With cedram.org
Confluentes Mathematici
Search for an article
Search within the site
Table of contents for this issue | Previous article | Next article
Davide Gaiotto; Gregory W. Moore; Edward Witten
An Introduction to the Web-Based Formalism
Confluentes Mathematici, 9 no. 2 (2017), p. 5-48, doi: 10.5802/cml.40
Article PDF
Class. Math.: 37K40, 53D37, 81T30, 81T40, 81Q60
Keywords: Fukaya-Seidel category, supersymmetric quantum mechanics, two-dimensional field theory, soliton, wall-crossing

Résumé - Abstract

This paper summarizes our rather lengthy paper, “Algebra of the Infrared: String Field Theoretic Structures in Massive $\mathcal{N}=(2,2)$ Field Theory In Two Dimensions,” and is meant to be an informal, yet detailed, introduction and summary of that larger work.


[1] S. M. Carroll, S. Hellerman and M. Trodden, Domain wall junctions are 1/4 - BPS states, Phys. Rev. D 61:065001, 2000. arXiv:hep-th/9905217.
[2] S. Cecotti, P. Fendley, K. A. Intriligator and C. Vafa, A New supersymmetric index, Nucl. Phys. B 386:405, 1992. arXiv:hep-th/9204102.
[3] S. Cecotti and C. Vafa, On classification of $N=2$ supersymmetric theories, Commun. Math. Phys. 158:569, 1993. arXiv:hep-th/9211097.
[4] F. Chapoton and M. Livernet, Pre-Lie Algebras and the Rooted Trees Operad, Intl. Math. Res. Notices 8:395–408, 2001.
[5] H. Fan, T. J. Jarvis and Y. Ruan, The Witten equation, mirror symmetry and quantum singularity theory. arXiv:math.AG/0712.4021.
[6] P. Fendley and K. A. Intriligator, Scattering and thermodynamics in integrable N=2 theories, Nucl. Phys. B 380:265, 1992. arXiv:hep-th/9202011.
[7] D. Gaiotto and E. Witten, Knot Invariants from Four-Dimensional Gauge Theory. arXiv:hep-th/1106.4789.
[8] D. Gaiotto, G. W. Moore and A. Neitzke, Spectral networks. arXiv:hep-th/1204.4824.
[9] D. Gaiotto, G. W. Moore and E. Witten, Algebra of the Infrared: String Field Theoretic Structures in Massive ${\mathcal{N}}=(2,2)$ Field Theory In Two Dimensions. arXiv:hep-th/1506.04087.
[10] G. W. Gibbons and P. K. Townsend, A Bogomolny equation for intersecting domain walls, Phys. Rev. Lett. 83:1727, 1999. arXiv:hep-th/9905196.
[11] A. Haydys, Seidel-Fukaya Category And Gauge Theory. arXiv:1010.2353.
[12] M. Kapranov, M. Kontsevich and Y. Soibelman, Algebra of the infrared and secondary polytopes. arXiv:math.SG/1408.2673.
[13] M. Kontsevich and Y. Soibelman, Stability structures, motivic Donaldson-Thomas invariants and cluster transformations. arXiv:math.AG/0811.2435.
[14] H. Oda, K. Ito, M. Naganuma and N. Sakai, An Exact solution of BPS domain wall junction, Phys. Lett. B 471, 140, 1999. doi:10.1016/S0370-2693(99)01355-6, arXiv:hep-th/9910095.
[15] P. Seidel, Fukaya categories and Picard-Lefschetz theory, European Mathematical Society, Zürich, 2008
[16] E. Witten, Supersymmetry and Morse theory, J. Diff. Geom. 17:661, 1982.
[17] E.   Witten, Algebraic geometry associated with matrix models of two-dimensional gravity, in Topological methods in modern mathematics, Stony Brook, NY, 1991, Publish or Perish, Houston, TX, 1993, pages 235–269.
[18] E. Witten, Fivebranes and Knots. arXiv:hep-th/1101.3216.
[19] E. Witten, Khovanov Homology And Gauge Theory, arXiv:math.GT/1108.3103.
[20] E. Witten, Two Lectures On The Jones Polynomial And Khovanov Homology. arXiv: math.GT/1401.6996.
eISSN : 1793-7434