Dualization of higher derivative heterotic supergravities in 6D and 10D

Abstract

Abstract There exist two four-derivative extensions of N = (1, 0) supergravity in six dimensions. A particular combination of them is known to dualize to the analog of the Bergshoeff-de Roo (BdR) action in 10D. Here we first show that the two extensions are not related to each other by any field redefinitions. Next, we dualize them separately thereby obtaining a two parameter dual theory. This is done directly at the level of the action, thus avoiding the laborious method of integrating equations of motion of the dualized theory into an action. To explore whether a similar phenomenon exists in 10D, we study the dualization of the BdR action in 10D in detail. We find an obstacle in the separation of the result into a sum of two independent invariants because of the presence of terms which do not lift from 6D to 10D. We also compare the dual of the BdR action with an existing result obtained in superspace. We find that the bosonic actions agree modulo field redefinitions.