D-brane interaction, the open string pair production and its enhancement plus its possible detection

Jian-Xin Lu; Nan Zhang

doi:10.7498/aps.69.20200037

Journals >Acta Physica Sinica >Volume 69 >Issue 10 >Page 101101-1 > Article

Acta Physica Sinica
Vol. 69, Issue 10, 101101-1 (2020)

D-brane interaction, the open string pair production and its enhancement plus its possible detection

Jian-Xin Lu^* and Nan Zhang

Author Affiliations

Peng Huanwu Center for Fundamental Theory, The Interdisciplinary Center for Theoretical Study, University of Science and Technology of China, Hefei 230026, China

show less

DOI: 10.7498/aps.69.20200037 Cite this Article

Jian-Xin Lu, Nan Zhang. D-brane interaction, the open string pair production and its enhancement plus its possible detection[J]. Acta Physica Sinica, 2020, 69(10): 101101-1 Copy Citation Text

show less

Fig. 1. D-brane

Download full size | View in the Article

Fig. 2. Virtual open string pair

Download full size | View in the Article

Fig. 3. The equivalence of a closed string tree-level cylinder amplitude and an open string one-loop annulus amplitude

Download full size | View in the Article

Fig. 4. A virtual open string circulating a closed time loop can be viewed as a pair of virtual open stringand virtual anti open string creating and annihilating.

Download full size | View in the Article

p	本征值满足的关系
0	$\lambda = 1$
1	$\lambda_{0} + \lambda^{-1}_{0} = {\rm{tr} } { {w}}$
2	$\lambda_{0} + \lambda^{-1}_{0} = {\rm{tr} } { {w}} - 1$, $\lambda = 1$
3	$\displaystyle\sum_{\alpha =0}^{1} (\lambda_{\alpha} + \lambda^{-1}_{\alpha}) = {\rm{tr} } { {w}}, \;\;\displaystyle\sum_{\alpha =0}^{1} (\lambda^{2}_{\alpha} + \lambda^{-2}_{\alpha}) = {\rm{tr} } { {w}}^{2}$
4	$\displaystyle\sum_{\alpha =0}^{1} (\lambda_{\alpha} + \lambda^{-1}_{\alpha}) = {\rm{tr} } { {w}} - 1, \;\;\displaystyle\sum_{\alpha =0}^{1} (\lambda^{2}_{\alpha} + \lambda^{-2}_{\alpha}) = {\rm{tr} } { {w}}^{2} - 1, \, \lambda = 1$
5	$\displaystyle\sum_{\alpha =0}^{2} (\lambda_{\alpha} + \lambda^{-1}_{\alpha}) = {\rm{tr} } { {w}}, \;\;\displaystyle\sum_{\alpha =0}^{2} (\lambda^{2}_{\alpha} + \lambda^{-2}_{\alpha}) = {\rm{tr} } { {w}}^{2}, \;\;\displaystyle\sum_{\alpha =0}^{2} (\lambda^{3}_{\alpha} + \lambda^{-3}_{\alpha}) = {\rm{tr} } { {w}}^{3}$
6	$\displaystyle\sum_{\alpha =0}^{2} (\lambda_{\alpha} + \lambda^{-1}_{\alpha}) = {\rm{tr} } { {w}} - 1, \;\;\displaystyle\sum_{\alpha =0}^{2} (\lambda^{2}_{\alpha} + \lambda^{-2}_{\alpha}) = {\rm{tr} } { {w}}^{2} - 1, $$\displaystyle\sum_{\alpha =0}^{2} (\lambda^{3}_{\alpha} + \lambda^{-3}_{\alpha}) = {\rm{tr} } { {w}}^{3} - 1,$$ \lambda = 1$

Table 1. The equations needed to determine the corresponding eigenvalues for

p	振幅表达式((44)式)方括号中 $\theta$项及其简化
0	$\theta^{4}_{3} (0 \|it) - \theta^{4}_{4} (0 \|it) - \theta^{4}_{2} (0 \| it) = 2\, \theta^{4}_{1} (0 \| it) = 0$
1 或 2	$\theta^{3}_{3} (0 \|it) \theta_{3} (\nu_{0} \|it) - \theta^{3}_{4} (0 \|it) \theta_{4} (\nu_{0} \|it) - \theta^{3}_{2} (0 \|it) \theta_{2} (\nu_{0} \| it) = 2\, \theta^{4}_{1} \left(\left.\dfrac{\nu_{0}}{2}\right\| it \right)$
3 或 4	$\theta^{2}_{3} (0 \|it) \theta_{3} (\nu_{0} \|it) \theta_{3} (\nu_{1} \|it)- \theta^{2}_{4} (0 \|it) \theta_{4} (\nu_{0} \|it) \theta_{4} (\nu_{1} \|it)- \theta^{2}_{2} (0 \|it) \theta_{2} (\nu_{0} \| it)\theta_{2} (\nu_{1} \| it)$$= 2\, \theta^{2}_{1} \left(\left.\dfrac{\nu_{0} + \nu_{1} }{2}\right\|it \right) \theta^{2}_{1} \left(\left.\dfrac{\nu_{0} - \nu_{1} }{2}\right\|it \right)$
5 或 6	$\theta_{3} (0 \|it) \theta_{3} (\nu_{0} \|it) \theta_{3} (\nu_{1} \|it) \theta_{3} (\nu_{2} \|it) - \theta_{4} (0 \|it) \theta_{4} (\nu_{0} \|it) \theta_{4} (\nu_{1} \|it) \theta_{4} (\nu_{2} \|it)$$ - \theta_{2} (0 \|it) \theta_{2} (\nu_{0} \| it)\theta_{2} (\nu_{1} \| it) \theta_{2} (\nu_{2} \| it) $$= 2\, \theta_{1} \left(\left.\dfrac{\nu_{0} + \nu_{1} + \nu_{2} }{2}\right\| it \right) \theta_{1} \left(\left.\dfrac{\nu_{0} - \nu_{1} + \nu_{2} }{2}\right\| it \right) \theta_{1} \left(\left.\dfrac{\nu_{0} + \nu_{1} - \nu_{2} }{2}\right\| it \right)\theta_{1} \left(\left.\dfrac{\nu_{0} - \nu_{1} - \nu_{2} }{2}\right\| it \right) $

Table 2. The

-terms in the square bracket in Eq. (44) and their simplification.

Jian-Xin Lu, Nan Zhang. D-brane interaction, the open string pair production and its enhancement plus its possible detection[J]. Acta Physica Sinica, 2020, 69(10): 101101-1

Download Citation

Tools

Save the article for my favorites

Paper Information