×

zbMATH — the first resource for mathematics

Duality between string junctions and D-branes on del Pezzo surfaces. (English) Zbl 0972.81141
Summary: We revisit local mirror symmetry associated with del Pezzo surfaces in Calabi-Yau threefolds in view of five-dimensional \(N=1\) E\(_N\) theories compactified on a circle. The mirror partner of singular Calabi-Yau with a shrinking del Pezzo four-cycle is described as the affine 7-brane backgrounds probed by a D3-brane. Evaluating the mirror map and the BPS central charge we relate junction charges to RR charges of D-branes wrapped on del Pezzo surfaces. This enables us to determine how the string junctions are mapped to D-branes on del Pezzo surfaces.

MSC:
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
14J32 Calabi-Yau manifolds (algebro-geometric aspects)
14J81 Relationships with physics
PDF BibTeX XML Cite
Full Text: DOI arXiv
References:
[1] Seiberg, N., Five-dimensional SUSY field theories, non-trivial fixed points and string dynamics, Phys. lett. B, 388, 753, (1996)
[2] Morrison, D.R.; Seiberg, N., Extremal transitions and five-dimensional supersymmetric field theories, Nucl. phys. B, 483, 229, (1997) · Zbl 0925.81228
[3] Douglas, M.R.; Katz, S.; Vafa, C., Small instantons, del Pezzo surfaces and type \( I′\) theory, Nucl. phys. B, 497, 155, (1997) · Zbl 0935.81057
[4] De Wolfe, O.; Hanany, A.; Iqbal, A.; Katz, E., Five-branes, seven-branes and five-dimensional \(En\) field theories, Jhep, 9903, 006, (1999)
[5] Looijenga, E.; Pinkham, H.C., Simple elliptic singularities, del Pezzo surfaces and Cremona transformations, Invent. math., Proc. symp. pure math., 30, 69, (1977) · Zbl 0391.14006
[6] De Wolfe, O., Affine Lie algebras, string junctions and 7-branes, Nucl. phys. B, 550, 622, (1999) · Zbl 0947.81024
[7] De Wolfe, O.; Hauer, T.; Iqbal, A.; Zwiebach, B., Uncovering infinite symmetries on \([p,q]\) 7-branes: kac – moody algebras and beyond, Adv. theor. math. phys., 3, (1999) · Zbl 0967.81052
[8] Yamada, Y.; Yang, S.-K., Affine 7-brane backgrounds and five-dimensional \(EN\) theories on \(S\^{}\{1\}\), Nucl. phys. B, 566, 642, (2000) · Zbl 0951.81035
[9] Lerche, W.; Mayr, P.; Warner, N.P., Non-critical strings, del Pezzo singularities and seiberg – witten curves, Nucl. phys. B, 499, 125, (1997) · Zbl 0934.81036
[10] Minahan, J.A.; Nemeschansky, D.; Warner, N.P., Investigating the BPS spectrum of non-critical \(En\) strings, Nucl. phys. B, 508, 64, (1997) · Zbl 0925.81282
[11] Hauer, T.; Iqbal, A., Del Pezzo surfaces and affine 7-brane backgrounds, Jhep, 0001, 043, (2000) · Zbl 0990.81581
[12] Sen, A.; Zwiebach, B., Stable non-BPS states in F-theory, Jhep, 0003, 036, (2000) · Zbl 0959.81045
[13] Whittaker, E.T.; Watson, G.N., A course of modern analysis, (1927), Cambridge Univ. Press · Zbl 0108.26903
[14] Fukae, M.; Yamada, Y.; Yang, S.-K., Mordell – weil lattice via string junctions, Nucl. phys. B, 572, 71, (2000) · Zbl 1068.81588
[15] Greene, B.R.; Lazaroiu, C.I., Collapsing D-branes in calabi – yau moduli space: I · Zbl 0983.81075
[16] Minahan, J.A.; Nemeschansky, D.; Warner, N.P., Partition functions for BPS states of the non-critical \(E8\) string, Adv. theor. math. phys., 1, 167, (1998) · Zbl 0898.32013
[17] Klemm, A.; Zaslow, E., Local mirror symmetry at higher genus · Zbl 1079.14523
[18] Aspinwall, P.S.; Greene, B.R.; Morrison, D.R., Measuring small distances in \(N=2\) sigma models, Nucl. phys. B, 420, 184, (1994) · Zbl 0990.81689
[19] Minahan, J.A.; Nemeschansky, D.; Minahan, J.A.; Nemeschansky, D., Superconformal fixed points with \(En\) global symmetry, Nucl. phys. B, Nucl. phys. B, 489, 24, (1997) · Zbl 0925.81382
[20] Noguchi, M.; Terashima, S.; Yang, S.-K., \(N=2\) superconformal field theory with ADE global symmetry on a D3-brane probe, Nucl. phys. B, 556, 115, (1999) · Zbl 0958.81135
[21] Candelas, P.; de la Ossa, X.C.; Green, P.S.; Parkes, L., A pair of calabi – yau manifolds as an exactly soluble superconformal theory, Nucl. phys. B, 359, 21, (1991) · Zbl 1098.32506
[22] Klemm, A.; Mayr, P.; Vafa, C., BPS states of exceptional non-critical strings, Nucl. phys. B (proc. suppl.), 58, 177, (1997) · Zbl 0976.81503
[23] Mukai, S., On the moduli space of bundles on \(K3\) spaces, I, () · Zbl 0674.14023
[24] Harvey, J.A.; Moore, G., On the algebra of BPS states, Commun. math. phys., 197, 489, (1998) · Zbl 1055.81616
[25] Brunner, I.; Douglas, M.R.; Lawrence, A.; Römelsberger, C., D-branes on quintic, Jhep, 0008, 015, (2000) · Zbl 0989.81100
[26] Diaconescu, D.-E.; Römelsberger, C.; Kaste, P.; Lerche, W.; Lütken, C.A.; Walcher, J.; Scheidegger, E., D-branes on some one- and two-parameter calabi – yau hypersurfaces, Nucl. phys. B, Nucl. phys. B, Jhep, 0004, 003, (2000)
[27] Hirzebruch, F., Topological methods in algebraic geometry, (1978), Springer-Verlag
[28] D. Huybrechts, M. Lehn, The Geometry of Moduli Spaces of Sheaves, Aspects Math. E 31, Vieweg, 1997 · Zbl 0872.14002
[29] Sharpe, E., Notes on heterotic compactifications, Phys. lett. B, 432, 326, (1998)
[30] Greene, B.R.; Kanter, Y., Small volumes in compacitified string theory, Nucl. phys. B, 497, 127, (1997) · Zbl 0935.81055
[31] Lazaroiu, C.I., Collapsing D-branes in one-parameter models and small/large radius duality · Zbl 0969.83531
[32] Chiang, C.M.; Klemm, A.; Yau, S.-T.; Zaslow, E., Local mirror symmetry: calculations and interpretations, Adv. theor. math. phys., 3, (1999) · Zbl 0976.32012
[33] Kawai, T.; Kawai, T.; Yoshioka, K., String partition functions and infinite products, (), Adv. theor. math. phys., 4, (2000) · Zbl 1013.81043
[34] Hosono, S.; Saito, M.-H.; Takahashi, A., Holomorphic anomaly equation and BPS state counting of rational elliptic surface, Adv. theor. math. phys., 3, 177, (1999) · Zbl 1062.14504
[35] Borel, A.; Serre, J.-P., Le théorème de riemann – roch, d’après Grothendieck, Bull. soc. math. France, 86, 97, (1958) · Zbl 0091.33004
[36] Danilov, V.I., Algebraic varieties and schemes, () · Zbl 0787.14001
[37] Hartshorne, R., Algebraic geometry, (1987), Springer-Verlag · Zbl 0532.14001
[38] Green, M.; Harvey, J.A.; Moore, G.; Minasian, R.; Moore, G., \(K\)-theory and Ramond-Ramond charge, Class. quant. grav., Jhep, 9711, 002, (1997) · Zbl 0949.81511
[39] Cheung, Y.-K.E.; Yin, Z., Anomalies, branes and currents, Nucl. phys. B, 517, 69, (1998) · Zbl 0945.81061
[40] Diaconescu, D.-E.; Gomis, J., Fractional branes and boundary states in orbifold theories, Jhep, 0010, 001, (2000) · Zbl 0965.81055
[41] Friedman, R.; Morgan, J.; Witten, E., Vector bundles and \(F\) theory, Commun. math. phys., 189, 679, (1997) · Zbl 0919.14010
[42] Douglas, M.R.; Fiol, B.; Römelsberger, C., The spectrum of BPS branes on a noncompact calabi – yau
[43] Mohri, K.; Onjo, Y.; Yang, S.-K., Closed sub-monodromy problem and branes on orbifolds, to appear in Rev. Math. Phys
[44] Sharpe, E., Kähler cone substructure, Adv. theor. math. phys., 2, 1441, (1999) · Zbl 1059.14500
[45] Minahan, J.A.; Nemeschansky, D.; Vafa, C.; Warner, N.P., E-strings and \(N=4\) topological yang – mills theories, Nucl. phys. B, 527, 581, (1998) · Zbl 0951.81025
[46] K. Mohri, Y. Ohtake, S.-K. Yang, in progress
[47] Eguchi, T.; Kanno, H., Five-dimensional gauge theories and local mirror symmetry, Nucl. phys. B, 586, 331, (2000) · Zbl 1043.81714
[48] Douglas, M.R.; Douglas, M.R.; Fiol, B.; Römelsberger, C.; Denef, F.; Fiol, B.; Mariño, M., BPS states and algebras from quivers, Class. quant. grav., Jhep, Jhep, 0007, 031, (2000) · Zbl 0965.81067
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.