Quantum phase transition and Resurgence: Lessons from 3d $\mathcal{N}=4$ SQED

Fujimori, Toshiaki; Honda, Masazumi; Kamata, Syo; Misumi, Tatsuhiro; Sakai, Norisuke; Yoda, Takuya

doi:10.48550/arxiv.2103.13654

Cited by 2 publications

(3 citation statements)

References 99 publications

(127 reference statements)

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“…It should be stressed that, at the moment, we do not have a rigorous argument favouring (130) or (131). For recent discussions showing the consistency of this scenario with various anomalies, see [107,113,114,115,116], while [98] has the most recent lattice results, unfortunately not yet decisive.…”

Section: Possible (New) Large-l Phasesmentioning

confidence: 88%

“…There has, however, been progress for BPS observables in supersymmetric theories (where the path integral localizes to a finite dimensional one), in topological, or in integrable theories; for some recent studies see e.g. [131,132], while more references and discussion can be found in the review article [22]. To conclude, despite the difficulties mentioned above, we nonetheless find the agreement of the result of the BZJ procedure with SYM (as further stressed in [133]) and with quantum mechanical examples impressive and offering an important consistency check.…”

Section: Possible (New) Large-l Phasesmentioning

confidence: 99%

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Notes on Confinement on $\mathbf{R^3 \times S^1}$: From Yang-Mills, super-Yang-Mills, and QCD(adj) to QCD(F)

Poppitz

2021

Preprint

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This is a pedagogical introduction to the physics of confinement on R 3 × S 1 , using SU (2) Yang-Mills with massive or massless adjoint fermions as the prime example; at the end, we also add fundamental flavours. The small-S 1 limit is remarkable, allowing for controlled semiclassical determination of the nonperturbative physics in these, mostly non-supersymmetric, theories. We begin by reviewing the Polyakov confinement mechanism on R 3 . Moving on to R 3 × S 1 , we show how introducing adjoint fermions stabilizes center symmetry, leading to abelianization and semiclassical calculability. We explain how monopole-instantons and twisted monopole-instantons arise. We describe the role of various novel topological excitations in extending Polyakov's confinement to the locally four-dimensional case, discuss the nature of the confining string, and the θ-angle dependence. We study the global symmetry realization and, when available, present evidence for the absence of phase transitions as a function of the S 1 size. As our aim is not to cover all work on the subject, but to prepare the interested reader for its study, we also include brief descriptions of topics not covered in detail: the necessity for analytic continuation of path integrals, the study of more general theories, and the 't Hooft anomalies involving higher-form symmetries.

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Section: Possible (New) Large-l Phasesmentioning

confidence: 88%

Section: Possible (New) Large-l Phasesmentioning

confidence: 99%

Notes on Confinement on $\mathbf{R^3 \times S^1}$: From Yang-Mills, super-Yang-Mills, and QCD(adj) to QCD(F)

Poppitz

2021

Preprint

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“…The holomorphic blocks also exist in 4d and 5d theories where factorization of partition functions is again observed[27][28][29]. The 4d holomorphic blocks were later derived directly by localization on D 2 × T 2 in[30], which also includes an analysis of boundary conditions on T 3 .2 The exact result for partition functions like Z S 3 when cast as a resurgent transseries can exhibit a different kind of Stokes phenomenon as studied in[31,32].…”

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confidence: 98%

Stokes Phenomena in 3d $\mathcal{N}=2$ SQED$_2$ and $\mathbb{CP}^1$ Models

Jain,

Manna

2021

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We propose a novel approach of uncovering Stokes phenomenon exhibited by the holomorphic blocks of CP 1 model by considering it as a specific decoupling limit of SQED 2 model. This approach involves using a Z 3 symmetry that leaves the supersymmetric parameter space of SQED 2 model invariant to transform a pair of SQED 2 holomorphic blocks to get two new pairs of blocks. The original pair obtained by solving the line operator identities of the SQED 2 model and the two new transformed pairs turn out to be related by Stokes-like matrices. These three pairs of holomorphic blocks can be reduced to the known triplet of CP 1 blocks in a particular decoupling limit where two of the chiral multiplets in the SQED 2 model are made infinitely massive. This reduction then correctly reproduces the Stokes matrices of the CP 1 blocks.

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Quantum phase transition and Resurgence: Lessons from 3d $\mathcal{N}=4$ SQED

Cited by 2 publications

References 99 publications

Notes on Confinement on $\mathbf{R^3 \times S^1}$: From Yang-Mills, super-Yang-Mills, and QCD(adj) to QCD(F)

Notes on Confinement on $\mathbf{R^3 \times S^1}$: From Yang-Mills, super-Yang-Mills, and QCD(adj) to QCD(F)

Stokes Phenomena in 3d $\mathcal{N}=2$ SQED$_2$ and $\mathbb{CP}^1$ Models

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