
  • Introductory concepts in supersymmetry
NEXT STEPS
  • Read "Quantum Fields and Strings: A Course for Mathematicians" by Witten and Deligne for foundational concepts
  • Explore the arXiv paper "1209.2199" for insights on supermanifolds
  • Investigate the arXiv paper "hep-ph/9709356" for applications in supersymmetric quantum field theories
  • Study introductory texts on sheaves and schemes to build foundational knowledge for future research
USEFUL FOR

Undergraduate students in mathematics and physics, particularly those focusing on supersymmetry and supermanifolds, as well as educators seeking accessible teaching materials on these advanced topics.

N1k1tA
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I've decided to work on some topics about supersymmetry for my undergraduate thesis. My background is that I have had a one-semester course in differentiable manifolds, plus typical undergrad math courses, real analysis and module theory (graduate algebra).

So, I went to the library and found a book written by some famous mathematicians and physicists like Witten and Delign. It's called Quantum Fields and Strings: A course for mathematicians. I started reading the first two chapter. My main problem with the book is that it defines supermanifolds by sheaf of algebras and I don't know anything about sheaves or schemes and I don't have time to study algebraic geometry this semester. Is there a good book that covers general topics that students need to know about supersymmetry without using sheaves and schemes?

What books do you think I should look at? Thanks in advance.
 
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If I understand your question right, you are looking for a reference about super manifolds, and not necessarily about supersymmetry in quantum field theory, which is what people usually mean when they say supersymmetry? If so, you can try to have a look at
http://arxiv.org/abs/1209.2199
if you are interested in supersymmetric quantum field theories, have a look at
http://arxiv.org/abs/hep-ph/9709356
 

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