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M-theory frozen singularities are (locally) $D$ - or $E$ -type orbifold singularities with a background fractional $C_3$ -monodromy surrounding them. In this paper, we revisit such backgrounds and address several puzzling features of their physics. We first give a top-down derivation of how the $D$ - or $E$ -type 7D $\mathcal{N}=1$ gauge theory directly “freezes” to a lower-rank gauge theory due to the $C_3$ background. This relies on a Hanany-Witten effect of fractional M5 branes and the presence of a gauge anomaly of fractional $\mathrm{D}p$ probes in the circle reduction. Additionally, we compute defect groups and 8D symmetry topological field theories of the 7D frozen theories in several duality frames. We apply our results to understanding the evenness condition of strings ending on $\mathrm{O}{7}^{+}$ planes, and calculating the global forms of supergravity gauge groups of M-theory compactified on $T^4/\mathrm{\Gamma }$ with frozen singularities. We also revisit IIA $ADE$ singularities with a $C_1$ -monodromy along a 1-cycle in the boundary lens space and show that this freezes the gauge degrees of freedom via confinement. Published by the American Physical Society 2025

Abstract Much of the analysis of F-theory-based Standard Models boils down to computing cohomologies of line bundles on matter curves. By varying parameters one can degenerate such matter curves to singular ones, typically with many nodes, where the computation is combinatorial and straightforward. The question remains to relate the (a priori possibly smaller) value on the original curve to the singular one. In this work, we introduce some elementary techniques (pruning trees and removing interior edges) for simplifying the resulting nodal curves to a small collection of terminal ones that can be handled directly. When applied to the QSMs, these techniques yield optimal results in the sense that obtaining more precise answers would require currently unavailable information about the QSM geometries. This provides us with an opportunity to enhance the statistical bounds established in earlier research regarding the absence of vector-like exotics on the quark-doublet curve.

The stringy realization of generalized symmetry operators involves wrapping “branes at infinity”. We argue that in the case of continuous (as opposed to discrete) symmetries, the appropriate objects are fluxbranes. We use this perspective to revisit the phase structure of Verlinde’s monopole, a proposed particle satisfies the Bogomol’nyi-Prasad-Sommerfield (BPS) condition when gravity is decoupled, but is non-BPS and metastable when gravity is switched on. Geometrically, this monopole is obtained from branes wrapped on locally stable but globally trivial cycles of a compactification geometry. The fluxbrane picture allows us to characterize electric (respectively magnetic) confinement (respectively screening) in the 4D theory as a result of monopole decay. In the presence of the fluxbrane, this decay also creates lower-dimensional fluxbranes, which in the field theory is interpreted as the creation of an additional topological field theory sector. Published by the American Physical Society 2024

Generalized global symmetries are a common feature of many quantum field theories decoupled from gravity. By contrast, in quantum gravity/the Swampland program, it is widely expected that all global symmetries are either gauged or broken, and this breaking is in turn related to the expected completeness of the spectrum of charged states in quantum gravity. We investigate the fate of such symmetries in the context of 7D and 5D vacua realized by compact Calabi-Yau spaces with localized singularities in M theory. We explicitly show how gravitational backgrounds support additional dynamical degrees of freedom which trivialize (i.e., “break”) the higher symmetries of the local geometric models. Local compatibility conditions across these different sectors lead to gluing conditions for gauging higher-form and (in the 5D case) higher-group symmetries. This also leads to a preferred global structure of the gauge group and higher-form gauge symmetries. In cases based on a genus-one fibered Calabi-Yau space, we also get an F-theory model in one higher dimension with corresponding constraints on the global form of the gauge group. Published by the American Physical Society 2024

Root bundles appear prominently in studies of vector-like spectra of 4d F-theory compactifications. Of particular importance to phenomenology are the Quadrillion F-theory Standard Models (F-theory QSMs). In this work, we analyze a superset of the physical root bundles whose cohomologies encode the vector-like spectra for the matter representations ($$3$$, $$2$$)_1/6, ($$\overline{3}$$, $$1$$)_-2/3 and ($$1$$, $$1$$)₁. For the family B₃(Δ$$^{°}_{4}$$) consisting of $$\mathcal{O}$$(10¹¹) F-theory QSM geometries, we argue that more than 99.995% of the roots in this superset have no vector-like exotics. This indicates that absence of vector-like exotics in those representations is a very likely scenario in the O(10¹¹) QSM geometries B₃(Δ$$^{°}_{4}$$). The QSM geometries come in families of toric 3-folds B₃(Δ°) obtained from triangulations of certain 3-dimensional polytopes Δ°. The matter curves in X_Σ $$\large{ϵ}$$ B₃(Δ°) can be deformed to nodal curves which are the same for all spaces in B₃(Δ°). Therefore, one can probe the vector-like spectra on the entire family B₃(Δ°) from studies of a few nodal curves. We compute the cohomologies of all limit roots on these nodal curves. In our applications, for the majority of limit roots the cohomologies are determined by line bundle cohomology on rational tree-like curves. For this, we present a computer algorithm. The remaining limit roots, corresponding to circuit-like graphs, are handled by hand. The cohomologies are independent of the relative position of the nodes, except for a few circuits. On these jumping circuits, line bundle cohomologies can jump if nodes are specially aligned. This mirrors classical Brill-Noether jumps. B₃(Δ°) admits a jumping circuit, but the root bundle constraints pick the canonical bundle and no jump happens.

Orbifold singularities of M-theory constitute the building blocks of a broad class of supersymmetric quantum field theories (SQFTs). In this paper we show how the local data of these geometries determine global data on the resulting higher symmetries of these systems. In particular, via a process of cutting and gluing, we show how local orbifold singularities encode the 0-form, 1-form, and 2-group symmetries of the resulting SQFTs. Geometrically, this is obtained from the possible singularities that extend to the boundary of the noncompact geometry. The resulting category of boundary conditions then captures these symmetries and is equivalently specified by the orbifold homology of the boundary geometry. We illustrate these general points in the context of a number of examples, including five-dimensional (5D) superconformal field theories engineered via orbifold singularities, 5D gauge theories engineered via singular elliptically fibered Calabi-Yau threefolds, as well as four-dimensional supersymmetric quantum chromodynamics-like theories engineered via M-theory on noncompact G₂ spaces.

String and 5-brane junctions are shown to succinctly classify all known 8D $$\mathscr{N}$$ = 1 string vacua. This requires an extension of the description for ordinary [p,q] -7-branes to consistently include O7⁺ planes, which then naturally encodes the dynamics of sp_n gauge algebras, including their p-form center symmetries. Central to this analysis are loop junctions, i.e., strings/5-branes which encircle stacks of 7-branes and O7⁺s . Loop junctions further signal the appearance of affine symmetries of emergent 9D descriptions at the 8D moduli space’s boundaries. Such limits reproduce all 9D string vacua, including the two disconnected rank (1,1) moduli components.

We argue for the quantum-gravitational inconsistency of certain 6D $$\mathscr{N}$$ = (1,0) supergravity theories, whose anomaly-free gauge algebra g and hypermultiplet spectrum M were observed by Raghuram et al.to be realizable only as part of a larger gauge sector (g' ⊃ g, M' ⊃ M) in F-theory. To detach any reference to a string theoretic method of construction, we utilize flavor symmetries to provide compelling reasons why the vast majority of such (g, M) theories are not compatible with quantum gravity constraints, and how the “automatic enhancement” to (g',M') remedies this. In the first class of models, with g' = g ⊕ h, we show that there exists an unbroken flavor symmetry h acting on the matter M, which, if ungauged, would violate the no-global-symmetries hypothesis. This argument also applies to 1-form center symmetries, which govern the gauge group topology and massive states in representations different from those of massless states. In a second class, we find that g is incompatible with the flavor symmetry of certain supersymmetric strings that must exist by the completeness hypothesis.

We use Higgs bundles to study the 3D $$\mathscr{N}$$ = 1 vacua obtained from M-theory compactified on a local Spin(7) space given as a four-manifold M₄ of ADE singularities with further generic enhancements in the singularity type along one-dimensional subspaces. There can be strong quantum corrections to the massless degrees of freedom in the low energy effective field theory, but topologically robust quantities such as “parity” anomalies are still calculable. We show how geometric reflections of the compactification space descend to 3D reflections and discrete symmetries. The parity anomalies of the effective field theory descend from topological data of the compactification. The geometric perspective also allows us to track various perturbative and nonperturbative corrections to the 3D effective field theory. We also provide some explicit constructions of well-known 3D theories, including those which arise as edge modes of 4D topological insulators, and 3D $$\mathscr{N}$$ = 1 analogs of grand unified theories. An additional result of our analysis is that we are able to track the spectrum of extended objects and their transformations under higher-form symmetries.

We explore higher-form symmetries of M- and F-theory compactified on elliptic fibrations, determined by the topology of their asymptotic boundaries. The underlying geometric structures are shown to be equivalent to known characterizations of the gauge group topology in F-theory via Mordell-Weil torsion and string junctions. We further study dimensional reductions of the 11d Chern-Simons term in the presence of torsional boundary G₄-fluxes, which encode background gauge fields of center one-form symmetries in the lower-dimensional effective gauge theory. We find contributions that can be interpreted as ’t Hooft anomalies involving the one-form symmetry which originate from a fractionalization of the instanton number of non-Abelian gauge theories in F-/M-theory compactifications to 8d/7d and 6d/5d.