Multiple elliptic gamma functions associated to cones

Self Cite

Abstract:We construct 4D N = 2 theories on an infinite family of 4D toric manifolds with the topology of connected sums of S 2 × S 2 . These theories are constructed through the dimensional reduction along a non-trivial U(1)-fiber of 5D theories on toric SasakiEinstein manifolds. We discuss the conditions under which such reductions can be carried out and give a partial classification result of the resulting 4D manifolds. We calculate the partition functions of these 4D theories and they involve both instanton and anti-instanton contributions, thus generalizing Pestun's famous result on S 4 .

“…where we recognize ρ defined in (56). Using these two results, we can write both ρ and Vol M as a sum over the corners of ∆ µ .…”

Section: Comparison With Flat Space Resultsmentioning

confidence: 99%

“…From the computation of [49], the perturbative contribution to the partition function of the 5D N = 1 vector multiplet couple to hypermultiplet in representation R reads where ̺ = Vol(M)/Vol(S 5 ), and S C 3 is the generalized triple sine associated to the cone C [55,56], which is defined as…”

Section: Perturbative Sectormentioning

confidence: 99%

N = 2 $$ \mathcal{N}=2 $$ supersymmetric gauge theory on connected sums of S 2 × S 2

Festuccia¹,

Qiu²,

Winding³

et al. 2017

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“…In the above discussions we allowed for general Reebs R = (ω 1 , ω 2 , ω 3 , ω 4 ) within the dual moment map cone. However, the generalised quadruple sine functions are also defined for complex R as long as the real part can be rotated to lie in the dual cone [35]. Thinking of our quadruple sines as complex functions we can use factorisation results for these special functions and apply them to our perturbative partition function.…”

Section: Factorisationmentioning

confidence: 99%

“…We will start by defining some additional notions. We refer the reader to [35] for a thorough treatment of generalised quadruple sine functions and their factorisations, some of which are also summarised in Appendix C.…”

Section: Factorisationmentioning

confidence: 99%

See 1 more Smart Citation

7D supersymmetric Yang-Mills on curved manifolds

Polydorou

Rocén

Zabzine

2017

We study 7D maximally supersymmetric Yang-Mills theory on curved manifolds that admit Killing spinors. If the manifold admits at least two Killing spinors (Sasaki-Einstein manifolds) we are able to rewrite the supersymmetric theory in terms of a cohomological complex. In principle this cohomological complex makes sense for any K-contact manifold. For the case of toric Sasaki-Einstein manifolds we derive explicitly the perturbative part of the partition function and speculate about the non-perturbative part. We also briefly discuss the case of 3-Sasaki manifolds and suggest a plausible form for the full non-perturbative answer.

7D supersymmetric Yang-Mills on a 3-Sasakian manifold

Rocén

2018

In this paper we study 7D maximally supersymmetric Yang-Mills on a specific 3-Sasakian manifold that is the total space of an SO(3)-bundle over CP 2 . The novelty of this example is that the manifold is not a toric Sasaki-Einstein manifold. The hyperkähler cone of this manifold is a Swann bundle with hypertoric symmetry and this allows us to calculate the perturbative part of the partition function of the theory. The result is also verified by an index calculation. We also discuss a factorisation of this result and compare it with analogous results for S 7 .