Abstract
While the study of bordered (pseudo-)holomorphic curves with boundary on Lagrangian submanifolds has a long history, a similar problem that involves (special) Lagrangian submanifolds with boundary on complex surfaces appears to be largely overlooked in both physics and math literature. We relate this problem to geometry of coassociative submanifolds in G2 holonomy spaces and to Spin(7) metrics on 8-manifolds with T2 fibrations. As an application to physics, we propose a large class of brane models in type IIA string theory that generalize brane brick models on the one hand and 2d theories T[M4] on the other.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
P.S. Aspinwall et al., Dirichlet branes and mirror symmetry, vol. 4 of Clay Mathematics Monographs, American Mathematical Society, Providence, RI, Clay Mathematics Institute, Cambridge, MA, U.S.A. (2009).
A. Butscher, Deformations of minimal Lagrangian submanifolds with boundary, Proc. Am. Math. Soc. 131 (2003) 1953.
S. Franco, S. Lee and R.-K. Seong, Brane Brick Models, Toric Calabi-Yau 4-Folds and 2d (0,2) Quivers, JHEP 02 (2016) 047 [arXiv:1510.01744] [INSPIRE].
S. Franco, S. Lee and R.-K. Seong, Brane brick models and 2d (0, 2) triality, JHEP 05 (2016) 020 [arXiv:1602.01834] [INSPIRE].
S. Franco, S. Lee, R.-K. Seong and C. Vafa, Brane Brick Models in the Mirror, JHEP 02 (2017) 106 [arXiv:1609.01723] [INSPIRE].
E. Witten, Solutions of four-dimensional field theories via M-theory, Nucl. Phys. B 500 (1997) 3 [hep-th/9703166] [INSPIRE].
M. Atiyah, J.M. Maldacena and C. Vafa, An M-theory flop as a large N duality, J. Math. Phys. 42 (2001) 3209 [hep-th/0011256] [INSPIRE].
M. Atiyah and E. Witten, M theory dynamics on a manifold of G2 holonomy, Adv. Theor. Math. Phys. 6 (2003) 1 [hep-th/0107177] [INSPIRE].
S. Gukov and J. Sparks, M theory on spin(7) manifolds. 1, Nucl. Phys. B 625 (2002) 3 [hep-th/0109025] [INSPIRE].
S. Gukov, J. Sparks and D. Tong, Conifold transitions and five-brane condensation in M-theory on spin(7) manifolds, Class. Quant. Grav. 20 (2003) 665 [hep-th/0207244] [INSPIRE].
M. Bershadsky, C. Vafa and V. Sadov, D-branes and topological field theories, Nucl. Phys. B 463 (1996) 420 [hep-th/9511222] [INSPIRE].
K. Becker, M. Becker, D.R. Morrison, H. Ooguri, Y. Oz and Z. Yin, Supersymmetric cycles in exceptional holonomy manifolds and Calabi-Yau 4 folds, Nucl. Phys. B 480 (1996) 225 [hep-th/9608116] [INSPIRE].
M. Blau and G. Thompson, Aspects of NT ≥ 2 topological gauge theories and D-branes, Nucl. Phys. B 492 (1997) 545 [hep-th/9612143] [INSPIRE].
R. Fintushel and R.J. Stern, Knots, links, and 4-manifolds, Invent. Math. 134 (1998) 363.
A. Gadde, S. Gukov and P. Putrov, Fivebranes and 4-manifolds, Prog. Math. 319 (2016) 155 [arXiv:1306.4320] [INSPIRE].
L. Foscolo, M. Haskins and J. Nordström, Complete non-compact G2-manifolds from asymptotically conical Calabi-Yau 3-folds, arXiv:1709.04904 [INSPIRE].
L. Foscolo, M. Haskins and J. Nordström, Infinitely many new families of complete cohomogeneity one G2-manifolds: G2 analogues of the Taub-NUT and Eguchi-Hanson spaces, arXiv:1805.02612 [INSPIRE].
R. Harvey and H.B. Lawson Jr., Calibrated geometries, Acta Math. 148 (1982) 47 [INSPIRE].
I.A. Bandos, A. Nurmagambetov and D.P. Sorokin, The Type IIA NS5-brane, Nucl. Phys. B 586 (2000) 315 [hep-th/0003169] [INSPIRE].
B.S. Acharya and C. Vafa, On domain walls of N = 1 supersymmetric Yang-Mills in four-dimensions, hep-th/0103011 [INSPIRE].
S. Gukov, C. Vafa and E. Witten, CFT’s from Calabi-Yau four folds, Nucl. Phys. B 584 (2000) 69 [Erratum ibid. 608 (2001) 477] [hep-th/9906070] [INSPIRE].
L. Foscolo, Complete non-compact Spin(7) manifolds from self-dual Einstein 4-orbifolds, arXiv:1901.04074 [INSPIRE].
D.S. Freed and E. Witten, Anomalies in string theory with D-branes, Asian J. Math. 3 (1999) 819 [hep-th/9907189] [INSPIRE].
M. Dedushenko, S. Gukov and P. Putrov, Vertex algebras and 4-manifold invariants, arXiv:1705.01645 [INSPIRE].
E. Witten, Duality relations among topological effects in string theory, JHEP 05 (2000) 031 [hep-th/9912086] [INSPIRE].
R. Dijkgraaf, L. Hollands, P. Sulkowski and C. Vafa, Supersymmetric gauge theories, intersecting branes and free fermions, JHEP 02 (2008) 106 [arXiv:0709.4446] [INSPIRE].
B. Feigin and S. Gukov, VOA[M4], J. Math. Phys. 61 (2020) 012302 [arXiv:1806.02470] [INSPIRE].
A. Hanany and E. Witten, Type IIB superstrings, BPS monopoles, and three-dimensional gauge dynamics, Nucl. Phys. B 492 (1997) 152 [hep-th/9611230] [INSPIRE].
N. Ohta and P.K. Townsend, Supersymmetry of M-branes at angles, Phys. Lett. B 418 (1998) 77 [hep-th/9710129] [INSPIRE].
T. Kitao, K. Ohta and N. Ohta, Three-dimensional gauge dynamics from brane configurations with (p,q)-fivebrane, Nucl. Phys. B 539 (1999) 79 [hep-th/9808111] [INSPIRE].
O. Bergman, A. Hanany, A. Karch and B. Kol, Branes and supersymmetry breaking in three-dimensional gauge theories, JHEP 10 (1999) 036 [hep-th/9908075] [INSPIRE].
A. Armoni and V. Niarchos, Defects in Chern-Simons theory, gauged WZW models on the brane, and level-rank duality, JHEP 07 (2015) 062 [arXiv:1505.02916] [INSPIRE].
H. Garcia-Compean and A.M. Uranga, Brane box realization of chiral gauge theories in two-dimensions, Nucl. Phys. B 539 (1999) 329 [hep-th/9806177] [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: 1910.01645
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
Franco, S., Gukov, S., Lee, S. et al. “Lagrangian disks” in M-theory. J. High Energ. Phys. 2020, 33 (2020). https://doi.org/10.1007/JHEP11(2020)033
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2020)033