Three-Pronged Strings and 1/4 BPS States in N=4 Super-Yang-Mills Theory

TL;DR

This work constructs explicit 1/4 BPS states in four-dimensional N=4 SYM with gauge group SU(3) by realizing them as three-pronged string junctions between D3-branes and matching their charges and masses to field-theoretic BPS formulas. Using the D3-brane picture, the authors relate W-bosons, monopoles, and dyons to (fundamental, D-, and (p,q)) strings, and show how three-pronged strings can connect three branes to realize non-parallel electric and magnetic charge vectors, yielding 1/4 BPS states. A central result is the derivation of curves of marginal stability in moduli space (C1–C3) where these 1/4 BPS states decay into two 1/2 BPS states, interpreted geometrically as prong degeneration and open-string dissociation on a D3-brane. The findings provide a concrete geometric realization of the 1/4 BPS spectrum, illuminate the stability structure under varying moduli, and suggest avenues for entropy counting and extensions to other duality frames and to N=2 theories.

Abstract

We provide an explicit construction of 1/4 BPS states in four-dimensional N=4 Super-Yang-Mills theory with a gauge group SU(3). These states correspond to three-pronged strings connecting three D3-branes. We also find curves of marginal stability in the moduli space of the theory, at which the above states can decay into two 1/2 BPS states.

Figures (5)

• Figure 1: D3-brane representation of $N=4$$SU(3)$ SYM.
• Figure 2: Three-pronged string, (a) in the general case, and (b) for $(1,0),(0,1)$ and $(1,1)$ prongs. The angle between the $(1,0)$ and $(0,1)$ prongs is $90^\circ$, and the angle $\theta$ is given by $\tan\theta = 1/g_s$.
• Figure 3: Three-pronged string ending on three D3-branes, which are transverse to the plane defined by the sting.
• Figure 4: A $((1,0),(0,1))$ three-pronged string ending on three D3-branes at $R_1^I,R_2^I$ and $0$. The angles of the triangle defined by these points are $\alpha,\beta$ and $\gamma$, respectively, and the lengths of the corresponding prongs are $A_1,A_2$ and $A_3$. The angle $\theta$ is given by $\tan\theta = 1/g_s$.
• Figure 5: Moving a D3-brane through the curve of marginal stability. In (a) $\gamma<90^\circ$, and the D3-branes can be connected by the $((1,0),(0,1))$ three-pronged string. In (b) $\gamma=90^\circ$, and the three-pronged string becomes degenerate with a $(1,0)$ string plus a $(0,1)$ string. In (c) $\gamma<90^\circ$, and only the two open string state exists.