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1. Exact results in softly broken supersymmetric chiral gauge theories with flavor

   https://doi.org/10.1103/wvb3-gybj  

   Leedom, Jacob M; Murayama, Hitoshi; Singh, Gup; Suter, Bethany; Wong, Jason (July 2025, Physical Review D)

   We present exact results in softly broken supersymmetric $\mathrm{SU}\left(N_C\right)$chiral gauge theories with charged fermions in one antisymmetric, $N_F$fundamental, and $N_C+N_F-4$antifundamental representations. We achieve this by considering the supersymmetric version of these theories and utilizing anomaly mediated supersymmetry breaking at a scale $m\ll \mathrm{\Lambda }$to generate a vacuum. The connection to nonsupersymmetric theories is then conjectured in the limit $m\to \infty$. For odd $N_C$, we determine the massless fermions and unbroken global symmetries in the infrared. For even $N_C$, we find global symmetries are nonanomalous and no massless fermions. In all cases, the symmetry breaking patterns differ from what the tumbling hypothesis would suggest. 

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2. Discrete and higher-form symmetries in SCFTs from wrapped M5-branes

   https://doi.org/10.1007/JHEP03(2021)196  

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

   A bstract We analyze topological mass terms of BF type arising in supersymmetric M-theory compactifications to AdS 5 . These describe spontaneously broken higher-form gauge symmetries in the bulk. Different choices of boundary conditions for the BF terms yield dual field theories with distinct global discrete symmetries. We discuss in detail these symmetries and their ’t Hooft anomalies for 4d $$ \mathcal{N} $$ N = 1 SCFTs arising from M5-branes wrapped on a Riemann surface without punctures, including theories from M5-branes at a ℤ 2 orbifold singularity. The anomaly polynomial is computed via inflow and contains background fields for discrete global 0-, 1-, and 2-form symmetries and continuous 0-form symmetries, as well as axionic background fields. The latter are properly interpreted in the context of anomalies in the space of coupling constants. 

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3. Generalized symmetries of topological field theories

   https://doi.org/10.1007/JHEP03(2023)087  

   Gripaios, Ben; Randal-Williams, Oscar; Tooby-Smith, Joseph (March 2023, Journal of High Energy Physics)

   A bstract We study generalized symmetries in a simplified arena in which the usual quantum field theories of physics are replaced with topological field theories and the smooth structure with which the symmetry groups of physics are usually endowed is forgotten. Doing so allows many questions of physical interest to be answered using the tools of homotopy theory. We study both global and gauge symmetries, as well as ‘t Hooft anomalies, which we show fall into one of two classes. Our approach also allows some insight into earlier work on symmetries (generalized or not) of topological field theories. 

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4. Spontaneously broken subsystem symmetries

   https://doi.org/10.1007/JHEP03(2022)016  

   Distler, Jacques; Karch, Andreas; Raz, Amir (March 2022, Journal of High Energy Physics)

   A bstract We investigate the spontaneous breaking of subsystem symmetries directly in the context of continuum field theories by calculating the correlation function of charged operators. Our methods confirm the lack of spontaneous symmetry breaking in some of the existing continuum field theories with subsystem symmetries, as had previously been established based on a careful analysis of the spectrum. We present some novel continuum field theory constructions that do exhibit spontaneous symmetry breaking whenever allowed by general principles. These interesting patterns of symmetry breaking occur despite the fact that all the theories we study are non-interacting. 

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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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