Cosmology and String Theory by Horaţiu Năstase

Author:Horaţiu Năstase
Language: eng
Format: epub, pdf
ISBN: 9783030150778
Publisher: Springer International Publishing

(19.16)

That means that we expect to find in front of the D-brane action a factor . But it follows logically that the full dependence of the D-brane action on must be via a factor of , as

(19.17)

In this way we have shown the coupling of the D-brane with all the massless modes of the closed bosonic string. But we have only shown how it couples to , the massless scalars on the worldvolume, whereas there are other massless open string fields. In particular, as we saw in general for Neumann boundary conditions in the last chapter, there are massless vectors coming from , and on the D-brane we have the same boundary conditions. The mode should couple gauge invariantly to the D-brane, i.e., through , and for small fields, we expect to have the usual Maxwell action . Moreover, it should fit inside the determinant.

Luckily, there is such a simple action, the Born–Infeld action for electromagnetism found in the 1930s, as an action without the singularities of the Maxwell action, that has a maximum electric field (and never reaches infinite values). It amounts to adding to the metric inside the determinant, so the full Dirac–Born–Infeld (DBI) action is

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