String Junction Transitions in the Moduli Space of N=2 SYM

TL;DR

The work analyzes how BPS states in the moduli space of $N=2$ $SU(2)$ SYM, realized via a D3-brane in a 7-brane background, can transition between a single open string and a string web due to string creation. It develops a geometric framework based on $(p,q)$-geodesics and constant-phase curves of Seiberg-Witten data $(a(z), a_D(z))$ to classify BPS configurations and track transitions across moduli space. A four-region phase diagram is derived, with explicit two-step transitions for dyons like $(4,1)$, illustrating string creation and the generalized s-rule in multi-string contexts. These results unify the string-creation mechanism with BPS stability across moduli space, offering a coherent picture of how the BPS spectrum reconfigures in $ olinebreak[N=2]$ theories and informing nonperturbative dynamics in string-theory realizations of gauge theories.

Abstract

The string theory description of BPS states in D-brane world-volume field theories may undergo transitions from open strings to string webs, as well as between different string webs, as one moves in the field theory moduli space. These transitions are driven by the string creation phenomenon. We demonstrate such transitions in the D3-brane realization of N=2 SU(2) Super-Yang-Mills theory.

Figures (6)

• Figure 1: Multiple string creation in $(p,q)$ 7-brane -- $(r,s)$ string background.
• Figure 2: The configuration in (a) appears to be supersymmetric, but is not if $n>|ps-qr|$, as can be seen from the configuration in (b), which is obtained by crossing the branes.
• Figure 3: The supersymmetric ground state is removed from the spectrum by the orientifold projection in the classical picture (a), and by the s-rule in the quantum picture (b).
• Figure 4: Phase diagram for $(2n,1)$ dyons with $n\geq2$.
• Figure 5: String $\rightarrow$ Web and Web $\rightarrow$ Web transitions for the $(4,1)$ dyon.