Open giant magnons suspended between dual giant gravitons in N $$ \mathcal{N} $$ = 4 SYM

Abstract We study classical solutions to the Nambu-Goto string on AdS 2 × S 1 and AdS 3 × S 1 corresponding to strings stretched between wrapped branes extending in AdS. The solutions are obtained by analytic continuation of giant magnon solutions, cut at the position of the branes. These solutions carry one or two SO(2, 4) charges and a single SO(6) charge. We compute their energies and show their relation to 1 2 $$ \frac{1}{2} $$ -BPS geometries. Their relevance to the SL(2) sector of N $$ \mathcal{N} $$ = 4 SYM is also discussed.