×

Beijing lectures on the grade restriction rule. (English) Zbl 1373.32019

Summary: The authors describe the relationships between categories of B-branes in different phases of the non-abelian gauged linear sigma model. The relationship is described explicitly for the model proposed by Hori and Tong with non-abelian gauge group that connects two non-birational Calabi-Yau varieties studied by Rødland. A grade restriction rule for this model is derived using the hemisphere partition function and it is used to map B-type D-branes between the two Calabi-Yau varieties.

MSC:

32Q25 Calabi-Yau theory (complex-analytic aspects)
14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
14J32 Calabi-Yau manifolds (algebro-geometric aspects)
81T13 Yang-Mills and other gauge theories in quantum field theory
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Hori, K. and Tong, D., Aspects of non-Abelian gauge dynamics in two-dimensional N = (2; 2) theories, JHEP, 0705, 2007, 079 [hep-th/0609032]. · doi:10.1088/1126-6708/2007/05/079
[2] Borisov, L. and Caldararu, A., The Pfaffian-Grassmannian derived equivalence, arXiv: math/0608404. · Zbl 1181.14020
[3] Rødland, E. A., The Pfaffian Calabi-Yau, its mirror, and their link to the Grassmannian G(2; 7), Compositio Math., 122(2), 2000, 135-149. · Zbl 0974.14026 · doi:10.1023/A:1001847914402
[4] Kuznetsov, A., Homological projective duality for Grassmannians of lines, arXiv: math/0610957. · Zbl 0994.18007
[5] Addington, N., Donovan, W. and Segal, E., The Pfaffian-Grassmannian equivalence revisited, Algebr. Geom., 2(3), 2015, 332-364. · Zbl 1322.14037 · doi:10.14231/AG-2015-015
[6] Herbst, M., Hori, K. and Page, D., Phases of N=2 theories in 1+1 dimensions with boundary, arXiv: 0803. 2045 [hep-th]. · Zbl 1082.14005
[7] Eager, R., Hori, K., Knapp, J. and Romo, M., to appear. · Zbl 1342.81620
[8] Witten, E., Phases of N = 2 theories in two-dimensions, Nucl. Phys. B, 403, 1993, 159. [hep-th/9301042]. · Zbl 0910.14020 · doi:10.1016/0550-3213(93)90033-L
[9] Aspinwall, P. S., Greene, B. R. and Morrison, D. R., Measuring small distances in N = 2 sigma models, Nucl. Phys. B, 420, 1994, 184. [hep-th/9311042]. · Zbl 0990.81689 · doi:10.1016/0550-3213(94)90379-4
[10] Gel′fand, I. M., Kapranov, M. M. and Zelevinsky, A. V., Discriminants, Resultants, and Multidimensional Determinants, Mathematics: Theory & Applications, Birkhäuser Boston, Inc., Boston, MA, 1994. · Zbl 0827.14036 · doi:10.1007/978-0-8176-4771-1
[11] Kawamata, Y., Log crepant birational maps and deived categories, arXiv: math.AG/0311139. · Zbl 1095.14014
[12] Bergh, M., Non-commutative Crepant Resolutions, 749-770 (2004), Berlin · Zbl 1082.14005 · doi:10.1007/978-3-642-18908-1_26
[13] Segal, E., Equivalences between GIT quotients of Landau-Ginzburg B-models, Commun. Math. Phys., 304, 2011, 411-432. · Zbl 1216.81122 · doi:10.1007/s00220-011-1232-y
[14] Halpern-Leistner, D., The derived category of a GIT quotient, arXiv: 1203.0276 [math.AG]. · Zbl 1354.14029
[15] Ballard, M., Favero, D. and Katzarkov, L., Variation of geometric invariant theory quotients and derived categories, arXiv: 1203.6643 [math.AG]. · Zbl 1400.14048
[16] Hori, K. and Romo, M., Exact results in two-dimensional (2, 2) supersymmetric gauge theories with boundary, arXiv: 1308.2438 [hep-th]. · Zbl 1322.14037
[17] Sugishita, S.; Terashima, S., Exact results in supersymmetric field theories on manifolds with boundaries (2013) · Zbl 1342.81620
[18] Honda, D.; Okuda, T., Exact results for boundaries and domain walls in 2d supersymmetric theories (2015) · Zbl 1388.81218
[19] Bondal, A. and Orlov, D., Reconstruction of a variety from the derived category and groups of autoequivalences, Compositio Math., 125(3), 2001, 327-344. · Zbl 0994.18007 · doi:10.1023/A:1002470302976
[20] Hosono, S. and Takagi, H., Mirror symmetry and projective geometry of Fourier-Mukai partners, arXiv: 1410.1254 [math.AG]. · Zbl 1298.14043
[21] Hosono, S. and Takagi, H., Double quintic symmetroids, Reye congruences, and their derived equivalence, arXiv: 1302.5883 [math.AG]. · Zbl 1364.32018
[22] Miura, M., Minuscule Schubert varieties and mirror symmetry, arXiv: 1301.7632 [math.AG]. · Zbl 1386.14149
[23] Galkin S., Explicit Construction of Miura’s Varieties, based on a work by Galkin, S., Kuznetsov, A. and Movshev, M., Calabi-Yau Manifolds, Mirror Symmetry and Related Topics, University of Tokyo, Komaba, Tokyo, February 17-21, 2014.
[24] Gerhardus, A. and Jockers, H., Dual pairs of gauged linear sigma models and derived equivalences of Calabi-Yau threefolds, arXiv: 1505.00099 [hep-th]. · Zbl 1359.81136
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.