Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2010-12-13
JHEP 1102:008,2011
Physics
High Energy Physics
High Energy Physics - Theory
23 pages, Latex file, 1 figure; v2:typos corrected, to appear in JHEP
Scientific paper
10.1007/JHEP02(2011)008
Recently, it has been found that there are couplings of the RR field strength $F^{(p)}$ and the B-field strength $H$ on the world volume of D$_p$-branes at order ${\cal O}(\alpha'^2)$. These couplings which have both world-volume and transverse indices, are invariant under the linear T-duality transformations. Consistency with the nonlinear T-duality indicates that the RR field strength $F^{(p)}$ in these couplings should be replaced by ${\cal F}^{(p)}=d{\cal C}^{(p-1)}$ where ${\cal C}=e^{B}C$. This replacement, however, reproduces some non-gauge invariant terms. On the other hand, the nonlinear terms are invariant under the linear T-duality transformations at the level of two B-fields. This allows one to remove some of the nonlinear terms in ${\cal F}^{(p)}$. We fix this by comparing the nonlinear couplings with the S-matrix element of one RR and two NSNS vertex operators. Our results indicate that in the expansion of ${\cal F}^{(p)}$ one should keep only the B-field gauge invariant terms, e.g. $B\wedge dC^{(p-3)}$ where both indices of B-field lie along the brane. Moreover, in this case one should replace $B$ with $B+2\pi\alpha'f$ to have the $B$-field gauge invariance.
Garousi Mohammad R.
Mir Mozhgan
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