We investigate the fusion of B-type interfaces in two-dimensional supersymmetric Landau-Ginzburg models. In particular, we propose to describe the fusion of an interface in terms of a fusion functor that acts on the category of modules of the underlying polynomial rings of chiral superfields. This uplift of a functor on the category of matrix factorisations simplifies the actual computation of interface fusion. Besides a brief discussion of minimal models, we illustrate the power of this approach in the SU(3)/U(2) Kazama-Suzuki model where we find fusion functors for a set of elementary topological defects from which all rational B-type topological defects can be generated.
C. P. Bachas, On the symmetries of classical string theory, talk given at the Workshop on Quantum Mechanics of Fundamental Systems: the Quest for Beauty and Simplicity , January 10–1,Valdivia, Chile (2009) [arXiv:0808.2777] [INSPIRE].
C. Vafa and N. P. Warner, Catastrophes and the classification of conformal theories, Phys. Lett. B 218 (1989) 51 [INSPIRE].
M. Kontsevich, unpublished.
D. Orlov, Triangulated categories of singularities and D-branes in Landau-Ginzburg models math/0302304.
Y. Yoshino, Tensor products of matrix factorizations, Nagoya Math. J. 152 (1998) 39.
M. Khovanov and L. Rozansky, Matrix factorizations and link homology, Fund. Math. 199 (2008) 1 [math/0401268].
Y. Kazama and H. Suzuki, Characterization of N = 2 superconformal models generated by coset space method, Phys. Lett. B 216 (1989) 112 [INSPIRE].
Y. Kazama and H. Suzuki, New N = 2 superconformal field theories and superstring compactification, Nucl. Phys. B 321 (1989) 232 [INSPIRE].
J. L. Cardy, Boundary conditions, fusion rules and the Verlinde formula, Nucl. Phys. B 324 (1989) 581 [INSPIRE].
P. D. Francesco, P. Mathieu and D. Sénéchal, Conformal field theory, Graduate Texts in Contemporary Physics, Springer, Germany (1999).
W. Lerche, C. Vafa and N. P. Warner, Chiral rings in N = 2 superconformal theories, Nucl. Phys. B 324 (1989) 427 [INSPIRE].
D. Gepner, Scalar field theory and string compactification, Nucl. Phys. B 322 (1989) 65 [INSPIRE].
M. Mackaay and Y. Yonezawa, sl(N)-web categories, arXiv:1306.6242.
H. Wu, A colored sl(N)-homology for links in S3, arXiv:0907.0695.
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ArXiv ePrint: 2012.14225
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Behr, N., Fredenhagen, S. Fusion of interfaces in Landau-Ginzburg models: a functorial approach. J. High Energ. Phys. 2021, 235 (2021). https://doi.org/10.1007/JHEP04(2021)235