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Introduction to Topological String Theories

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Book cover Superschool on Derived Categories and D-branes (SDCD 2016)

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Abstract

These notes are for a talk in Superschool on derived categories and D-branes at University of Alberta in summer of 2016. The purpose of these notes is to give a main idea of topological string theories as one of examples of mirror symmetry without any technical details. This means that some definitions are somewhat mathematically less rigorous but we rather show intuitive analyses instead. Readers should be familiar with GR, QFT, SUSY, CFT and some basics of string theories.

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Notes

  1. 1.

    Do not be confused with type (k,l) tensors.

  2. 2.

    This is called a spin connection in supergravity.

  3. 3.

    This is not a coincidence. One can intuitively see from the isomorphism between d-cohomology and \(Q_A\)-cohomology by using the transformation laws of \(\phi , \chi \).

  4. 4.

    This result should be rigorously achieved by the Fadeev-Popov method so that the contracting tensor is suggested to be fermionic and \(G_{zz},\bar{G}_{\bar{z}\bar{z}}\) are the most natural choice.

References

  1. Bouchard V. Lectures on complex geometry, Calabi–Yau manifolds and toric geometry. arXiv preprint hep-th/0702063. 2007 Feb 8.

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  2. Vonk M. A mini-course on topological strings. arXiv preprint hep-th/0504147. 2005 Apr 18.

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  3. Witten E. Mirror manifolds and topological field theory. arXiv preprint hep-th/9112056. 1991 Dec 19.

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Author information

Authors and Affiliations

  1. Department of Physics, University of Alberta, Edmonton, Alberta, T6G 2E1, Canada

    Kento Osuga

Authors
  1. Kento Osuga
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Correspondence to Kento Osuga .

Editor information

Editors and Affiliations

  1. Department of Mathematics, University of South Carolina, Columbia, South Carolina, USA

    Matthew Ballard

  2. Department of Mathematics and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada

    Charles Doran

  3. Department of Mathematics and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada

    David Favero

  4. Department of Physics, Virginia Tech, Blacksburg, Virginia, USA

    Eric Sharpe

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Osuga, K. (2018). Introduction to Topological String Theories. In: Ballard, M., Doran, C., Favero, D., Sharpe, E. (eds) Superschool on Derived Categories and D-branes. SDCD 2016. Springer Proceedings in Mathematics & Statistics, vol 240. Springer, Cham. https://doi.org/10.1007/978-3-319-91626-2_15

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