Localization for $$\mathcal {N}=2$$ Supersymmetric Gauge Theories in Four Dimensions

Pestun, Vasily

doi:10.1007/978-3-319-18769-3_6

Cited by 34 publications

(67 citation statements)

References 67 publications

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“…Thus Ω is an equivariant extension of the canonical volume form. Indeed one can argue that the lowest component Ω 0 of the equivariant extension Ω of any volume form on S 4 (e.g., that corresponding to the squashed S 4 considered in [16,17] ) always has a different sign at the two poles. Applying our observations to Pestun's theory on a round S 4 [1], we can see that modulo the θ-term the supersymmetric action can be rewritten as…”

Section: Example: Smentioning

confidence: 99%

Twisting with a Flip (The Art of Pestunization)

Festuccia

Qiu

Winding

et al. 2020

Commun. Math. Phys.

128

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We construct N = 2 supersymmetric Yang-Mills theory on 4D manifolds with a Killing vector field with isolated fixed points. It turns out that for every fixed point one can allocate either instanton or anti-instanton contributions to the partition function, and that this is compatible with supersymmetry. The equivariant Donaldson-Witten theory is a special case of our construction. We present a unified treatment of Pestun's calculation on S 4 and equivariant Donaldson-Witten theory by generalizing the notion of self-duality on manifolds with a vector field. We conjecture the full partition function for a N = 2 theory on any 4D manifold with a Killing vector. Using this new notion of self-duality to localize a supersymmetric theory is what we call "Pestunization". C Transverse elliptic problems in 4D and 5D 48 D Full cohomological complex 52 E Supergravity background 53

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Section: Example: Smentioning

confidence: 99%

Twisting with a Flip (The Art of Pestunization)

Festuccia

Qiu

Winding

et al. 2020

Commun. Math. Phys.

128

View full text Add to dashboard Cite

show abstract

“…The equations describing such configurations are obtained by setting to zero the supergravity variations of the gravitino and other fermionic fields in the supergravity multiplet. 12 For N = 2 supersymmetric theories the relevant equations have been analyzed in [28,29], and in particular applied to the (squashed) four-sphere. 13 On the four-sphere, the result of the above analysis (or the shortcut described in footnote 13) is that the Killing spinors ξ I ,ξ I describing supersymmetry variations should solve the 12 One can similarly couple the theory to a nontrivial background for flavor symmetries.…”

Section: N = 2 Supersymmetry On Smentioning

confidence: 99%

“…Indeed, given the monopole chargem = 1 2 , {Y m jm |j ∈ N + |m|, m ∈ {−j, −j + 1, .. . , +j}} forms an orthonormal basis for the space of sections Γ(S − ) of the nontrivial anti-chiral spinor bundle S − 29. The first order differential operator ℘ can be viewed as ∂ − iaz on Γ(S − ), where a is the U (1) connection on S − , taking the monopole profile a = 1 2 (±1 − cos ρ)dχ on U N/S .…”

mentioning

confidence: 99%

Chiral algebras, localization and surface defects

Pan

Peelaers

2018

J. High Energ. Phys.

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Four-dimensional N = 2 superconformal quantum field theories contain a subsector carrying the structure of a chiral algebra. Using localization techniques, we show for the free hypermultiplet that this structure can be accessed directly from the path integral on the four-sphere. We extend the localization computation to include supersymmetric surface defects described by a generic 4d/2d coupled system. The presence of a defect corresponds to considering a module of the chiral algebra: our results provide a calculational window into its structure constants.

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“…On the four-ball B 4 , we choose a supergravity background, such that a theory with 4d N = 2 supersymmetry can be put on it, preserving some supercharges. Such backgrounds are reviewed in [71], the Omega-background being a particular example. 44 It is expected that the supersymmetric observables do not depend on much of the details of the background.…”

Section: Conformal Blocks Corners and Liouvillementioning

confidence: 99%

Teichmüller TQFT vs. Chern-Simons theory

Mikhaylov¹

2018

J. High Energ. Phys.

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Teichmüller TQFT is a unitary 3d topological theory whose Hilbert spaces are spanned by Liouville conformal blocks. It is related but not identical to PSL(2, R) ChernSimons theory. To physicists, it is known in particular in the context of 3d-3d correspondence and also in the holographic description of Virasoro conformal blocks. We propose that this theory can be defined by an analytically-continued Chern-Simons path-integral with an unusual integration cycle. On hyperbolic three-manifolds, this cycle is singled out by the requirement of invertible vielbein. Mathematically, our proposal translates a known conjecture by Andersen and Kashaev into a conjecture about the Kapustin-Witten equations. We further explain that Teichmüller TQFT is dual to complex SL(2, C) Chern-Simons theory at integer level k = 1, clarifying some puzzles previously encountered in the 3d-3d correspondence literature. We also present a new simple derivation of complex Chern-Simons theories from the 6d (2,0) theory on a lens space with a transversely-holomorphic foliation.

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Localization for $$\mathcal {N}=2$$ Supersymmetric Gauge Theories in Four Dimensions

Cited by 34 publications

References 67 publications

Twisting with a Flip (The Art of Pestunization)

Twisting with a Flip (The Art of Pestunization)

Chiral algebras, localization and surface defects

Teichmüller TQFT vs. Chern-Simons theory

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