From surface operators to non-Abelian volume operators in puff field theory

Puff field theory (PFT) is a low energy decoupling regime of string theory that still retains the nonlocal attributes of the parent theory—while preserving isotropy for its nonlocal degrees of freedom. It realizes an extended holographic dictionary at strong coupling and dynamical nonlocal states akin to defects or the surface operators of local gauge theories. In this work, we probe the nonlocal features of PFT using D3 branes. We find supersymmetric configurations that end on defects endowed with non-Abelian degrees of freedom. These are $2+1$ dimensional defects in the $3+1$ dimensional PFT that may be viewed as volume operators. We determine their $R$ charge, vacuum expectation value, energy, and gauge group structure.

Figure 1

A cartoon of how a correlator of two nonlocal operator insertions in the PFT would look in the holographic dual picture.

Figure 2

(a) The clover defect of Sec. 4c1. The defect is a spatially two-dimensional planar configuration on the worldvolume of the source branes. The angular direction shown represents the Melvin twist angle $\varphi$. (b) A depiction of the figure eight defect of Sec. 4c2. In this case, we have half as many branches of the probe brane landing on the defect. There are two possible configurations shown separately with solid and dashed lines differing also in coordinate embeddings not shown. Each breaks a different set of supersymmetries, shown in the third and fourth row of the table in the text. Each of (a) and (b) has four parameters, two of which are most apparent in this figure: (1) a shift in $\varphi$, and (2) the maximum distance in the bulk away from the defect the probes extend.

Figure 3

(a) A profile of the D3 probe in the $T$ vs $w$ plane; the shaded area is the worldvolume of the D3 branes. (b) The probe as seen from the $\cos \theta$ versus $w$ plane for $C_3=1/2$ and various time snapshots $T=0,1,2,3$.

Figure 4

The branches of $\cos \varphi$ versus $w$ for the clover defect of scenario IIa. There are two separate configurations depicted as solid and dashed lines. They are related by a rotation by $\pi /4$ in $\varphi$.

Figure 5

The probe D3 brane in the $w$ versus $\varphi$ plane with $C_2=1$, $C_3=0$, and $C_4=1$, and for time snapshots of $T=-4,0,4$ from light gray to black.

Figure 6

The probe D3 brane in the (a) $\cos \theta$ and (b) $\cos \phi$ versus $\varphi$ plane; we set $C_2=1$, $C_3=0$, and $C_4=1$, and consider time snapshots $T=1,3,5$ from light gray to black. The vertical bars correspond to the location of the defect in the UV.