Strings from domain walls in supersymmetric Yang-Mills theory and adjoint QCD

Abstract

We study strings between static quarks in QCD with $n_f$ adjoint fermions, including $N=1$ Super Yang-Mills (SYM), in the calculable regime on $\mathbb R^3\times \mathbb S^1$. We find that they have many qualitatively new features not previously known. The difference from other realizations of abelian confinement is due to the composite nature of magnetic bions, whose Dirac quantum with fundamental quarks is two, and to the unbroken part of the Weyl group. In particular we show that strings are composed of two domain walls, that quarks are not confined on domain walls, that strings can end on domain walls, and that "Y" or "$Δ$" baryons can form. We briefly discuss their lightest modes and decompactification limit.

Figures (4)

• Figure 1: Left: the Wilson loop and the monodromy of $\sigma$. Right: Sketch of the confining string configuration $\bar{\sigma}$ with the correct monodromy, composed of two domain walls. The dot and cross represent probe quarks a distance $R$ apart. The maximum distance between the walls, of thickness $1/m$, is $d$.
• Figure 2: The action density of the confining string $\bar{\sigma}$ obtained by numerically minimizing, via Gauss-Seidel relaxation, the action (\ref{['su2string1']}) with the correct monodromies. The lattice has spacing $1/M$, size $100 \times 100$, and $M/m=20$. The classical $\log R$ growth of the transverse separation from the model of Fig. \ref{['fig:111']} is also seen to hold upon studying different size strings.
• Figure 3: A sketch of how a $q\bar{q}$ pair can fuse into the DW (from left to right). The shaded and white regions represent distinct vacua of the theory. The solid black line represents the BPS$_1$ DW, while the dashed line represents the anti-BPS$_2$ DW, while the arrows represent their electric fluxes. The black dots are the quark and the anti-quark. The inlay in the upper left corner shows a fundamental string ending on a DW.
• Figure 4: A sketch of the abelian string spectrum, corresponding to the tower of $W\overline W$-bosons pairs attached to the double string, and the breather mode excitations $m_{br}$.