Zp charged branes in flux compactifications

TL;DR

The paper identifies a broad class of ${\bf Z}_p$-valued charges for particles, strings, and domain walls in flux compactifications, arising from flux-catalyzed decays governed by Freed-Witten anomalies and Chern-Simons couplings. It develops a coherent BF-coupling framework to realize discrete ${\bf Z}_p$ (and even non-Abelian) gauges in type II and F-theory setups, including massive IIA, NSNS/RR fluxes, and G4-flux in F-theory, with explicit brane realizations and decay/junction mechanisms. The authors extend the analysis to domain walls, axion stabilization, and dualities, showing that unstable domain walls encode duality transformations and that fluxes can identify distinct vacua modulo axion shifts. They connect flux-catalyzed discretes to torsion (co)homology and M-/F-theory uplifts, suggesting that the proper mathematical framework generalizes K-theory in the presence of fluxes, strings, and NS5branes. Overall, the work provides a physical classification of discrete brane charges and highlights rich structures (non-Abelian groups, domain walls, axion dynamics) arising from fluxes in string compactifications, with potential implications for axion physics and string phenomenology.

Abstract

We consider 4d string compactifications in the presence of fluxes, and classify particles, strings and domain walls arising from wrapped branes which have charges conserved modulo an integer p, and whose annihilation is catalized by fluxes, through the Freed-Witten anomaly or its dual versions. The Z_p-valued strings and particles are associated to Z_p discrete gauge symmetries, which we show are realized as discrete subgroups of 4d U(1) symmetries broken by their Chern-Simons couplings to the background fluxes. We also describe examples where the discrete gauge symmetry group is actually non-Abelian. The Z_p-valued domain walls separate vacua which have different flux quanta, yet are actually equivalent by an integer shift of axion fields (or further string duality symmetries). We argue that certain examples are related by T-duality to the realization of discrete gauge symmetries and Z_p charges from torsion (co)homology. At a formal level, the groups classifying these discrete charges should correspond to a generalization of K-theory in the presence of general fluxes (and including fundamental strings and NS5-branes).

Figures (5)

• Figure 1: a) A 4d domain wall obtained by $p$ D6-branes wrapped on a 4-cycle in a CY compactification of massive IIA theory. It separates two regions of 4d spacetime which differ by $p$ units of RR $F_2$ flux on the dual 2-cycle. b) The domain wall is unstable by nucleation of holes bounded by strings, realized as one NS5-brane wrapped on the 4-cycle. The two vacua with differing flux must therefore be equivalent.
• Figure 2: Collision of holes in unstable D2-brane domain walls in 4d compactifications with ${\overline F}_4$ and ${\overline H}_3$ fluxes.
• Figure 3: In compactifications with ${\overline H}_3$ fluxes, crossing of 4d strings (wrapped D4-branes) with attached domain walls (D2-branes) produces 4d strings with no domain wall (F1s).
• Figure 4: Brane creation effect by crossing D8-branes and NS5-branes. Regarding the D8-brane as a source of ${\overline F}_0$ flux, it also shows that in the presence of a type IIA mass parameter ${\overline F}_0=p$, an NS5-brane can exist only with $p$ D6-branes ending on it.
• Figure 5: Brane creation effect by crossing D8- and D0-branes. Regarding the D8-brane as a source of ${\overline F}_0$ flux, it also shows that in the presence of a type IIA mass parameter $p$, a D0-brane can exist only with $p$ fundamental strings ending on it.