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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

R7-branes are a class of recently discovered nonsupersymmetric 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 nonsupersymmetric branes which carry a conserved charge. Published by the American Physical Society 2024

The swampland cobordism conjecture successfully predicts the supersymmetric spectrum of 7-branes of IIB/F-theory. Including reflections on the F-theory torus, it also predicts the existence of new nonsupersymmetric objects, which we dub reflection 7-branes (R7-branes). We present evidence that these R7-branes only exist at strong coupling. R7-branes serve as end of the world branes for 9D theories obtained from type IIB asymmetric orbifold and Dabholkar-Park orientifold backgrounds, and an anomaly inflow analysis suggests the existence of a gapless Weyl fermion, which would have the quantum numbers of a goldstino. Using general arguments, we conclude that different kinds of branes are able to end on the R7, and accounting for their charge requires exotic localized degrees of freedom, for which the simplest possibility is a massless 3-form field on the R7-brane worldvolume. We also show how to generalize the standard F-theory formalism to account for reflections.

The project involved an integrated program of research which focused on the use of the extra-dimensional geometry of string theory as a tool in understanding a variety of phenomena in quantum field theory. This was used to construct and study new examples of quantum field theories with the eventual aim of also using these results to develop new particle physics and cosmology scenarios. The research involved the development of new methods for constructing such extra-dimensional geometries, and also the study of the resulting quantum field theories generated by this process.

The proposal details plans for an upcoming meeting as part of the annual Geometry and Strings conference series. This series was formerly known as the ``F-theory'' conference series and has since broadened to include more general approaches to high energy physics centered on geometry, quantum field theory and string theory. The University of Pennsylvania has agreed to host the 2023 installment of the conference, which will take place on the UPenn campus in March 2023. The main thrust of the activities will center on several interconnected areas within the subject, including: The Swampland Program in quantum gravity and its geometric manifestations. The Geometric Engineering Program in string theory and its application to numerous question in quantum field theory. The Generalized Symmetries Program in quantum field theory and string theory. The Machine Learning Program aimed at understanding the large number of vacua present in string theory. The conference will adhere to a code of conduct aimed at making the event accessible to all participants. Additionally, particular attention will be paid to having a balanced mix of junior, mid-level and senior speakers from diverse backgrounds.

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.

Type IIB supergravity enjoys a discrete non-Abelian duality group, which has potential quantum anomalies. In this paper we explicitly compute these, and present the bordism group that controls them, modulo some physically motivated assumptions. Quite surprisingly, we find that they do not vanish, which naively would signal an inconsistency of F-theory. Remarkably, a subtle modification of the standard 10d Chern-Simons term cancels these anomalies, a fact which relies on the specific field content of type IIB supergravity. We also discover other ways to cancel this anomaly, via a topological analog of the Green-Schwarz mechanism. These alternative type IIB theories have the same low energy supergravity limit as ordinary type IIB, but a different spectrum of extended objects. They could either be part of the Swampland, or connect to the standard theory via domain walls.

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.

Compactifications of the Chaudhuri-Hockney-Lykken (CHL) string to eight dimensions can be characterized by embeddings of root lattices into the rank 12 momentum lattice Λ_M, the so-called Mikhailov lattice. Based on these data, we devise a method to determine the global gauge group structure including all U(1) factors. The key observation is that, while the physical states correspond to vectors in the momentum lattice, the gauge group topology is encoded in its dual. Interpreting a nontrivial π₁(G) ≡ $$\mathscr{L}$$ for the non-Abelian gauge group G as having gauged a $$\mathscr{L}$$ 1-form symmetry, we also prove that all CHL gauge groups are free of a certain anomaly [1] that would obstruct this gauging. We verify this by explicitly computing $$\mathscr{L}$$ for all 8D CHL vacua with rank(G) = 10. Since our method applies also to T² compactifications of heterotic strings, we further establish a map that determines any CHL gauge group topology from that of a “parent” heterotic model.

We study the cobordism conjecture of McNamara and Vafa which asserts that the bordism group of quantum gravity is trivial. In the context of type IIB string theory compactified on a circle, this predicts the presence of D7-branes. On the other hand, the non-Abelian structure of the IIB duality group SL (2, Z) implies the existence of additional [p, q] 7-branes. We find that this additional information is instead captured by the space of closed paths on the moduli space of elliptic curves parameterizing distinct values of the type IIB axio-dilaton. This description allows to recover the full structure of non-Abelian braid statistics for 7-branes. Combining the cobordism conjecture with an earlier Swampland conjecture by Ooguri and Vafa, we argue that only certain congruence subgroups $$\Gamma\subset$$ SL(2, Z) specifying genus zero modular curves can appear in 8D F-theory vacua. This leads to a successful prediction for the allowed Mordell–Weil torsion groups for 8D F-theory vacua.