Fermions, T-duality and effective actions for D-branes in bosonic backgrounds

Abstract

We find the effective action for any D-brane in a general bosonic background of supergravity. The results are explicit in component fields up to second order in the fermions and are obtained in a covariant manner. No interaction terms between fermions and the field f = b + F , characteristic of the bosonic actions, are considered. These are reserved for future work. In order to obtain the actions, we reduce directly from the M2-brane world-volume action to the D2-brane worldvolume action. Then, by means of T-duality, we obtain the other Dp-brane actions. The resulting Dp-brane actions can be written in a single compact and elegant expression.

D 3 ¯ $$ \overline{\mathrm{D}3} $$ and dS

“…In the gauge (2.14) θ 1 and θ 2 are not proportional, and our gauge therefore does not belong to that class of gauges. However, we will use below the construction of the classical (not gauge-fixed) action quadratic in θ for the D3 and D3 brane, based on the superspace of d = 11 supergravity for the M2 brane background and a T-duality as in [39,46,47].…”

Localized modes at a D-brane—O-plane intersection and heterotic Alice strings

“…The fermionic Dp-brane actions in general bosonic supergravity backgrounds have been worked out very explicitly to quadratic order in fermions in [41]. They restricted attention to the Abelian case, but to quadratic order in 3-3 modes, one can trivially generalize to the non-Abelian case by adding a trace.…”

“…In other words, their results are applicable up to three-point couplings of the fermions with the gauge field and the scalars. After some work, one reduces the general formula of [41], in the case of D3-branes in a background metric, dilaton, and R-R 1-form field strength, to the following effective action:…”

“…If the operator acts on y 1 the top sign is chosen, if it acts on y 2 the bottom sign is chosen. One important step has already been taken relative to the formulae presented in [41]. Their results are given in string frame and we have converted to Einstein frame using g (s)…”

“…Finally, the conventions of [41] are such that 2πα ′ = 1, and therefore T D3 = 1/2π. Putting all of this together, we obtain the desired result S f erm.…”