Vertex algebras and 4-manifold invariants

Dedushenko, Mykola; Gukov, Sergei; Putrov, Pavel

doi:10.48550/arxiv.1705.01645

Cited by 18 publications

(35 citation statements)

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“…Various interesting properties of 4d theory using 2d VOA are studied in [4,8,9,11,13,15,[29][30][31][47][48][49][50][51][52][53][54][55][56]. See also [19,55,57] for VOAs corresponding to 6d (2, 0) theory on a four manifold. Moreover VOAs corresponding to three dimensional N = 4 theory are discussed in [58,59].…”

Section: Known Resultsmentioning

confidence: 99%

W algebra, Cosets and VOA for 4d N = 2 SCFT from M5 branes

Xie,

Yan

2019

Preprint

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We identify vertex operator algebras (VOAs) of a class of Argyres-Douglas (AD) matters with two types of non-abelian flavor symmetries. They are the W algebra defined using nilpotent orbit with partition [q m , 1 s ]. Gauging above AD matters, we can find VOAs for more general N = 2 SCFTs engineered from 6d (2, 0) theories. For example, the VOA for general (A N −1 , A k−1 ) theory is found as the coset of a collection of above W algebras. Various new interesting properties of 2d VOAs such as level-rank duality, conformal embedding, collapsing levels, coset constructions for known VOAs can be derived from 4d theory.

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Section: Known Resultsmentioning

confidence: 99%

W algebra, Cosets and VOA for 4d N = 2 SCFT from M5 branes

Xie,

Yan

2019

Preprint

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“…where W is a 7-fold of G 2 holonomy with parallel 3-form Φ 3 [20,21], and H a hyperKähler 4-fold; neither space is supposed to be compact or complete. This geometric compactification of M-theory has been considered in [9]. This geometry preserves two supersymmetries.…”

Section: The Geometric Setupmentioning

confidence: 99%

“…We are thus led to consider FI terms of abelian gauge theories. The FI deformation of topological theory under consideration has also been considered in [9].…”

Section: Physical Interpretation Of the Deformation 31 Generalitiesmentioning

confidence: 99%

“…It is natural to expect that the result of the gauging the extra U( 1) is related to the residue of the pole in topological amplitudes in the original theory as ǫ i m i → 0. This may have a particularly simple interpretation in the setup [9] which relates the topological amplitudes to correlators of chiral operator insertions on C, as the subtraction needed to remove the singularity for coincident chiral operators. It would be worthwhile developing this further.…”

Section: Application To S[a 1 ] Theorymentioning

confidence: 99%

“…We would then consider M-theory on the 11-dimensional manifold W × T * C and wrap M5 branes around X 4 × C. The low energy, supersymmetric partition function of this theory is naturally captured by N = 2 TQFT of the 4d QFT labeled by the curve C on the 4-manifold X. Precisely this geometric realization of 4d TQFT in M-theory, using the G 2 structure has already been constructed and studied in [9]. Indeed many elements of what we encounter in this paper have been considered there as well.…”

Section: Introductionmentioning

confidence: 99%

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G2 holonomy, Taubes’ construction of Seiberg-Witten invariants and superconducting vortices

Cecotti

Gerig

Vafa

2020

J. High Energ. Phys.

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Using a reformulation of topological N = 2 QFT's in M-theory setup, where QFT is realized via M5 branes wrapping co-associative cycles in a G 2 manifold constructed from the space of self-dual 2-forms over X 4 , we show that superconducting vortices are mapped to M2 branes stretched between M5 branes. This setup provides a physical explanation of Taubes' construction of the Seiberg-Witten invariants when X 4 is symplectic and the superconducting vortices are realized as pseudo-holomorphic curves. This setup is general enough to realize topological QFT's arising from N = 2 QFT's from all Gaiotto theories on arbitrary 4-manifolds.

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On extensions of $$ \mathfrak{gl}\widehat{\left(\left.m\right|n\right)} $$ Kac-Moody algebras and Calabi-Yau singularities

Rapčák

2020

J. High Energ. Phys.

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We discuss a class of vertex operator algebras W m|n×∞ generated by a supermatrix of fields for each integral spin 1, 2, 3,. .. . The algebras admit a large family of truncations that are in correspondence with holomorphic functions on the Calabi-Yau singularity given by solutions to xy = z m w n. We propose a free-field realization of such truncations generalizing the Miura transformation for W N algebras. Relations in the ring of holomorphic functions lead to bosonization-like relations between different free-field realizations. The discussion provides a concrete example of a non-trivial interplay between vertex operator algebras, algebraic geometry and gauge theory.

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Vertex algebras and 4-manifold invariants

Cited by 18 publications

References 0 publications

W algebra, Cosets and VOA for 4d N = 2 SCFT from M5 branes

W algebra, Cosets and VOA for 4d N = 2 SCFT from M5 branes

G2 holonomy, Taubes’ construction of Seiberg-Witten invariants and superconducting vortices

On extensions of $$ \mathfrak{gl}\widehat{\left(\left.m\right|n\right)} $$ Kac-Moody algebras and Calabi-Yau singularities

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