R7-Branes as Charge Conjugation Operators

TL;DR

R7-branes are proposed as a new class of non-supersymmetric cobordism defects that realize a zero-form charge-conjugation symmetry in certain 6D SCFTs, notably the $\mathcal{N}=(2,0)$ theories, with their action extending to lower-dimensional compactifications. The authors derive explicit fusion rules for the associated topological operators using differential cohomology and reveal a non-invertible structure arising from projection operators, supported by holographic evidence from AdS/CFT. They further analyze how these charge-conjugation operators behave under compactification, orientation-reversal, and in other brane systems, showing that similar symmetry operators can be engineered from non-supersymmetric branes in heterotic and Type I string theory. The work connects high-dimensional string constructions to lower-dimensional QFT symmetries, highlighting a pathway to realize and test cobordism-defect-induced symmetries via holography and brane engineering, with potential extensions to little string theories and beyond.

Abstract

R7-branes are a class of recently discovered non-supersymmetric real codimension-two duality defects in type IIB string theory predicted by the Swampland Cobordism Conjecture. For type IIB realizations of 6D SCFTs with $\mathcal{N} = (2,0)$ supersymmetry, wrapping an R7-brane "at infinity" leads to a topological operator associated with a zero-form charge conjugation symmetry that squares to the identity. Similar considerations hold for those theories obtained from further toroidal compactification, but this can be obstructed by bundle curvature effects. Using some minimal data on the topological sector of the R7-branes, we extract the associated fusion rules for these charge conjugation operators. More broadly, we sketch a top down realization of various topological operators / interfaces associated with $\mathsf{C}$, $\mathsf{R}$, and $\mathsf{T}$ transformations. We also use holography to provide strong evidence for the existence of the R7-brane which is complementary to the Cobordism Conjecture. Similar considerations apply to other string-realized QFTs with symmetry operators constructed via non-supersymmetric branes which carry a conserved charge.

Figures (3)

• Figure 1: Here we illustrate the effect of dragging a D3-brane (oriented black line) through an R7-brane (red star) whose cut associated to the monodromy action $C_4\rightarrow -C_4$ is denoted by the dashed red line. We also denote the submanifolds of $\mathbb{C}^2/\Gamma$ wrapped by these branes, here $\gamma \in H_1(S^3/\Gamma)$ is the torsion 1-cycle, relevant to constructing the 0-form charge conjugation operator for 6D SCFTs.
• Figure 2: Spacetime view of the Hanany-Witten process illustrated in Figure \ref{['fig:hweffect']} where we now indicate the spacetime submanifolds where these operators are supported. As the charged string defect operator $W_\gamma(M_2)$ passes through the charge conjugation operator $\mathcal{U}_{\Omega}(M_5)$, the 2-form symmetry operator $\mathcal{U}^{(2)}_{2\gamma}$ is created and stretches between $W_{-\gamma}(M_2)$ and $\mathcal{U}_{\Omega}(M_5)$.
• Figure 3: Depiction of $N$ D3-branes (at $r=0$) in the presence of an R7-brane (at $r=\infty$). Because the R7-brane sends D3-branes to anti-D3-branes, there is a large jump in the flux and a number of D3-branes extend out from the D3 to the R7-brane at infinity. The jump in the flux emanates from the branch cut (dashed red). In this case the R7-brane does not produce a topological operator due to the significant change to the QFT sector. Rather, it becomes a non-supersymmetric interface between $\mathcal{N}=4$ SYM to itself.