Generalized Symmetries, Gravity, and the Swampland

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 compatability 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.Comment: 62 pages + appendices + ref

IIB Explored: Reflection 7-Branes

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 non-supersymmetric 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.Comment: 44 pages, 3 figure

Reflections on the Matter of 3d N=1\mathcal{N} = 1 Vacua and Local Spin(7)Spin(7) Compactifications

We use Higgs bundles to study the 3d $\mathcal{N} = 1$ vacua obtained from M-theory compactified on a local $Spin(7)$ space given as a four-manifold $M_4$ 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 non-perturbative 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 $\mathcal{N} = 1$ 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.Comment: 85 pages, 4 figure

The Branes Behind Generalized Symmetry Operators

The modern approach to $m$-form global symmetries in a $d$-dimensional quantum field theory (QFT) entails specifying dimension $d-m-1$ topological generalized symmetry operators which non-trivially link with $m$-dimensional defect operators. In QFTs engineered via string constructions on a non-compact geometry $X$, these defects descend from branes wrapped on non-compact cycles which extend from a localized source / singularity to the boundary $\partial X$. The generalized symmetry operators which link with these defects arise from magnetic dual branes wrapped on cycles in $\partial X$. This provides a systematic way to read off various properties of such topological operators, including their worldvolume topological field theories, and the resulting fusion rules. We illustrate these general features in the context of 6D superconformal field theories, where we use the F-theory realization of these theories to read off the worldvolume theory on the generalized symmetry operators. Defects of dimension 3 which are charged under a suitable 3-form symmetry detect a non-invertible fusion rule for these operators. We also sketch how similar considerations hold for related systems.Comment: v2: 21 pages + references, 1 figure; typos corrected, clarifications added, references adde

Top Down Approach to Topological Duality Defects

Topological duality defects arise as codimension one generalized symmetry operators in quantum field theories (QFTs) with a duality symmetry. Recent investigations have shown that in the case of 4D $\mathcal{N} = 4$ Super Yang-Mills (SYM) theory, an appropriate choice of (complexified) gauge coupling and global form of the gauge group can lead to a rather rich fusion algebra for the associated defects, leading to examples of non-invertible symmetries. In this work we present a top down construction of these duality defects which generalizes to QFTs with lower supersymmetry, where other 0-form symmetries are often present. We realize the QFTs of interest via D3-branes probing $X$ a Calabi-Yau threefold cone with an isolated singularity at the tip of the cone. The IIB duality group descends to dualities of the 4D worldvolume theory. Non-trivial codimension one topological interfaces arise from configurations of 7-branes "at infinity" which implement a suitable $SL(2, \mathbb{Z})$ transformation when they are crossed. Reduction on the boundary topology $\partial X$ results in a 5D symmetry TFT. Different realizations of duality defects, such as the gauging of 1-form symmetries with certain mixed anomalies and half-space gauging constructions, simply amount to distinct choices of where to place the branch cuts in the 5D bulk.Comment: Comments: 41+8 pages, 22 figure

Simultaneous Bilateral Patellar Tendon Rupture in a Young Adult Male: A Case Report and Review of the Literature.

A bilateral patellar tendon rupture is extremely rare and has only been documented in case reports. Although the etiology remains unknown, predisposing factors include steroid usage, systemic diseases, and tendinopathies. In the present case, a healthy 33-year-old male with a prior history of bilateral patellar tendonitis and a diagnosis of Osgood-Schlatter disease during adolescence experienced simultaneous bilateral patellar tendon rupture after playing volleyball. He underwent bilateral patellar repair without complications. In the absence of trauma, spontaneous bilateral patellar tendon ruptures are associated with several predisposing factors, including systemic diseases, prior corticosteroid or fluoroquinolone usage, and history of tendinopathy. Injuries can be classified based on the location of the rupture. Bilateral patellar tendon ruptures can be misdiagnosed due to the rarity of cases and the lack of a normal comparative knee. Radiographic techniques can aid in the diagnosis, leading to early surgical treatment and improved outcomes. Early diagnosis and prompt surgical repair contribute to good functional outcomes in this potentially debilitating injury pattern

T-Branes and G2G_2 Backgrounds

Compactification of M- / string theory on manifolds with $G_2$ structure yields a wide variety of 4D and 3D physical theories. We analyze the local geometry of such compactifications as captured by a gauge theory obtained from a three-manifold of ADE singularities. Generic gauge theory solutions include a non-trivial gauge field flux as well as normal deformations to the three-manifold captured by non-commuting matrix coordinates, a signal of T-brane phenomena. Solutions of the 3D gauge theory on a three-manifold are given by a deformation of the Hitchin system on a marked Riemann surface which is fibered over an interval. We present explicit examples of such backgrounds as well as the profile of the corresponding zero modes for localized chiral matter. We also provide a purely algebraic prescription for characterizing localized matter for such T-brane configurations. The geometric interpretation of this gauge theory description provides a generalization of twisted connected sums with codimension seven singularities at localized regions of the geometry. It also indicates that geometric codimension six singularities can sometimes support 4D chiral matter due to physical structure "hidden" in T-branes.Comment: v2: 47 pages, 3 figures, references and clarifications added, typos correcte

SymTrees and Multi-Sector QFTs

The global symmetries of a $D$-dimensional QFT can, in many cases, be captured in terms of a $(D+1)$-dimensional symmetry topological field theory (SymTFT). In this work we construct a $(D+1)$-dimensional theory which governs the symmetries of QFTs with multiple sectors which have connected correlators that admit a decoupling limit. The associated symmetry field theory decomposes into a SymTree, namely a treelike structure of SymTFTs fused along possibly non-topological junctions. In string-realized multi-sector QFTs, these junctions are smoothed out in the extra-dimensional geometry, as we demonstrate in examples. We further use this perspective to study the fate of higher-form symmetries in the context of holographic large $M$ averaging where the topological sectors of different large $M$ replicas become dressed by additional extended operators associated with the SymTree.Comment: 69 pages + appendices + ref

Geometric Unification of Higgs Bundle Vacua

Higgs bundles are a central tool used to study a range of intersecting brane systems in string compactifications. Solutions to the internal gauge theory equations of motion for the corresponding worldvolume theories of branes give rise to different low energy effective field theories. This has been heavily used in the study of M-theory on local $G_2$ spaces and F-theory on local elliptically fibered Calabi-Yau fourfolds. In this paper we show that the 3D $\mathcal{N} = 1$ effective field theory defined by M-theory on a local $Spin(7)$ space unifies the Higgs bundle data associated with 4D $\mathcal{N} = 1$ M- and F-theory vacua. This 3D system appears as an interface with finite thickness between different 4D vacua. We develop the general formalism of M-theory on such local $Spin(7)$ spaces, and build explicit interpolating solutions. This provides a complementary local gauge theory analysis of a recently proposed approach to constructing $Spin(7)$ spaces from generalized connected sums.Comment: v2: 65 pages, 5 figures, typos corrected, reference and clarifications adde