3-String Junction and BPS Saturated Solutions in SU(3) Supersymmetric Yang-Mills Theory

TL;DR

The paper constructs BPS saturated, regular configurations in ${\cal N}=4$ SU(3) SYM that carry non-parallel electric and magnetic charges, corresponding to 3-string junctions of IIB strings in the brane picture. By leveraging a spherically symmetric SU(3) monopole solution for $(A_i,Y)$ and solving $D_iD_iX=0$ under $D$-flatness, it yields a four-parameter family of solutions with magnetic charges $g_a=(-2,0,2)$ and explicit relations between charges and scalar profiles. Near the origin the three D3-branes meet, while at infinity the fields reproduce the expected three-pronged string configuration; an exact X-solution is obtained for a special choice of parameters, illustrating explicit brane bending and charge assignments. The work connects field-theoretic BPS states to string junctions, tests consistency with $SL(2,Z)$ duality, and points to extensions to general SU($N$) theories and deeper comparisons with the string picture.

Abstract

We construct BPS saturated regular configurations of N=4 SU(3) supersymmetric Yang-Mills theory carrying non-parallel electric and magnetic charges. These field theory BPS states correspond to the string theory BPS states of 3-string junctions connecting three different D3-branes by regarding the N=4 supersymmetric Yang-Mills theory as an effective field theory on parallel D3-branes.

Figures (3)

• Figure 1: "Tube-like" configuration of D3-brane surface representing a string.
• Figure 2: 3-string junction connecting three D3-branes.
• Figure 3: The D3-brane configurations (solid lines) and the three-pronged strings from the IIB picture (dashed lines).