Abstract
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.
Article PDF
References
J. Fröhlich, J. Fuchs, I. Runkel and C. Schweigert, Kramers-Wannier duality from conformal defects, Phys. Rev. Lett. 93 (2004) 070601 [cond-mat/0404051] [INSPIRE].
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. Bachas, I. Brunner and D. Roggenkamp, A worldsheet extension of O(d, d : Z), JHEP 10 (2012) 039 [arXiv:1205.4647] [INSPIRE].
J. Fröhlich, J. Fuchs, I. Runkel and C. Schweigert, Defect lines, dualities, and generalised orbifolds, arXiv:0909.5013 [INSPIRE].
N. Carqueville and I. Runkel, Orbifold completion of defect bicategories, Quantum Topol. 7 (2016) 203 [arXiv:1210.6363] [INSPIRE].
I. Brunner, N. Carqueville and D. Plencner, Orbifolds and topological defects, Commun. Math. Phys. 332 (2014) 669 [arXiv:1307.3141] [INSPIRE].
I. Brunner, N. Carqueville and D. Plencner, A quick guide to defect orbifolds, Proc. Symp. Pure Math. 88 (2014) 231 [arXiv:1310.0062] [INSPIRE].
I. Brunner and D. Roggenkamp, Defects and bulk perturbations of boundary Landau-Ginzburg orbifolds, JHEP 04 (2008) 001 [arXiv:0712.0188] [INSPIRE].
D. Gaiotto, Domain walls for two-dimensional renormalization group flows, JHEP 12 (2012) 103 [arXiv:1201.0767] [INSPIRE].
K. Graham and G. M. T. Watts, Defect lines and boundary flows, JHEP 04 (2004) 019 [hep-th/0306167] [INSPIRE].
C. Bachas and M. Gaberdiel, Loop operators and the Kondo problem, JHEP 11 (2004) 065 [hep-th/0411067] [INSPIRE].
I. Runkel, Perturbed defects and T-systems in conformal field theory, J. Phys. A 41 (2008) 105401 [arXiv:0711.0102] [INSPIRE].
C. Bachas and S. Monnier, Defect loops in gauged Wess-Zumino-Witten models, JHEP 02 (2010) 003 [arXiv:0911.1562] [INSPIRE].
I. Brunner, D. Roggenkamp and S. Rossi, Defect perturbations in Landau-Ginzburg models, JHEP 03 (2010) 015 [arXiv:0909.0696] [INSPIRE].
S. Fredenhagen, M. R. Gaberdiel and C. Schmidt-Colinet, Bulk flows in Virasoro minimal models with boundaries, J. Phys. A 42 (2009) 495403 [arXiv:0907.2560] [INSPIRE].
C. Vafa and N. P. Warner, Catastrophes and the classification of conformal theories, Phys. Lett. B 218 (1989) 51 [INSPIRE].
I. Brunner and D. Roggenkamp, B-type defects in Landau-Ginzburg models, JHEP 08 (2007) 093 [arXiv:0707.0922] [INSPIRE].
N. Carqueville and D. Murfet, Computing Khovanov-Rozansky homology and defect fusion, Algebr. Geom. Topol. 14 (2014) 489 [arXiv:1108.1081] [INSPIRE].
T. Dyckerhoff and D. Murfet, Pushing forward matrix factorizations, Duke Math. J. 162 (2013) 1249 [arXiv:1102.2957] [INSPIRE].
N. Carqueville and D. Murfet, A toolkit for defect computations in Landau-Ginzburg models, Proc. Symp. Pure Math. 90 (2015) 239 [arXiv:1303.1389] [INSPIRE].
M. Kontsevich, unpublished.
A. Kapustin and Y. Li, D branes in Landau-Ginzburg models and algebraic geometry, JHEP 12 (2003) 005 [hep-th/0210296] [INSPIRE].
D. Orlov, Triangulated categories of singularities and D-branes in Landau-Ginzburg models math/0302304.
I. Brunner, M. Herbst, W. Lerche and B. Scheuner, Landau-Ginzburg realization of open string TFT, JHEP 11 (2006) 043 [hep-th/0305133] [INSPIRE].
A. Kapustin and Y. Li, Topological correlators in Landau-Ginzburg models with boundaries, Adv. Theor. Math. Phys. 7 (2003) 727 [hep-th/0305136] [INSPIRE].
V. B. Petkova and J. B. Zuber, Generalized twisted partition functions, Phys. Lett. B 504 (2001) 157 [hep-th/0011021] [INSPIRE].
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].
S. K. Ashok, E. Dell’Aquila and D.-E. Diaconescu, Fractional branes in Landau-Ginzburg orbifolds, Adv. Theor. Math. Phys. 8 (2004) 461 [hep-th/0401135] [INSPIRE].
A. Kapustin and L. Rozansky, On the relation between open and closed topological strings, Commun. Math. Phys. 252 (2004) 393 [hep-th/0405232] [INSPIRE].
N. Carqueville and I. Runkel, On the monoidal structure of matrix bi-factorisations, J. Phys. A 43 (2010) 275401 [arXiv:0909.4381] [INSPIRE].
N. Carqueville and D. Murfet, Adjunctions and defects in Landau-Ginzburg models, Adv. Math. 289 (2016) 480 [arXiv:1208.1481] [INSPIRE].
N. Behr and S. Fredenhagen, Variable transformation defects, Proc. Symp. Pure Math. 85 (2012) 303 [arXiv:1202.1678] [INSPIRE].
A. Kapustin and Y. Li, D-branes in topological minimal models: The Landau-Ginzburg approach, JHEP 07 (2004) 045 [hep-th/0306001] [INSPIRE].
I. Brunner and M. R. Gaberdiel, Matrix factorisations and permutation branes, JHEP 07 (2005) 012 [hep-th/0503207] [INSPIRE].
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].
N. Behr and S. Fredenhagen, D-branes and matrix factorisations in supersymmetric coset models, JHEP 11 (2010) 136 [arXiv:1005.2117] [INSPIRE].
J. L. Cardy, Boundary conditions, fusion rules and the Verlinde formula, Nucl. Phys. B 324 (1989) 581 [INSPIRE].
J. M. Maldacena, G. W. Moore and N. Seiberg, Geometrical interpretation of D-branes in gauged WZW models, JHEP 07 (2001) 046 [hep-th/0105038] [INSPIRE].
H. Ishikawa, Boundary states in coset conformal field theories, Nucl. Phys. B 629 (2002) 209 [hep-th/0111230] [INSPIRE].
H. Ishikawa and T. Tani, Novel construction of boundary states in coset conformal field theories, Nucl. Phys. B 649 (2003) 205 [hep-th/0207177] [INSPIRE].
S. Fredenhagen, Organizing boundary RG flows, Nucl. Phys. B 660 (2003) 436 [hep-th/0301229] [INSPIRE].
H. Ishikawa and T. Tani, Twisted boundary states in Kazama-Suzuki models, Nucl. Phys. B 678 (2004) 363 [hep-th/0306227] [INSPIRE].
P. D. Francesco, P. Mathieu and D. Sénéchal, Conformal field theory, Graduate Texts in Contemporary Physics, Springer, Germany (1999).
M. R. Gaberdiel and T. Gannon, Boundary states for WZW models, Nucl. Phys. B 639 (2002) 471 [hep-th/0202067] [INSPIRE].
S. Fredenhagen and V. Schomerus, On boundary RG flows in coset conformal field theories, Phys. Rev. D 67 (2003) 085001 [hep-th/0205011] [INSPIRE].
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].
N. Behr and S. Fredenhagen, Matrix factorisations for rational boundary conditions by defect fusion, JHEP 05 (2015) 055 [arXiv:1407.7254] [INSPIRE].
A. Davydov, A. R. Camacho and I. Runkel, N = 2 minimal conformal field theories and matrix bifactorisations of xd, Commun. Math. Phys. 357 (2018) 597 [arXiv:1409.2144] [INSPIRE].
E. Witten, On the Landau-Ginzburg description of N = 2 minimal models, Int. J. Mod. Phys. A 9 (1994) 4783 [hep-th/9304026] [INSPIRE].
D. Nemeschansky and N. P. Warner, Refining the elliptic genus, Phys. Lett. B 329 (1994) 53 [hep-th/9403047] [INSPIRE].
H. Jockers and W. Lerche, Matrix factorizations, D-branes and their deformations, Nucl. Phys. B Proc. Suppl. 171 (2007) 196 [arXiv:0708.0157] [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.
S. Gukov, S. Nawata, I. Saberi, M. Stošić and P. Sułkowski, Sequencing BPS spectra, JHEP 03 (2016) 004 [arXiv:1512.07883] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2012.14225
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
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
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP04(2021)235