Baryons and String Creation from the Fivebrane Worldvolume Action

TL;DR

This work presents BPS-solutions of the D5-brane worldvolume action in backgroundsCreated by stacks of D3-branes, describing how dragging a D5-brane through the D3 stack creates a bundle of N fundamental strings (the Hanany–Witten effect) and realizing baryon-like configurations in AdS/CFT. Using Born–Infeld plus WZW terms, the authors derive a tractable first-order BPS condition in AdS_5×S^5 and a generalized condition in the full D3 background, yielding two-parameter families of embeddings that manifest as strings attached to a wrapped fivebrane. In AdS, the solutions include a baryon vertex (ν=0) and threshold bound states (ν=n/N) with tubes whose tension matches the corresponding number of strings, while in the D3 background they illustrate string creation across the brane stack and analyze flux balance, forces, and potential non-Abelian extensions. The results provide a concrete, string-theoretic realization of baryons and multi-quark states in holographic gauge theories and suggest avenues for exploring non-BPS and multi-center generalizations.

Abstract

We construct BPS-exact solutions of the worldvolume Born-Infeld plus WZW action of a D5-brane in the background of N D3-branes. The non-trivial background metric and RR five-form field strength play a crucial role in the solution. When a D5-brane is dragged across a stack of N D3-branes a bundle of N fundamental strings joining the two types of branes is created, as in the Hanany-Witten effect. Our solutions give a detailed description of this bundle in terms of a D5-brane wrapped on a sphere. We discuss extensions of these solutions which have an interpretation in terms of gauge theory multi-quark states via the AdS/CFT correspondence.

Figures (5)

• Figure 1: Polar plots of $r(\theta)$ for $AdS$ 'tube' solutions corresponding to $(1-\nu)N$ strings (with $\theta=\pi$ at the top of the plots). A cross-section of each 'tube' is an ${\rm \bf S}^{4}$.
• Figure 2: Upper/upper and upper/lower tube combinations. These configurations have vanishing charge at the origin (see text).
• Figure 3: Solutions describing the creation of $N$ fundamental strings as a D5-brane is dragged upward, across a stack of D3-branes. The number of strings connecting the two types of branes changes from 0 to $N$.
• Figure 4: Solutions describing the creation of $N$ fundamental strings as a D5-brane is dragged across a stack of D3-branes. The number of strings connecting the two types of branes changes from $-N/2$ to $+N/2$ (the signs indicate whether the strings originate or terminate on the fivebrane).
• Figure 5: Solution describing a system of two parallel D5-branes connected by $(1-\nu)N$ fundamental strings which run through the D3-branes at $r=0$. A 'point W-boson charge' lies at the origin.