$κ$-symmetric M5 brane web for defects in $AdS_7 / CFT_6$ holography

TL;DR

This work analyzes κ-symmetric M5-brane probes in $AdS_7\times S^4$ to model codimension-2 defects in the 6d $\mathcal{N}=(2,0)$ theory via AdS$_7$/CFT$_6$. By turning on a self-dual 3-form flux $h$ on the M5 worldvolume, embedding conditions are deformed, yielding a general class of deformed solutions governed by two holomorphic constraints $F^{(I)}(\Phi_0,\Phi_1,\Phi_2,\Phi_3,Z_1,Z_2)=0$ with scaling relations, and with $h$ proportional to a coordinate-dependent factor ${\mathcal F}(X^m)=\frac{\cos(\theta/2)-\sin(\theta/2)}{\cos(\theta/2)+\sin(\theta/2)}$. The analysis shows ${\mathcal F}$ fixes $h$ so that $h$ vanishes at $\theta=\frac{\pi}{2}$, implying a brane repositioning away from that locus, and recovers higher-supersymmetry cases in which simple embeddings like $AdS_5\times S^1$ emerge when $h=0$. Turning on flux components then reduces preserved supersymmetry to fractions such as 1/8, 1/16, or 1/32, producing ridge-like spike deformations and complex M5-brane webs that holographically encode defect data in the boundary theory. The results illuminate how defect couplings and the endstrings sourcing the flux may be read from the worldvolume geometry, and they connect to rigid vs non-rigid defect pictures in related AdS/CFT defect studies.

Abstract

In this work, we will continue our analysis of some general probe M5 brane solutions from our previous work in $AdS_7 \times S^4$ spacetime (appeared in arxiv:2109.08551). These are codimension-2 in $AdS_7$ and preserve at least 2 supercharges when the worldvolume 3-form flux field strength is zero. We will turn on the field strength and find that the embedding conditions are modified, excluding certain branes contained in the previous result. The new main result here is very general, so we pick simpler embedding conditions that describe highly symmetric examples that preserve half of the supersymmetry of the 11 dimensions. When the flux field is zero, worldvolumes have $AdS_5 \times S^1$ topology. We turn the flux field value non-zero in these examples and analyze how the shape of the worldvolume deforms as supersymmetry is broken by some additional fractions.

Figures (2)

• Figure 1: This figure depicts the probe M5 brane dual to a codimension-2 defect in the background spacetime geometry of $AdS_7 \times S^4$ that ends on the defect in the AdS boundary. The inset in this figure describes the dual defect in the gauge theory. The brane world volume carries no 3-form flux field.
• Figure 2: In this second figure, we have introduced deformations by allowing the field $h$ to take non-zero values and in our calculation, we find that embedding conditions get affected allowing for deformations under BPS constraints.