Transversally elliptic complex and cohomological field theory

Self Cite

We perform a systematic study of S-duality for $$ \mathcal{N} $$ N = 2 supersymmetric non-linear abelian theories on a curved manifold. Localization can be used to compute certain supersymmetric observables in these theories. We point out that localization and S-duality acting as a Legendre transform are not compatible. For these theories S-duality should be interpreted as Fourier transform and we provide some evidence for this. We also suggest the notion of a coholomological prepotential for an abelian theory that gives the same partition function as a given non-abelian supersymmetric theory.

Section: Jhep09(2020)128mentioning

confidence: 82%

Section: Jhep09(2020)128mentioning

confidence: 99%

Section: Cohomological Descriptionmentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

S-duality and supersymmetry on curved manifolds

Festuccia

Zabzine

2020

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“…All the theories considered in [1] can be written in terms of cohomological (twisted) fields which helps elucidating what data, of geometrical or other origin, their supersymmetric observables can depend on. These results were formulated in a more rigorous mathematical framework in [32].…”

Section: Introductionmentioning

confidence: 99%

Cohomological localization of $$ \mathcal{N} $$ = 2 gauge theories with matter

Festuccia

Gorantis

Pittelli

et al. 2020

Self Cite

We construct a large class of gauge theories with extended supersymmetry on four-dimensional manifolds with a Killing vector field and isolated fixed points. We extend previous results limited to super Yang-Mills theory to general $$ \mathcal{N} $$ N = 2 gauge theories including hypermultiplets. We present a general framework encompassing equivariant Donaldson-Witten theory and Pestun’s theory on S4 as two particular cases. This is achieved by expressing fields in cohomological variables, whose features are dictated by supersymmetry and require a generalized notion of self-duality for two-forms and of chirality for spinors. Finally, we implement localization techniques to compute the exact partition function of the cohomological theories we built up and write the explicit result for manifolds with diverse topologies.

Partition functions and fibering operators on the Coulomb branch of 5d SCFTs

Closset

Magureanu

2023

We study 5d $$ \mathcal{N} $$ N = 1 supersymmetric field theories on closed five-manifolds $$ \mathcal{M} $$ M 5 which are principal circle bundles over simply-connected Kähler four-manifolds, $$ \mathcal{M} $$ M 4, equipped with the Donaldson-Witten twist. We propose a new approach to compute the supersymmetric partition function on $$ \mathcal{M} $$ M 5 through the insertion of a fibering operator, which introduces a non-trivial fibration over $$ \mathcal{M} $$ M 4, in the 4d topologically twisted field theory. We determine the so-called Coulomb branch partition function on any such $$ \mathcal{M} $$ M 5, which is conjectured to be the holomorphic ‘integrand’ of the full partition function. We precisely match the low-energy effective field theory approach to explicit one-loop computations, and we discuss the effect of non-perturbative 5d BPS particles in this context. When $$ \mathcal{M} $$ M 4 is toric, we also reconstruct our Coulomb branch partition function by appropriately gluing Nekrasov partition functions. As a by-product of our analysis, we provide strong new evidence for the validity of the Lockhart-Vafa formula for the five-sphere partition function.