On D-brane anti D-brane effective actions and their corrections to all orders in alpha-prime

Abstract

Based on a four point function, the S-matrix elements at disk level of the scattering amplitude of one closed string Ramond-Ramond field ($C$), two tachyons and one scalar field, we find out new couplings in brane anti brane effective actions for $p=n,p+2=n$ cases. Using the infinite corrections of the vertex of one RR, one gauge and one scalar field and applying the correct expansion, it is investigated in detail how we produce the infinite gauge poles of the amplitude for $p=n$ case. By discovering new higher derivative corrections of two tachyon-two scalar couplings in brane anti brane systems to all orders in ${\alpha }^{\prime }$, we also obtain the infinite scalar poles in $t^{\prime }+s^{\prime }+u$-channel in field theory. Working with the complete form of the amplitude with the closed form of the expansion and comparing all the infinite contact terms of this amplitude, we derive several new Wess-Zumino couplings with all their infinite higher derivative corrections in the world volume of brane anti brane systems. In particular, in producing all the infinite scalar poles of $<V_C{V}_{\varphi }{V}_T{V}_T>$, one has to consider the fact that scalar 's vertex operator in $(-1)$-picture must carry the internal ${\sigma }_3$ Chan-Paton matrix. The symmetric trace effective action has a non-zero coupling between $D{\varphi }^{(1)i}$ and $D{\varphi }_i^{(2)}$ while this coupling does not exist in ordinary trace effective action.

32 pages, no figure, CERN-PH-TH/2012-341,V3. Acknowledgments, refs and some comments in the conclusion section are added. The version that has been accepted in JCAP

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