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

Closset, Cyril; Magureanu, Horia

doi:10.1007/jhep01(2023)035

Cited by 3 publications

(3 citation statements)

References 102 publications

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“…Among these, related to our work are studies of N = 2 topologically twisted theories on compact toric manifolds [7][8][9][10][11]. See also [12,13] for topologically twisted theories on M 4 × S 1 , where M 4 is a compact 4d toric Kähler manifold.…”

Section: Jhep10(2023)155mentioning

confidence: 99%

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From 5d flat connections to 4d fluxes (the art of slicing the cone)

Lundin,

Mauch,

Ruggeri

2023

J. High Energ. Phys.

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We compute the Coulomb branch partition function of the 4d $$ \mathcal{N} $$ N = 2 vector multiplet on closed simply-connected quasi-toric manifolds B. This includes a large class of theories, localising to either instantons or anti-instantons at the torus fixed points (including Donaldson-Witten and Pestun-like theories as examples). The main difficulty is to obtain flux contributions from the localisation procedure. We achieve this by taking a detour via the 5d $$ \mathcal{N} $$ N = 1 vector multiplet on closed simply-connected toric Sasaki-manifolds M which are principal S1-bundles over B. The perturbative partition function can be expressed as a product over slices of the toric cone. By taking finite quotients M/ℤh along the S1, the locus picks up non-trivial flat connections which, in the limit h → ∞, provide the sought-after fluxes on B. We compute the one-loop partition functions around each topological sector on M/ℤh and B explicitly, and then factorise them into contributions from the torus fixed points. This enables us to also write down the conjectured instanton part of the partition function on B.

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Section: Jhep10(2023)155mentioning

confidence: 99%

“…For simplicity, we assume G to be simply-connected 13. We can decompose a form ω ∈ Ω • (M ) as ω = r ∧ ιrω + ω, with ιr ω = 0.…”

mentioning

confidence: 99%

From 5d flat connections to 4d fluxes (the art of slicing the cone)

Lundin,

Mauch,

Ruggeri

2023

J. High Energ. Phys.

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“…The matrix models describing 5d quiver gauge theories were derived in [58,[67][68][69][70]. Here we leave the discussion of the ambient CFT schematic and focus on the defect contributions; all we need from the ambient CFT are the saddle points dominating the matrix models in the planar limit.…”

Section: Matrix Modelsmentioning

confidence: 99%

3d defects in 5d: RG flows and defect F-maximization

Santilli

Uhlemann

2023

J. High Energ. Phys.

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We use a combination of AdS/CFT and supersymmetric localization to study codimension-2 defects in 5d SCFTs and their gauge theory deformations. The 5d SCFTs are engineered by (p, q) 5-brane webs, with defects realized by D3-branes ending on the 5-brane webs. We obtain the defect free energies and find that gauge theory descriptions of the combined 5d/3d systems can be connected to the UV defect SCFTs through a form of F-maximization which extremizes over different gauge theory defects. This leads to a match between the defect free energies obtained from supersymmetric localization in the gauge theories on the one hand and string theory results on the other. We extend this match to defect RG flows.

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Topological twists of massive SQCD, Part II

Aspman,

Furrer,

Manschot

2024

Lett Math Phys

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This is the second and final part of ‘Topological twists of massive SQCD’. Part I is available at Lett. Math. Phys. 114 (2024) 3, 62. In this second part, we evaluate the contribution of the Coulomb branch to topological path integrals for $$\mathcal {N}=2$$ N = 2 supersymmetric QCD with $$N_f\le 3$$ N f ≤ 3 massive hypermultiplets on compact four-manifolds. Our analysis includes the decoupling of hypermultiplets, the massless limit and the merging of mutually non-local singularities at the Argyres–Douglas points. We give explicit mass expansions for the four-manifolds $$\mathbb {P}^2$$ P 2 and K3. For $$\mathbb {P}^2$$ P 2 , we find that the correlation functions are polynomial as function of the masses, while infinite series and (potential) singularities occur for K3. The mass dependence corresponds mathematically to the integration of the equivariant Chern class of the matter bundle over the moduli space of Q-fixed equations. We demonstrate that the physical partition functions agree with mathematical results on Segre numbers of instanton moduli spaces.

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

Cited by 3 publications

References 102 publications

From 5d flat connections to 4d fluxes (the art of slicing the cone)

From 5d flat connections to 4d fluxes (the art of slicing the cone)

3d defects in 5d: RG flows and defect F-maximization

Topological twists of massive SQCD, Part II

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