Abstract
We discuss D-brane monodromies from the point of view of the gauged linear sigma model. We give a prescription on how to extract monodromy matrices directly from the hemisphere partition function. We illustrate this procedure by recomputing the monodromy matrices associated to one-parameter Calabi-Yau hypersurfaces in weighted projected space.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
E. Witten, Phases of N = 2 theories in two-dimensions, Nucl. Phys. B 403 (1993) 159 [hep-th/9301042] [INSPIRE].
F. Benini and S. Cremonesi, Partition functions of \( \mathcal{N}=\left(2,2\right) \) gauge theories on S 2 and vortices, Commun. Math. Phys. 334 (2015) 1483 [arXiv:1206.2356] [INSPIRE].
N. Doroud, J. Gomis, B. Le Floch and S. Lee, Exact results in D = 2 supersymmetric gauge theories, JHEP 05 (2013) 093 [arXiv:1206.2606] [INSPIRE].
H. Jockers, V. Kumar, J.M. Lapan, D.R. Morrison and M. Romo, Two-sphere partition functions and Gromov-Witten invariants, Commun. Math. Phys. 325 (2014) 1139 [arXiv:1208.6244] [INSPIRE].
J. Gomis and S. Lee, Exact Kähler potential from gauge theory and mirror symmetry, JHEP 04 (2013) 019 [arXiv:1210.6022] [INSPIRE].
F. Benini, R. Eager, K. Hori and Y. Tachikawa, Elliptic genera of two-dimensional N = 2 gauge theories with rank-one gauge groups, Lett. Math. Phys. 104 (2014) 465 [arXiv:1305.0533] [INSPIRE].
F. Benini, R. Eager, K. Hori and Y. Tachikawa, Elliptic genera of 2d \( \mathcal{N}=2 \) gauge theories, Commun. Math. Phys. 333 (2015) 1241 [arXiv:1308.4896] [INSPIRE].
C. Closset, S. Cremonesi and D.S. Park, The equivariant A-twist and gauged linear σ-models on the two-sphere, JHEP 06 (2015) 076 [arXiv:1504.06308] [INSPIRE].
D. Honda and T. Okuda, Exact results for boundaries and domain walls in 2d supersymmetric theories, JHEP 09 (2015) 140 [arXiv:1308.2217] [INSPIRE].
K. Hori and M. Romo, Exact results in two-dimensional (2, 2) supersymmetric gauge theories with boundary, arXiv:1308.2438 [INSPIRE].
S. Sugishita and S. Terashima, Exact results in supersymmetric field theories on manifolds with boundaries, JHEP 11 (2013) 021 [arXiv:1308.1973] [INSPIRE].
P. Candelas, X.C. De La Ossa, P.S. Green and L. Parkes, A pair of Calabi-Yau manifolds as an exactly soluble superconformal theory, Nucl. Phys. B 359 (1991) 21 [INSPIRE].
R.P. Horja, Hypergeometric functions and mirror symmetry in toric varieties, ProQuest LLC, Ann Arbor, U.S.A. (1999).
P. Seidel and R.P. Thomas, Braid group actions on derived categories of coherent sheaves, Duke Math. J. 108 (2001) 37 [math/0001043] [INSPIRE].
D.R. Morrison, Geometric aspects of mirror symmetry, in Mathematics unlimited — 2001 and beyond, B. Engquist and W. Schmid eds., Springer, Berlin, (2001), math/0007090 [INSPIRE].
P. Mayr, Phases of supersymmetric D-branes on Kähler manifolds and the McKay correspondence, JHEP 01 (2001) 018 [hep-th/0010223] [INSPIRE].
M.R. Douglas, D-branes, categories and N = 1 supersymmetry, J. Math. Phys. 42 (2001) 2818 [hep-th/0011017] [INSPIRE].
R.P. Horja, Derived category automorphisms from mirror symmetry, Duke Math. J. 127 (2005) 1 [math/0103231] [INSPIRE].
P.S. Aspinwall and M.R. Douglas, D-brane stability and monodromy, JHEP 05 (2002) 031 [hep-th/0110071] [INSPIRE].
P.S. Aspinwall, R.L. Karp and R.P. Horja, Massless D-branes on Calabi-Yau threefolds and monodromy, Commun. Math. Phys. 259 (2005) 45 [hep-th/0209161] [INSPIRE].
J. Distler, H. Jockers and H.-j. Park, D-brane monodromies, derived categories and boundary linear σ-models, hep-th/0206242 [INSPIRE].
H. Jockers, D-brane monodromies from a matrix-factorization perspective, JHEP 02 (2007) 006 [hep-th/0612095] [INSPIRE].
M. Herbst, K. Hori and D. Page, Phases of N = 2 theories in 1 + 1 dimensions with boundary, arXiv:0803.2045 [INSPIRE].
M. Herbst and J. Walcher, On the unipotence of autoequivalences of toric complete intersection Calabi-Yau categories, Math. Ann. 353 (2012) 783 [arXiv:0911.4595] [INSPIRE].
J. Knapp, M. Romo and E. Scheidegger, Hemisphere partition function and analytic continuation to the conifold point, arXiv:1602.01382 [INSPIRE].
A. Font, Periods and duality symmetries in Calabi-Yau compactifications, Nucl. Phys. B 391 (1993) 358 [hep-th/9203084] [INSPIRE].
A. Klemm and S. Theisen, Considerations of one modulus Calabi-Yau compactifications: Picard-Fuchs equations, Kähler potentials and mirror maps, Nucl. Phys. B 389 (1993) 153 [hep-th/9205041] [INSPIRE].
R. Eager, K. Hori, J. Knapp and M. Romo, work in progress.
D. Erkinger, Boundaries in \( \mathcal{N}=\left(2,2\right) \) supersymmetric field theories, Master’s thesis, TU Wien, Wien, Austria (2016).
K. Hori and J. Knapp, A pair of Calabi-Yau manifolds from a two parameter non-Abelian gauged linear σ-model, arXiv:1612.06214 [INSPIRE].
C. van Enckevort and D. van Straten, Electronic data base of Calabi-Yau equations, http://www.mathematik.uni-mainz.de/CYequations/db/.
D. Orlov, Derived categories of coherent sheaves and triangulated categories of singularities, in Algebra, arithmetic, and geometry: in honor of Yu.I. Manin. Volume II, Y. Tschinkel and Y. Zarhin eds., Birkhäuser Boston Inc., Boston U.S.A. (2009).
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].
J. Knapp and E. Scheidegger, Towards open string mirror symmetry for one-parameter Calabi-Yau hypersurfaces, Adv. Theor. Math. Phys. 13 (2009) 991 [arXiv:0805.1013] [INSPIRE].
I. Brunner and M.R. Gaberdiel, Matrix factorisations and permutation branes, JHEP 07 (2005) 012 [hep-th/0503207] [INSPIRE].
H. Enger, A. Recknagel and D. Roggenkamp, Permutation branes and linear matrix factorisations, JHEP 01 (2006) 087 [hep-th/0508053] [INSPIRE].
C. Caviezel, S. Fredenhagen and M.R. Gaberdiel, The RR charges of A-type Gepner models, JHEP 01 (2006) 111 [hep-th/0511078] [INSPIRE].
S. Fredenhagen and M.R. Gaberdiel, Generalised N = 2 permutation branes, JHEP 11 (2006) 041 [hep-th/0607095] [INSPIRE].
P. Candelas, X. De La Ossa, A. Font, S.H. Katz and D.R. Morrison, Mirror symmetry for two parameter models. 1., Nucl. Phys. B 416 (1994) 481 [hep-th/9308083] [INSPIRE].
P. Candelas, A. Font, S.H. Katz and D.R. Morrison, Mirror symmetry for two parameter models. 2., Nucl. Phys. B 429 (1994) 626 [hep-th/9403187] [INSPIRE].
E.A. Rødland, The Pfaffian Calabi-Yau, its Mirror, and their link to the Grassmannian G(2, 7),” Composito Math. 122 (2000) 135 [math/9801092].
S. Hosono and H. Takagi, Mirror symmetry and projective geometry of Reye congruences I, J. Alg. Geom. 23 (2014) 279 [arXiv:1101.2746] [INSPIRE].
K. Hori and D. Tong, Aspects of non-abelian gauge dynamics in two-dimensional N = (2, 2) theories, JHEP 05 (2007) 079 [hep-th/0609032] [INSPIRE].
K. Hori, Duality in two-dimensional (2, 2) supersymmetric non-abelian gauge theories, JHEP 10 (2013) 121 [arXiv:1104.2853] [INSPIRE].
R. Eager, K. Hori, J. Knapp and M. Romo, Beijing lectures on the grade restriction rule, to appear in Chin. Ann. Math. Ser. B.
W. Donovan and E. Segal, Window shifts, flop equivalences and Grassmannian twists, Compos. Math. 150 (2014) 942 [arXiv:1206.0219].
N. Addington, W. Donovan and E. Segal, The Pfaffian-Grassmannian equivalence revisited, ALG-GEOM 2 (2015) 332 [arXiv:1401.3661] [INSPIRE].
J.V. Rennemo and E. Segal, Hori-mological projective duality, arXiv:1609.04045 [INSPIRE].
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1704.00901
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Erkinger, D., Knapp, J. Hemisphere partition function and monodromy. J. High Energ. Phys. 2017, 150 (2017). https://doi.org/10.1007/JHEP05(2017)150
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP05(2017)150