Generalized Symmetries of Non-Supersymmetric Orbifolds

TL;DR

This work extends the study of generalized global symmetries to non-supersymmetric type II string backgrounds of the form $\mathbb{R}^{3,1}\times\mathbb{R}^6/\Gamma$, showing that quiver-based adjacencies for fermionic degrees of freedom encode the Dirac pairing that determines 1-form (and related) symmetries. By comparing a quiver analysis with boundary geometry data $H_*(S^5/\Gamma)$, it demonstrates exact matches in sequestered-tachyon regimes and tractable, time- or scale-dependent transitions when tachyons reach the boundary, including higher-group structures via non-split sequences. In IIA, tachyon condensation induces transitions in the spectrum, 1-form/2-form symmetries, and the SymTFT level, while in IIB with D3-branes one observes scale-dependent symmetry evolution and duality interfaces, captured by SymTree-like pictures. Across explicit $\mathbb{Z}_N$ orbifolds, the defect groups evolve from initial torsion $(\mathbb{Z}_N)^2$ to sectorized or supersymmetric endpoints, illustrating robust predictions for how tachyon dynamics reorganize topological data. Overall, the paper provides a robust, quiver- and geometry-driven framework for tracking generalized symmetries under tachyon-driven dynamics in non-supersymmetric holographic-like setups, with potential extensions to non-abelian orbifolds and uplift to M-theory.

Abstract

We determine generalized symmetries for 4D theories engineered via type II strings on non-supersymmetric orbifold backgrounds $\mathbb{R}^{3,1} \times \mathbb{R}^6 / Γ$. Probe branes detect generalized symmetries via the adjacency matrix for fermionic degrees of freedom in an associated quiver gauge theory. In situations where the tachyons are sequestered away from the boundary $S^5 / Γ$, this exactly matches the result extracted from singular homology. In situations with an unsequestered tachyon which stretches out to the boundary, the presence of tachyonic pulses partitions up the space into several distinct sectors, and the net contribution again matches with the answer expected via quiver methods. For IIA backgrounds, the presence of a localized closed string tachyon leads to transitions in the spectrum of states, generalized symmetries, higher-group symmetries, as well as the level matrix of the associated symmetry topological field theory (SymTFT). For IIB backgrounds with a stack of spacetime filling probe D3-branes, the onset of a radiatively generated potential leads to similar considerations involving scale dependent transitions in the symmetries of the theory, including structures such as duality defects / interfaces.

Figures (21)

• Figure 1: Depiction of monodromy for a pair of worldlines for particles $P_1$ and $P_2$.
• Figure 2: Depiction of the SymTFT layout for time $t$ smaller and larger than $t_{n}$. We approximate the configuration via a step function jump at $t_n$, at which time the Euclidean interface theory, $\mathcal{T}^E_{n,n+1}$, and the late time Lorentzian theory $\mathcal{T}^L_{i+1}$ branch off from the early time Lorentzian theory $\mathcal{T}^L_{n}$. $\mathcal{S}_{n}$ and $\mathcal{S}_{n+1}$ are the associated 5D SymTFTs.
• Figure 3: Left/Right: Fermionic/Bosonic quiver for ${\mathbb R}^6/{\mathbb Z}_5^{(1,1,1,-3)}$.
• Figure 4: Left/Right: Fermionic/Bosonic quiver for ${\mathbb R}^6/{\mathbb Z}_{17}^{(4,6,-7,-3)}$.
• Figure 5: Left: Quiver for ${\mathbb R}^6/{\mathbb Z}_{7}^{(-3,-1,0,4)}$. Right: Quiver for ${\mathbb R}^6/{\mathbb Z}_3^{(1,1,1,0)}$