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Abstract

This review article reports the recent studies, based on a series of publications by one of the present authors along with his collaborators, regarding the interaction between two D-branes, the open string pair production and its possible enhancement in Type II superstring theories. Specifically, computed is the interaction amplitude between two D-branes, placed parallel at a separation, with each carrying a general worldvolume constant flux, and discussed are the amplitude properties, say, the repulsive or attractive nature of the interaction. When at least one of the D-branes carries an electric flux, the interaction amplitude can have an imaginary part, reflecting the instability of the underlying system via the open string pair production. The decay rate and the pair production rate are both computed. In addition, the enhancement of the latter is found when the added electric and magnetic fluxes are correlated in both magnitude and direction in a certain manner. In particular, when one of the branes is D3 and the other is D1, the corresponding pair production rate becomes large enough to be tested in an earthbound laboratory. Note that the pair production rate is related to the brane separation along the direction transverse to both branes, therefore, to the extra-dimensions with respect to the brane observer. So if the underlying string theory is relevant and the D3 can be taken as our own 4-dimensional world, measuring, say, the electric current due to the pair production and comparing it against the added electric and magnetic fields to see if the measurements agree with the prediction of the computations. This can be used to verify the existence of extra-dimensions. Further, this provides also a potential new means to test the underlying string theory without the need of compactifying it to four dimensions.

Keywords:

D-branes/
strings and branes

Authors and contacts

Corresponding author:Lu Jian-Xin,jxlu@ustc.edu.cn

Funds:Project supported by the National Natural Science Foundation of China (Grant Nos. 11775212, 11947301)

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References

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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$

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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) $

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Vol. 69, Issue 10 - 2020-05-20

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