String junction and 1/4 BPS state in N=4 SYM theory

This is a short summary of our results so far on 1/4 BPS states in N = 4 SYM theory, the string counterparts of which are multi-pronged strings ending on D3-branes. We show the constructions of their classical configurations in N = 4 SYM theory, and identify the bosonic and fermionic zero modes. The number of the fermionic zero modes is shown to agree with the result in type IIB string theory, while that of the bosonic zero modes differs from it. A possibility is that the discrepancy disappears when these states are treated quantum-theoretically. We comment briefly on their quantization in moduli-space approximation.