Non-Planar String Networks on Tori

TLDR: In this paper, a string-network representation of 1/8 supersymmetric BPS states is given by considering (periodic) non-planar (p, q, r)-string networks of eight dimensional type II string theory on T3.

Abstract: Type-II strings in D = 5 contain particle-like 1/8 supersymmetric BPS states. In this note we give a string-network representation of such states by considering (periodic) non-planar (p,q,r)-string networks of eight dimensional type II string theory on T3. We obtain the BPS mass formula of such states, in terms of charges and generating-vectors of the torus, and show its invariance under an SL(3,) ? SL(3,) group of transformations. Results are then generalized to string-networks associated with the SL(5,) U-duality in seven dimensions. We also discuss reinterpretation of the above (D = 5) mass formula in terms of BPS states in world-volume theories of U2-branes in D = 8.