5D BPS quivers and KK towers

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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“…Other recent discussions of BPS quivers in the present context include e.g. [88][89][90][91][92][93][94].…”

Section: Modularity On the U-planementioning

confidence: 99%

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

Closset

Magureanu

2022

SciPost Phys.

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“…Exploiting the Kaluza-Klein (KK) circle as an M-theory circle, it is clear that the 4d KK theory associated to X Γ is obtained from type IIA on the same Calabi-Yau threefold [94]. The 5D BPS quivers are therefore captured from the BPS quivers of IIA on X Γ [75] (see also [95]). For the case at hand, the structure of the quivers can be reproduced from the D0-brane probe of this singularity.…”

Section: B Quiver Approachmentioning

confidence: 99%

Higher symmetries of 5D orbifold SCFTs

et al. 2022

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We determine the higher symmetries of 5D SCFTs engineered from M-theory on a C 3 =Γ background for Γ a finite subgroup of SUð3Þ. This resolves a longstanding question as to how to extract this data when the resulting singularity is nontoric (when Γ is non-Abelian) and/or not isolated (when the action of Γ has fixed loci). The Bogomol'nyi-Prasad-Sommerfield (BPS) states of the theory are encoded in a 1D quiver quantum mechanics gauge theory which determines the possible 1-form and 2-form symmetries. We also show that this same data can also be extracted by a direct computation of the corresponding defect group associated with the orbifold singularity. Both methods agree, and these computations do not rely on the existence of a resolution of the singularity. We also observe that when the geometry faithfully captures the global 0-form symmetry, the abelianization of Γ detects a 2-group structure (when present). As such, this establishes that all of this data is indeed intrinsic to the superconformal fixed point rather than being an emergent property of an IR gauge theory phase.

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“…. , 1) in case of toric Calabi-Yau's [16,17]. Combined, this means that in the large radius limit of S 1 , the nonrelativistic requirement breaks down spectacularly.…”

Section: An Overviewmentioning

confidence: 99%

Aspects of 5d Seiberg-Witten theories on $$ {\mathbbm{S}}^1 $$

Jia

2022

J. High Energ. Phys.

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We study the infrared physics of 5d $$ \mathcal{N} $$ N = 1 Yang-Mills theories compactified on $$ {\mathbbm{S}}^1 $$ S 1 , with a view toward 4d and 5d limits. Global structures of the simplest Coulombic moduli spaces are outlined, with an emphasis on how multiple planar 4d Seiberg-Witten geometries are embedded in the cigar geometry of a single 5d theory on $$ {\mathbbm{S}}^1 $$ S 1 . The Coulomb phase boundaries in the decompactification limit are given particular attention and related to how the wall-crossings by 5d BPS particles turn off. On the other hand, the elliptic genera of magnetic BPS strings do wall-cross and retain the memory of 4d wall-crossings, which we review with the example of dP2 theory. Along the way, we also offer a general field theory proof of the odd shift of electric charge on Sp(k)π instanton solitons, previously observed via geometric engineering for low-rank supersymmetric theories.

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5D BPS quivers and KK towers

Cited by 7 publications

References 47 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

Higher symmetries of 5D orbifold SCFTs

Aspects of 5d Seiberg-Witten theories on $$ {\mathbbm{S}}^1 $$

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