S-duality and supersymmetry on curved manifolds

Festuccia, Guido; Zabzine, Maxim

doi:10.1007/jhep09(2020)128

Cited by 6 publications

(7 citation statements)

References 50 publications

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“…where A, B, Ã, B are complex constants. The spinors in (14) are solutions of the Killing spinor equations (10) provided that the background U (1) R connection vanishes while the two scalars H and H are constant.…”

Section: Killing Spinorsmentioning

confidence: 99%

“…Using these definitions it follows that P + τ = τ while P + τ = τ . Specifically we are interested in the round two sphere and we select the spinors (14) with A = Ã = 1, B = B = 0. With this choice the projectors P + is:…”

Section: Cohomological Complexmentioning

confidence: 99%

“…This construction is directly related to that of [11]. The cohomological description of these models and the corresponding localization are an interesting problem [14].…”

Section: Introductionmentioning

confidence: 99%

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Localizing non-linear $${{\mathcal {N}}}=(2,2)$$ sigma model on $$S^2$$

et al. 2022

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We present a systematic study of $${{\mathcal {N}}}=(2,2)$$ N = ( 2 , 2 ) supersymmetric non-linear sigma models on $$S^2$$ S 2 with the target being a Kähler manifold. We discuss their reformulation in terms of cohomological field theory. In the cohomological formulation we use a novel version of 2D self-duality which involves a U(1) action on $$S^2$$ S 2 . In addition to the generic model we discuss the theory with target space equivariance corresponding to a supersymmetric sigma model coupled to a non-dynamical supersymmetric background gauge multiplet. We discuss the localization locus and perform a one-loop calculation around the constant maps. We argue that the theory can be reduced to some exotic model over the moduli space of holomorphic disks.

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Section: Killing Spinorsmentioning

confidence: 99%

Section: Cohomological Complexmentioning

confidence: 99%

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Localizing non-linear $${{\mathcal {N}}}=(2,2)$$ sigma model on $$S^2$$

et al. 2022

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“…More recently, the derivation of the holomorphic anomaly for the twisted version of the N = 4 SYM and its relation with the mock modular forms has been discussed in [32]. It would be also interesting to extend our approach to the topologically twisted theories considered in [33,34] which generically localize both to point-like instantons and anti-instantons configurations.…”

Section: Introduction Summary and Open Questionsmentioning

confidence: 98%

Gauge theories on compact toric manifolds

et al. 2021

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We compute the $$\mathcal{N}=2$$ N = 2 supersymmetric partition function of a gauge theory on a four-dimensional compact toric manifold via equivariant localization. The result is given by a piecewise constant function of the Kähler form with jumps along the walls where the gauge symmetry gets enhanced. The partition function on such manifolds is written as a sum over the residues of a product of partition functions on $$\mathbb {C}^2$$ C 2 . The evaluation of these residues is greatly simplified by using an “abstruse duality” that relates the residues at the poles of the one-loop and instanton parts of the $$\mathbb {C}^2$$ C 2 partition function. As particular cases, our formulae compute the SU(2) and SU(3) equivariant Donaldson invariants of $$\mathbb {P}^2$$ P 2 and $$\mathbb {F}_n$$ F n and in the non-equivariant limit reproduce the results obtained via wall-crossing and blow up methods in the SU(2) case. Finally, we show that the U(1) self-dual connections induce an anomalous dependence on the gauge coupling, which turns out to satisfy a $$\mathcal {N}=2$$ N = 2 analog of the $$\mathcal {N}=4$$ N = 4 holomorphic anomaly equations.

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“…More recently, the derivation of the holomorphic anomaly for the twisted version of the N = 4 SYM and its relation with the mock modular forms has been discussed in [28]. It would be also interesting to extend our approach to the topologically twisted theories considered in [29,30] which generically localize both to point-like instantons and anti-instantons configurations.…”

mentioning

confidence: 98%

Gauge theories on compact toric manifolds

Bonelli,

Fucito,

Morales

et al. 2020

Preprint

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We compute the N = 2 supersymmetric partition function of a gauge theory on a four-dimensional compact toric manifold via equivariant localization. The result is given by a piecewise constant function of the Kähler form with jumps along the walls where the gauge symmetry gets enhanced. The partition function on such manifolds is written as a sum over the residues of a product of partition functions on C 2 . The evaluation of these residues is greatly simplified by using an "abstruse duality" that relates the residues at the poles of the one-loop and instanton parts of the C 2 partition function. As particular cases, our formulae compute the SU (2) and SU (3) equivariant Donaldson invariants of P 2 and F n and in the non-equivariant limit reproduce the results obtained via wall-crossing and blow up methods in the SU (2) case. Finally, we show that the U (1) self-dual connections induce an anomalous dependence on the gauge coupling, which turns out to satisfy a N = 2 analog of the N = 4 holomorphic anomaly equations.

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S-duality and supersymmetry on curved manifolds

Cited by 6 publications

References 50 publications

Localizing non-linear $${{\mathcal {N}}}=(2,2)$$ sigma model on $$S^2$$

Localizing non-linear $${{\mathcal {N}}}=(2,2)$$ sigma model on $$S^2$$

Gauge theories on compact toric manifolds

Gauge theories on compact toric manifolds

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