Non-invertible global symmetries and completeness of the spectrum

We test the refined distance conjecture in the vector multiplet moduli space of 4D $$ \mathcal{N} $$ N = 2 compactifications of the type IIA string that admit a dual heterotic description. In the weakly coupled regime of the heterotic string, the moduli space geometry is governed by the perturbative heterotic dualities, which allows for exact computations. This is reflected in the type IIA frame through the existence of a K3 fibration. We identify the degree d = 2N of the K3 fiber as a parameter that could potentially lead to large distances, which is substantiated by studying several explicit models. The moduli space geometry degenerates into the modular curve for the congruence subgroup Γ0(N)+. In order to probe the large N regime, we initiate the study of Calabi-Yau threefolds fibered by general degree d > 8 K3 surfaces by suggesting a construction as complete intersections in Grassmann bundles.

Section: Introductionmentioning

confidence: 99%

Modular curves and the refined distance conjecture

Klaewer

2021

“…As an example, in a U(1) gauge theory the existence of magnetic monopoles breaks the (d − 3)-form Chern-Weil symmetry generated by the current F (this simplest example of a Chern-Weil global symmetry is the familiar magnetic 1-form global symmetry in 4d Maxwell theory [3]). More generally, an incomplete JHEP11(2021)053 spectrum in a gauge theory implies the existence of certain topological operators, which generalize global symmetries [29,30]. In string theory, however, enumerating the set of charged objects (such as fundamental strings, D-branes, and NS5-branes) only tells a small fraction of the story.…”

Section: Jhep11(2021)053mentioning

confidence: 99%

“…We will discuss the proper definition of the Completeness Hypothesis, as well at its relationship to the absence of global symmetries in quantum gravity, in [30].…”

Section: Completeness Hypothesis and Abelian Higgs Modelmentioning

confidence: 99%

“…In this section, we consider a striking exception to this pattern, with no dynamical axion among the light fields of the theory. This is the case of Type IIB string theory compactified on a rigid Calabi-Yau three-fold, 30 as considered in [107] . Such a model describes a theory of N = 2 supergravity in d = 4 with only one U(1) gauge field (the graviphoton) and no vector multiplets.…”

Section: Rigid Calabi-yau Three-foldsmentioning

confidence: 99%

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Chern-Weil global symmetries and how quantum gravity avoids them

Heidenreich

McNamara

Montero

et al. 2021

Self Cite

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 F2 ∧ H3 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.

“…However, it would be very interesting to analyze those 2-form symmetries in 6D and 5D from the field theory perspective as e.g. done in [98,99].…”

Section: Jhep12(2021)132mentioning

confidence: 99%

Gauged 2-form symmetries in 6D SCFTs coupled to gravity

Braun

Larfors

Oehlmann

2021

We study six dimensional supergravity theories with superconformal sectors (SCFTs). Instances of such theories can be engineered using type IIB strings, or more generally F-Theory, which translates field theoretic constraints to geometry. Specifically, we study the fate of the discrete 2-form global symmetries of the SCFT sectors. For both (2, 0) and (1, 0) theories we show that whenever the charge lattice of the SCFT sectors is non-primitively embedded into the charge lattice of the supergravity theory, there is a subgroup of these 2-form symmetries that remains unbroken by BPS strings. By the absence of global symmetries in quantum gravity, this subgroup much be gauged. Using the embedding of the charge lattices also allows us to determine how the gauged 2-form symmetry embeds into the 2-form global symmetries of the SCFT sectors, and we present several concrete examples, as well as some general observations. As an alternative derivation, we recover our results for a large class of models from a dual perspective upon reduction to five dimensions.