$\alpha'$-corrections to DBI action via T-duality constraint

TL;DR

This paper derives $\alpha'$-corrections to the D-brane effective action by enforcing T-duality constraints, identifying 81 covariant couplings involving gauge fields and geometric quantities, consistent with known results.

Contribution

It extends the D-brane effective action to order $\alpha'$ by systematically incorporating T-duality constraints, revealing new covariant couplings involving gauge fields and geometry.

Findings

Identified 81 covariant couplings involving $DF$ and $\Omega$.

Fixed four gauge field couplings consistent with existing literature.

Extended the T-duality transformation rules to include $\alpha'$$ corrections.

Abstract

It is known that D$_p$-brane effective action at the leading order of $\alpha'$ in flat space-time which is given by DBI action, transforms to D$_{p-1}$-brane effective action under standard T-duality transformations of the open string gauge bosons and transverse scalar fields. Extending this duality to order $\alpha'$, one may find corrections to the DBI action which include the second fundamental form $\Omega$ and the covariant derivative of gauge field strength $DF$, as well as the corrections to the T-duality transformations. Using this idea, up to two parameters, we have found all 81 covariant couplings of $D FD F$ and $\Omega\Omega$ with zero, two, four and six $F$'s. The four gauge field couplings that the T-duality constraint fixes are consistent with the known couplings in the literature.