Universality in all-α′order corrections to BPS/non-BPS brane world volume theories

Abstract

Knowledge of all-α ′ higher derivative corrections to leading order BPS and non-BPS brane actions would serve in future endeavor of determining the complete form of the non-abelian BPS and tachyonic effective actions. In this paper, we note that there is a universality in the all-α ′ order corrections to BPS and non-BPS branes. We compute amplitudes between one Ramond-Ramond C-field vertex operator and several SYM gauge/scalar vertex operators. Specifically, we evaluate in closed form string correlators of two-point amplitudes A Cφ , A CA , a three-point amplitude A Cφφ , and a four-point amplitude A Cφφφ . We carry out pole and contact term analysis. In particular we reproduce some of the contact terms and the infinite massless poles of A Cφφφ by SYM vertices obtained through the universality.

All order α′ corrections to fermionic couplings of D-brane-Anti-D-brane effective actions

“…Notice to the important fact, if we make use of the coefficients a 0,0 = 2 ln(2) and b 0,0 = π/2 then we immediately reveal that one is not able to match the non-Abelian couplings at α ′ order by taking the symmetric trace of non-Abelian couplings of (24).…”

“…Note that some further remarks are given in section six of [37] for all order corrections of two scalar two tachyon couplings of D pDp . 11 The prescription for obtaining all order higher derivative corrections are provided in [24,47] accordingly, hence we first write down all order higher derivative corrections to 9 V a,α (Ψ 1 , Ψ 2 , A)G αβ ab (A)V b,β (A, T 3 , T 4 ). 10 (k 1 + k 2 + k 3 + k 4 ) a = 0 and on shell conditions γ a k 1aū A = γ a k 2a u B = 0 are also taken.…”

“…Having derived all new couplings with their exact coefficients in (24) in the world volume of D-brane Anti D-brane system, which include some new structures such as…”

“…The propagator can also be read off as iδ αβ (2πα ′ )Tp(t+s ′ +u ′ ) . Now we try to explore all order generalisation of the vertex of V β (T, T 3 ,Ψ 1 , Ψ 2 ) by employing the all order corrections of two fermion two tachyon couplings of the discovered higher derivative non-abelian couplings that are constructed in (24).…”

“…where k becomes the momentum of off-shell tachyon. We need to consider the other ordering, namely since the tachyon propagator is off-shell we need to consider Tr (λ 1 λ 2 λ β λ 3 ) ordering as well and also take into account the hermitian conjugate of the other terms in (24), then one is able to explore the ultimate form of vertex in an EFT for a n,m . The same is applied for b n,m as well.…”