Symmetry TFTs from String Theory

Apruzzi, Fabio; Bonetti, Federico; García-Etxebarria, Iñaki; Hosseini, Saghar S.; Schäfer‐Nameki, Sakura

doi:10.1007/s00220-023-04737-2

Cited by 50 publications

(27 citation statements)

References 113 publications

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“…One would then expect that the various global structures can be understood in terms of the Symmetry TFT [67] captured by ten-dimensional topological terms in string theorysee e.g. [41,42,52,59,[68][69][70][71]. This seems particularly interesting in the case of the local threefolds that engineer the 5d theories in Type IIA.…”

Section: Discussionmentioning

confidence: 99%

“…As it regards to the possible 4d global structures, the most important physical difference between the E 1 and the E 0 theory is that the 5d 1-form symmetry of the latter is anomalous [52]. There is a cubic anomaly for Γ [1] 5d = Z 3 (corresponding to a 6d term of the schematic form B 3 for the background gauge field B), which gives us a mixed anomaly between Z…”

Section: The Relative Theorymentioning

confidence: 99%

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The $U$-plane of rank-one 4d $\mathcal{N}=2$ KK theories

Closset

Magureanu

2022

SciPost Phys.

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The simplest non-trivial 5d superconformal field theories (SCFT) are the famous rank-one theories with E_nEn flavour symmetry. We study their UU-plane, which is the one-dimensional Coulomb branch of the theory on \mathbb{R}^4 \times S^1ℝ4×S1. The total space of the Seiberg-Witten (SW) geometry – the E_nEn SW curve fibered over the UU-plane – is described as a rational elliptic surface with a singular fiber of type I_{9-n}I9−n at infinity. A classification of all possible Coulomb branch configurations, for the E_nEn theories and their 4d descendants, is given by Persson’s classification of rational elliptic surfaces. We show that the global form of the flavour symmetry group is encoded in the Mordell-Weil group of the SW elliptic fibration. We study in detail many special points in parameters space, such as points where the flavour symmetry enhances, and/or where Argyres-Douglas and Minahan-Nemeschansky theories appear. In a number of important instances, including in the massless limit, the UU-plane is a modular curve, and we use modularity to investigate aspects of the low-energy physics, such as the spectrum of light particles at strong coupling and the associated BPS quivers. We also study the gravitational couplings on the UU-plane, matching the infrared expectation for the couplings A(U)A(U) and B(U)B(U) to the UV computation using the Nekrasov partition function.

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Section: Discussionmentioning

confidence: 99%

Section: The Relative Theorymentioning

confidence: 99%

The $U$-plane of rank-one 4d $\mathcal{N}=2$ KK theories

Closset

Magureanu

2022

SciPost Phys.

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“…A holographic realisation of this mixed anomaly would also be an interesting direction of study. In contrast to the perturbative anomaly, where the bulk anomaly theory is provided by the Chern-Simons differential form, the Z 4 torsion nature of the mixed U(1) × Z 2 anomaly implies that its corresponding bulk anomaly theory cannot be written in terms of a differential form, and that a more general mathematical structure such as those in [82,83] is required. Finding a holographic dictionary and extracting the observable hydrodynamic data would not only be interesting in itself, but could also provide a window to explicitly check our predictions for the transport coefficients at strong coupling.…”

Section: Discussion and Outlookmentioning

confidence: 99%

Omega vs. pi, and 6d anomaly cancellation

Davighi

Lohitsiri

2021

J. High Energ. Phys.

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In this note we review the role of homotopy groups in determining non-perturbative (henceforth ‘global’) gauge anomalies, in light of recent progress understanding global anomalies using bordism. We explain why non-vanishing of πd(G) is neither a necessary nor a sufficient condition for there being a possible global anomaly in a d-dimensional chiral gauge theory with gauge group G. To showcase the failure of sufficiency, we revisit ‘global anomalies’ that have been previously studied in 6d gauge theories with G = SU(2), SU(3), or G2. Even though π6(G) ≠ 0, the bordism groups $$ {\Omega}_7^{\mathrm{Spin}}(BG) $$ Ω 7 Spin BG vanish in all three cases, implying there are no global anomalies. In the case of G = SU(2) we carefully scrutinize the role of homotopy, and explain why any 7-dimensional mapping torus must be trivial from the bordism perspective. In all these 6d examples, the conditions previously thought to be necessary for global anomaly cancellation are in fact necessary conditions for the local anomalies to vanish.

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“…1 However, the physical meaning of holographic categorical symmetry remains mysterious. There are even other names for the same notion, such as symmetry TFT [24] and topological symmetry [25]. Ref.…”

Section: Introductionmentioning

confidence: 99%

Quantum current and holographic categorical symmetry

Lan,

Zhou

2024

SciPost Phys.

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We establish the formulation for quantum current. Given a symmetry group G, let \mathcal{C}𝒞:=Rep G be its representation category. Physically, symmetry charges are objects of \mathcal{C}𝒞 and symmetric operators are morphisms in \mathcal{C}𝒞. The addition of charges is given by the tensor product of representations. For any symmetric operator O crossing two subsystems, the exact symmetry charge transported by O can be extracted. The quantum current is defined as symmetric operators that can transport symmetry charges over an arbitrary long distance. A quantum current exactly corresponds to an object in the Drinfeld center Z_1(\mathcal{C})Z1(𝒞). The condition for quantum currents to be is also specified, which corresponds to condensation of anyons in one higher dimension. To express the local conservation, the internal hom must be used to compute the charge difference, and the framework of enriched category is inevitable. To illustrate these ideas, we develop a rigorous scheme of renormalization in one-dimensional lattice systems and analyse the fixed-point models. It is proved that in the fixed-point models, superconducting quantum currents form a Lagrangian algebra in Z_1(\mathcal{C})Z1(𝒞) and the boundary-bulk correspondence is verified in the enriched setting. Overall, the quantum current provides a natural physical interpretation to the holographic categorical symmetry.

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Symmetry TFTs from String Theory

Cited by 50 publications

References 113 publications

The $U$-plane of rank-one 4d $\mathcal{N}=2$ KK theories

The $U$-plane of rank-one 4d $\mathcal{N}=2$ KK theories

Omega vs. pi, and 6d anomaly cancellation

Quantum current and holographic categorical symmetry

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