Another representation of the β form of the inhomogeneous Picard-Fuchs equation

  • In this letter we give another representation of the β form in the inhomogeneous Picard-Fuchs equation for open topological string for some one-parameter Calabi-Yau hypersurfaces in weighted projective spaces. Furthermore, the corresponding domain wall tensions calculated by using these β forms are consistent with the results that appear in literature. The β form is essential for the calculation of the D-brane domain wall tension, and a convenient choice of β forms should simplify the calculation. The freedom of the choice of β forms shows some symmetries in Calabi-Yau space.
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  • [1] Candelas P, DeLaOssa X C, Green P S, Parkes L. Nucl. Phys. B, 1991, 359: 21-74[2] Bershadsky M, Cecotti S, Ooguri H, Vafa C. Commun. Math. Phys., 1994, 165: 311-428[3] Walcher J. Commun. Math. Phys., 2007, 276: 671-689[4] Aganagic M, Vafa C. arXiv: hepth/0012041[5] Morrison D R, Wachler J. Adv. Theor. Math. Phys., 2009, 13: 553-598[6] Li S, Lian B H, Yau Shing-Tung. Amer. J. Math., 2012, 134: 1345-1384[7] Witten E. Nucl. Phys. B, 1997, 507: 658-690[8] Walcher J. Nucl. Phys. B, 2009, 817: 167-207[9] Knapp J, Scheidegger E. Adv. Theor. Math. Phys., 2009, 13: 991-1075[10] Krefl D, Walcher J. JHEP, 2008, 09: 031-067[11] Walcher J. JHEP, 2009, 0909: 129[12] Lerche W, Mayr P, Warner N. arXiv: hepth/0208039[13] Lerche W, Mayr P, Warner N. arXiv: hepth/0207259
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XU Feng-Jun and YANG Fu-Zhong. Another representation of the β form of the inhomogeneous Picard-Fuchs equation[J]. Chinese Physics C, 2013, 37(10): 101001. doi: 10.1088/1674-1137/37/10/101001
XU Feng-Jun and YANG Fu-Zhong. Another representation of the β form of the inhomogeneous Picard-Fuchs equation[J]. Chinese Physics C, 2013, 37(10): 101001.  doi: 10.1088/1674-1137/37/10/101001 shu
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Received: 2013-04-11
Revised: 1900-01-01
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Another representation of the β form of the inhomogeneous Picard-Fuchs equation

    Corresponding author: YANG Fu-Zhong,

Abstract: In this letter we give another representation of the β form in the inhomogeneous Picard-Fuchs equation for open topological string for some one-parameter Calabi-Yau hypersurfaces in weighted projective spaces. Furthermore, the corresponding domain wall tensions calculated by using these β forms are consistent with the results that appear in literature. The β form is essential for the calculation of the D-brane domain wall tension, and a convenient choice of β forms should simplify the calculation. The freedom of the choice of β forms shows some symmetries in Calabi-Yau space.

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