膜相互作用及相关动力学
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摘要
本文我们利用弦论及有效场论的方法研究了膜之间的相互作用以及相关的动力学问题。
·膜的相互作用
我们重新研究了D0-膜与D8-膜之间的相互作用。我们发现无论是在NS-NS分支还是在R-R分支,相互作用势能密度中都存在着发散部分。该发散部分在以前的研究中一直被忽视,我们则指出该发散部分正反映出D8-膜不能作为一个独立物体存在的自然特性。我们知道在该系统的R-R分支中存在着反直觉的非零贡献,对其我们也已有了一些解释。我们将在考虑上述发散部分的前提下对以前关于该系统的解释作一些改进。进一步研究表明,即便在D8-膜上加入一些flux也无法改变D8-膜不能单独存在的本质。特别值得指出的是,对于D8-膜携带电flux的情形,我们推广了以往处理R-R分支费米零模的正规化方案从而在计算中得到一个有意义的结果。
我们还利用有效场论的方法计算了任意维度下两堆平行放置且相距一定距离的p-膜之间的长程相互作用。特别地,如果将上述计算的对象限定为10维下的Dp-膜,我们用同样的方法计算了这些Dp-膜携带一些特殊非阿贝尔flux后的长程相互作用。这些计算不但证实了我们已知的一些事实,而且还帮助我们更好地理解这些Dp-膜系统。譬如,对于文中所构造的(D0,D8)构型,与以往结论所不同的是我们的计算表明该构型很可能是一个边缘束缚态。
·膜的动力学
我们在Ⅱ型超弦理论中发现了一类超引力解,该解描述相交的非超对称Dp-膜系统。该解由一些参数来刻画,当这些参数由一组特值连续变化到另一组特值时,它所描述的构型也由黑Dp-膜平滑地变成与之对应的静态Kaluza-Klein "bubble of nothing" (KK BON)。我们称该解为interpolation族解。我们的研究表明,在一定的条件下,该interpolation族解暗示着黑Dp-膜到稳定的静态bubble的一种可能的转变,而转变的机制则可解释为闭弦快子凝聚。
我们还展示了另外一些超引力interpolation族解,即交叉非超对称D1／D5构型和交叉非超对称F／NS5构型,我们对这些解也作了类似的讨论。
We study two aspects of sring/M theory:brane interactions and the related dy-namics. These have been investigated from both the stringy and the effective theory approaches.
·Brane Interactions
We re-study the interacting D0-D8 system, pointing out that the divergent piece of the interaction potential energy density in either NS-NS sector or R-R sector is not something which can be ignored but reflects the D8-brane nature of non-existence as an independent object. Along with this, we have also addressed a few subtle issues regarding the existing two interpretations for the non-vanishing counter-intuitive R-R potential and improved them each by considering the divergence piece of the potential. Further studies show that the persistence of divergence for the potential in either sector in the presence of a flux on the D8-branes indicates that adding a flux/fluxes on the D8-branes doesn't help to improve its nature of existence as an independent object. Furthermore, we resolve a subtle issue regarding the regularization of fermionic zero-modes in the R-R sector when the D8-branes carry an electric flux so that a meaningful result for the potential can be calculated.
We also calculate the long-range interaction between two p-branes placed parallel at a separation in diverse dimensions via an effective field theory approach. In particu-lar, we considered cases when the p-branes are 10-dimensional Dp-branes carrying with them a special world-volume non-abelian flux. The interaction so computed for each of such systems gives not only the known facts about the underlying system but also some new evidences which may help us to understand the system better. For example, in the case of (Do, D8) system, in contrast to the previous study, our computations indicated that the so constructed (D0, D8) system may well be a marginal bound state.
·Brane Dynamics
We find a family of supergravity solutions, characterized by a few parameters, in typeⅡstring theories, which represents the intersecting non-supersymmetric Dp-branes and nicely interpolates between the corresponding black Dp-branes and the Kaluza-Klein "bubble of nothing" (KK BON) by continuously changing some of these param-eters from one set of values to another. We proposed that this interpolation implies a possible transition from black Dp-branes to stable static bubbles (under certain condi-tions) via the closed string tachyon condensation.
We also find other families of supergravity interpolation solutions, i.e., the inter-secting non-supersymmetric D1/D5 configuration or the intersecting non-supersymmetric F/NS5 configuration. Similar consideration are applied to them.
·膜的相互作用
我们重新研究了D0-膜与D8-膜之间的相互作用。我们发现无论是在NS-NS分支还是在R-R分支,相互作用势能密度中都存在着发散部分。该发散部分在以前的研究中一直被忽视,我们则指出该发散部分正反映出D8-膜不能作为一个独立物体存在的自然特性。我们知道在该系统的R-R分支中存在着反直觉的非零贡献,对其我们也已有了一些解释。我们将在考虑上述发散部分的前提下对以前关于该系统的解释作一些改进。进一步研究表明,即便在D8-膜上加入一些flux也无法改变D8-膜不能单独存在的本质。特别值得指出的是,对于D8-膜携带电flux的情形,我们推广了以往处理R-R分支费米零模的正规化方案从而在计算中得到一个有意义的结果。
我们还利用有效场论的方法计算了任意维度下两堆平行放置且相距一定距离的p-膜之间的长程相互作用。特别地,如果将上述计算的对象限定为10维下的Dp-膜,我们用同样的方法计算了这些Dp-膜携带一些特殊非阿贝尔flux后的长程相互作用。这些计算不但证实了我们已知的一些事实,而且还帮助我们更好地理解这些Dp-膜系统。譬如,对于文中所构造的(D0,D8)构型,与以往结论所不同的是我们的计算表明该构型很可能是一个边缘束缚态。
·膜的动力学
我们在Ⅱ型超弦理论中发现了一类超引力解,该解描述相交的非超对称Dp-膜系统。该解由一些参数来刻画,当这些参数由一组特值连续变化到另一组特值时,它所描述的构型也由黑Dp-膜平滑地变成与之对应的静态Kaluza-Klein "bubble of nothing" (KK BON)。我们称该解为interpolation族解。我们的研究表明,在一定的条件下,该interpolation族解暗示着黑Dp-膜到稳定的静态bubble的一种可能的转变,而转变的机制则可解释为闭弦快子凝聚。
我们还展示了另外一些超引力interpolation族解,即交叉非超对称D1／D5构型和交叉非超对称F／NS5构型,我们对这些解也作了类似的讨论。
We study two aspects of sring/M theory:brane interactions and the related dy-namics. These have been investigated from both the stringy and the effective theory approaches.
·Brane Interactions
We re-study the interacting D0-D8 system, pointing out that the divergent piece of the interaction potential energy density in either NS-NS sector or R-R sector is not something which can be ignored but reflects the D8-brane nature of non-existence as an independent object. Along with this, we have also addressed a few subtle issues regarding the existing two interpretations for the non-vanishing counter-intuitive R-R potential and improved them each by considering the divergence piece of the potential. Further studies show that the persistence of divergence for the potential in either sector in the presence of a flux on the D8-branes indicates that adding a flux/fluxes on the D8-branes doesn't help to improve its nature of existence as an independent object. Furthermore, we resolve a subtle issue regarding the regularization of fermionic zero-modes in the R-R sector when the D8-branes carry an electric flux so that a meaningful result for the potential can be calculated.
We also calculate the long-range interaction between two p-branes placed parallel at a separation in diverse dimensions via an effective field theory approach. In particu-lar, we considered cases when the p-branes are 10-dimensional Dp-branes carrying with them a special world-volume non-abelian flux. The interaction so computed for each of such systems gives not only the known facts about the underlying system but also some new evidences which may help us to understand the system better. For example, in the case of (Do, D8) system, in contrast to the previous study, our computations indicated that the so constructed (D0, D8) system may well be a marginal bound state.
·Brane Dynamics
We find a family of supergravity solutions, characterized by a few parameters, in typeⅡstring theories, which represents the intersecting non-supersymmetric Dp-branes and nicely interpolates between the corresponding black Dp-branes and the Kaluza-Klein "bubble of nothing" (KK BON) by continuously changing some of these param-eters from one set of values to another. We proposed that this interpolation implies a possible transition from black Dp-branes to stable static bubbles (under certain condi-tions) via the closed string tachyon condensation.
We also find other families of supergravity interpolation solutions, i.e., the inter-secting non-supersymmetric D1/D5 configuration or the intersecting non-supersymmetric F/NS5 configuration. Similar consideration are applied to them.
引文
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[2]J. Polchinski, "String theory," Vols.1 and 2. Cambridge:Cambridge University Press (1998)
[3]K. Becker, M. Becker and J. Schwarz, "String theory and M-theory." Cambridge:Cambridge University Press (2007)
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[5]W. Taylor, "Lectures on D-branes, gauge theory and M(atrices)," arXiv:hep-th/9801182; "Lectures on D-branes, tachyon condensation, and string field theory," arXiv:hep-th/0301094.
[6]P. Di Vecchia and A. Liccardo, "D-branes in string theory, I," NATO Adv. Study Inst. Ser. C. Math. Phys. Sci.556,1 (2000) [arXiv:hep-th/9912161]; "D-branes in string theory, II," arXiv:hep-th/9912275.
[7]M. J. Duff, R. R. Khuri and J. X. Lu, "String solitons," Phys. Rept.259,213 (1995) [arXiv: hep-th/9412184].
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[9]E. Witten, "Bound states of strings and p-branes," Nucl. Phys. B 460,335 (1996) [arXiv: hep-th/9510135].
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[13]R. C. Myers, "Dielectric-branes," JHEP 9912,022 (1999) [arXiv:hep-th/9910053].
[14]P. Di Vecchia, M. Frau, I. Pesando, S. Sciuto, A. Lerda and R. Russo, "Classical p-branes from boundary state," Nucl. Phys. B 507,259 (1997) [arXiv:hep-th/9707068].
[15]M. Billo, P. Di Vecchia, M. Frau, A. Lerda, I. Pesando, R. Russo and S. Sciuto, "Microscopic string analysis of the D0-D8 brane system and dual R-R states," Nucl. Phys. B 526,199 (1998) [arXiv:hep-th/9802088].
[16]P. Di Vecchia, M. Frau, A. Lerda and A. Liccardo, "(F, Dp) bound states from the boundary state," Nucl. Phys. B 565,397 (2000) [arXiv:hep-th/9906214].
[17]M. Frau, I. Pesando, S. Sciuto, A. Lerda and R. Russo, "Scattering of closed strings from many D-branes," Phys. Lett. B 400,52 (1997) [arXiv:hep-th/9702037].
[18]J. X. Lu and S. Roy, "Static, non-SUSY p-branes in diverse dimensions," JHEP 0502,001 (2005) [arXiv:hep-th/0408242].
[19]I. Chepelev and A. A. Tseytlin, "Long-distance interactions of D-brane bound states and longitudinal five-brane in M(atrix) theory," Phys. Rev. D 56,3672 (1997) [arXiv:hep-th/9704127].
[20]J. X. Lu, B. Ning, R. Wei and S.-S. Xu, "Interaction between two nonthreshold bound states," Phys. Rev. D 79,126002 (2009) [arXiv:0902.1716 [hep-th]].
[21]J. X. Lu and R.-J. Wu, "The D0-D8 system revisited," JHEP 0911,004 (2009) [arXiv: 0909.0980 [hep-th]].
[22]G. Lifschytz, "Comparing D-branes to black-branes," Phys. Lett. B 388,720 (1996) [arXiv: hep-th/9604156].
[23]U. Danielsson, G. Ferretti and I. R. Klebanov, "Creation of fundamental strings by crossing Dirichlet branes," Phys. Rev. Lett.79,1984 (1997) [arXiv:hep-th/9705084].
[24]O. Bergman, M. R. Gaberdiel and G. Lifschytz, "Branes, orientifolds and the creation of elementary strings," Nucl. Phys. B 509,194 (1998) [arXiv:hep-th/9705130].
[25]J. Polchinski and A. Strominger, "New vacua for type Ⅱ string theory," Phys. Lett. B 388, 736 (1996) [arXiv:hep-th/9510227].
[26]A. Hanany and E. Witten, "Type ⅡB superstrings, BPS monopoles, and three-dimensional gauge dynamics," Nucl. Phys. B 492,152 (1997) [arXiv:hep-th/9611230],
[27]Scott A. Yost, "Bosonized superstring boundary states and partition functions," Nucl. Phys. B 321,629 (1989).
[28]T. Kitao, N. Ohta and J. G. Zhou, "Fermionic zero mode and string creation between D4-branes at angles," Phys. Lett. B 428,68 (1998) [arXiv:hep-th/9801135].
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