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1. G2 holonomy, Taubes’ construction of Seiberg-Witten invariants and superconducting vortices

   https://doi.org/10.1007/JHEP04(2020)038  

   Cecotti, S; Gerig, C; Vafa, C. (January 2020, Journal of high energy physics)

   null (Ed.)

   Using a reformulation of topological N=2 QFT's in M-theory setup, where QFT is realized via M5 branes wrapping co-associative cycles in a G2 manifold constructed from the space of self-dual 2-forms over X4, we show that superconducting vortices are mapped to M2 branes stretched between M5 branes. This setup provides a physical explanation of Taubes' construction of the Seiberg-Witten invariants when X4 is symplectic and the superconducting vortices are realized as pseudo-holomorphic curves. This setup is general enough to realize topological QFT's arising from N=2 QFT's from all Gaiotto theories on arbitrary 4-manifolds. 

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2. M5-brane sources, holography, and Argyres-Douglas theories

   https://doi.org/10.1007/JHEP11(2021)140  

   Bah, Ibrahima; Bonetti, Federico; Minasian, Ruben; Nardoni, Emily (November 2021, Journal of High Energy Physics)

   A bstract We initiate a study of the holographic duals of a class of four-dimensional $$ \mathcal{N} $$ N = 2 superconformal field theories that are engineered by wrapping M5-branes on a sphere with an irregular puncture. These notably include the strongly-coupled field theories of Argyres-Douglas type. Our solutions are obtained in 7d gauged supergravity, where they take the form of a warped product of AdS 5 and a “half-spindle.” The irregular puncture is modeled by a localized M5-brane source in the internal space of the gravity duals. Our solutions feature a realization of supersymmetry that is distinct from the usual topological twist, as well as an interesting Stückelberg mechanism involving the gauge field associated to a generator of the isometry algebra of the internal space. We check the proposed duality by computing the holographic central charge, the flavor symmetry central charge, and the dimensions of various supersymmetric probe M2-branes, and matching these with the dual Argyres-Douglas field theories. Furthermore, we compute the large- N ’t Hooft anomalies of the field theories using anomaly inflow methods in M-theory, and find perfect agreement with the proposed duality. 

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3. Spin(7) orientifolds and 2d $$ \mathcal{N} $$ = (0, 1) triality

   https://doi.org/10.1007/JHEP01(2022)058  

   Franco, Sebastián; Mininno, Alessandro; Uranga, Ángel M.; Yu, Xingyang (January 2022, Journal of High Energy Physics)

   A bstract We present a new, geometric perspective on the recently proposed triality of 2d $$ \mathcal{N} $$ N = (0 , 1) gauge theories, based on its engineering in terms of D1-branes probing Spin(7) orientifolds. In this context, triality translates into the fact that multiple gauge theories correspond to the same underlying orientifold. We show how Spin(7) orientifolds based on a particular involution, which we call the universal involution, give rise to precisely the original version of $$ \mathcal{N} $$ N = (0 , 1) triality. Interestingly, our work also shows that the space of possibilities is significantly richer. Indeed, general Spin(7) orientifolds extend triality to theories that can be regarded as consisting of coupled $$ \mathcal{N} $$ N = (0 , 2) and (0 , 1) sectors. The geometric construction of 2d gauge theories in terms of D1-branes at singularities therefore leads to extensions of triality that interpolate between the pure $$ \mathcal{N} $$ N = (0 , 2) and (0 , 1) cases. 

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4. Generalized symmetries in 2D from string theory: SymTFTs, intrinsic relativeness, and anomalies of non-invertible symmetries

   https://doi.org/10.1007/JHEP11(2024)004  

   Franco, Sebastián; Yu, Xingyang (November 2024, Journal of High Energy Physics)

   Generalized global symmetries, in particular non-invertible and categorical symmetries, have become a focal point in the recent study of quantum field theory (QFT). In this paper, we investigate aspects of symmetry topological field theories (SymTFTs) and anomalies of non-invertible symmetries for 2D QFTs from a string theory perspective. Our primary focus is on an infinite class of 2D QFTs engineered on D1-branes probing toric Calabi-Yau 4-fold singularities. We derive 3D SymTFTs from the topological sector of IIB supergravity and discuss the resulting 2D QFTs, which can be intrinsically relative or absolute. For intrinsically relative QFTs, we propose a sufficient condition for them to exist. For absolute QFTs, we show that they exhibit non-invertible symmetries with an elegant brane origin. Furthermore, we find that these non-invertible symmetries can suffer from anomalies, which we discuss from a top-down perspective. Explicit examples are provided, including theories for including theories for Y(p,k)(ℙ2), Y(2,0)(ℙ1×ℙ1), and ℂ4/ℤ4 geometries. 

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5. Chern-Weil global symmetries and how quantum gravity avoids them

   https://doi.org/10.1007/JHEP11(2021)053  

   Heidenreich, Ben; McNamara, Jacob; Montero, Miguel; Reece, Matthew; Rudelius, Tom; Valenzuela, Irene (November 2021, Journal of High Energy Physics)

   A bstract We draw attention to a class of generalized global symmetries, which we call “Chern-Weil global symmetries,” that arise ubiquitously in gauge theories. The Noether currents of these Chern-Weil global symmetries are given by wedge products of gauge field strengths, such as F 2 ∧ H 3 and tr( $$ {F}_2^2 $$ F 2 2 ), and their conservation follows from Bianchi identities. As a result, they are not easy to break. However, it is widely believed that exact global symmetries are not allowed in a consistent theory of quantum gravity. As a result, any Chern-Weil global symmetry in a low-energy effective field theory must be either broken or gauged when the theory is coupled to gravity. In this paper, we explore the processes by which Chern-Weil symmetries may be broken or gauged in effective field theory and string theory. We will see that many familiar phenomena in string theory, such as axions, Chern-Simons terms, worldvolume degrees of freedom, and branes ending on or dissolving in other branes, can be interpreted as consequences of the absence of Chern-Weil symmetries in quantum gravity, suggesting that they might be general features of quantum gravity. We further discuss implications of breaking and gauging Chern-Weil symmetries for particle phenomenology and for boundary CFTs of AdS bulk theories. Chern-Weil global symmetries thus offer a unified framework for understanding many familiar aspects of quantum field theory and quantum gravity. 

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