BPS invariants for Seifert manifolds by Hee-Joong Chung

“…Abstract We calculate the homological blocks for Seifert manifolds from the exact ex- pression for the G = SU(N ) Witten-Reshetikhin-Turaev invariants of Seifert manifolds obtained by Lawrence, Rozansky, and Mariño. …”
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BPS invariants for a Knot in Seifert manifolds by Hee-Joong Chung

“…Abstract We calculate homological blocks for a knot in Seifert manifolds when the gauge group is SU(N). We obtain the homological blocks with a given representation of the gauge group from the expectation value of the Wilson loop operator by analytically continuing the Chern-Simons level. …”
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Finite, Fiber- and Orientation-Preserving Group Actions on Totally Orientable Seifert Manifolds by Peet Benjamin

“…In this paper we consider the finite groups that act fiber- and orientation-preservingly on closed, compact, and orientable Seifert manifolds that fiber over an orientable base space. …”
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Three-dimensional N=2 supersymmetric gauge theories and partition functions on Seifert manifolds: a review by Closset, C, Kim, H

Refined 3d-3d correspondence by Alday, L, Genolini, P, Bullimore, M, van Loon, M

“…We give a prescription for computing the squashed three-sphere partition functions of such 3d $\mathcal{N}=2$ theories constructed from boundary conditions and interfaces in a 4d $\mathcal{N}=2^*$ theory, mirroring the construction of Seifert manifold invariants via Dehn surgery. This is extended to include links in the Seifert manifold by the insertion of supersymmetric Wilson-'t Hooft loops in the 4d $\mathcal{N}=2^*$ theory. …”

Refined 3d-3d correspondence by Luis F. Alday, Pietro Benetti Genolini, Mathew Bullimore, Mark van Loon

“…We give a prescription for computing the squashed three-sphere partition functions of such 3d N $$ \mathcal{N} $$ = 2 theories constructed from boundary conditions and interfaces in a 4d N $$ \mathcal{N} $$ = 2∗ theory, mirroring the construction of Seifert manifold invariants via Dehn surgery. This is extended to include links in the Seifert manifold by the insertion of supersymmetric Wilson-’t Hooft loops in the 4d N $$ \mathcal{N} $$ = 2∗ theory. …”
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Bundles over Quantum RealWeighted Projective Spaces by Tomasz Brzeziński, Simon A. Fairfax

“…It is also shown that the circle (co)actions on the quantum Seifert manifold that define quantum real weighted projective spaces are almost free.…”
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Higher-Form Symmetries, Bethe Vacua, and the 3d-3d Correspondence by Eckhard, J, Kim, H, Schafer-Nameki, S, Willett, B

“…This is carried out in detail for $M_3$ a Seifert manifold, where we compute a refined version of the Witten index. …”

Higher-form symmetries, Bethe vacua, and the 3d-3d correspondence by Julius Eckhard, Heeyeon Kim, Sakura Schäfer-Nameki, Brian Willett

“…This is carried out in detail for M 3 a Seifert manifold, where we compute a refined version of the Witten index. …”
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T T ¯ $$ T\overline{T} $$ -deformation of q-Yang-Mills theory by Leonardo Santilli, Richard J. Szabo, Miguel Tierz

“…We show that the T T ¯ $$ T\overline{T} $$ -deformation results in a breakdown of the connection with a Chern-Simons theory on a Seifert manifold, and of the large N factorization into chiral and anti-chiral sectors. …”
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Seifert fibering operators in 3d N=2 theories by Closset, C, Kim, H, Willett, B

“…We study 3d N = 2 supersymmetric gauge theories on closed oriented Seifert manifolds — circle bundles over an orbifold Riemann surface —, with a gauge group G given by a product of simply-connected and/or unitary Lie groups. …”

Seifert fibering operators in 3d N = 2 $$ \mathcal{N}=2 $$ theories by Cyril Closset, Heeyeon Kim, Brian Willett

“…Our main result is an exact formula for the supersymmetric partition function on any Seifert manifold, generalizing previous results on lens spaces. …”
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Aspects of supersymmetric gauge theories and conformal field theories in five and three dimensions by Eckhard, J

“…For <em>M</em>₃ a Seifert manifold and gauge algebra 𝖌=𝖘𝖚(2) we verify this explicitly by counting the solutions to the resulting Bethe equations. …”

Localization and non-renormalization in Chern-Simons theory by Yale Fan

“…We illustrate this approach explicitly for SU(2) Chern-Simons theory in flat space, on Seifert manifolds, and on a solid torus.…”
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BPS invariants for 3-manifolds at rational level K by Hee-Joong Chung

“…From the exact expression for the G = SU(2) Witten-Reshetikhin-Turaev invariants of the Seifert manifolds at a rational level obtained by Lawrence and Rozansky, we provide an expected form of the structure of the Witten-Reshetikhin-Turaev invariants in terms of the homological blocks at a rational level. …”
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Resurgent analysis for some 3-manifold invariants by Hee-Joong Chung

“…We discuss the case of an infinite family of Seifert manifolds for general roots of unity and the case of the torus knot complement in S 3. …”
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On N $$ \mathcal{N} $$ = 4 supersymmetry enhancements in three dimensions by Benjamin Assel, Yuji Tachikawa, Alessandro Tomasiello

“…We also show that some but not all of these N $$ \mathcal{N} $$ = 4 enhancements can be understood by considering M5-branes on a special class of Seifert manifolds. Our construction provides a large class of N $$ \mathcal{N} $$ = 4 theories which have not been studied previously.…”
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A generalized 4d Chern-Simons theory by David M. Schmidtt

“…The generalization relies on the use of contact 1-forms defined on non-trivial circle bundles over Riemann surfaces and mimics closely the approach used by Beasley and Witten to reformulate conventional 3d Chern-Simons theories on Seifert manifolds. We also show that the path integral of the generalized theory associated to integrable field theories of the PCM type, takes the canonical form of a symplectic integral over a subspace of the space of gauge connections, turning it a potential candidate for using the method of non-Abelian localization. …”
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Resurgent analysis of SU(2) Chern-Simons partition function on Brieskorn spheres Σ(2, 3, 6n + 5) by David H. Wu

“…The resurgent analysis of these Z ̂ $$ \hat{Z} $$ -invariants has been performed for the cases of Σ(2, 3, 5), Σ(2, 3, 7) by GMP, Σ(2, 5, 7) by Chun, and, more recently, some additional Seifert manifolds by Chung and Kucharski, independently. …”
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