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

168

We provide a formula for the partition function of five-dimensional N = 1 gauge theories on M 4 × S 1 , topologically twisted along M 4 in the presence of general background magnetic fluxes, where M 4 is a toric Kähler manifold. The result can be expressed as a contour integral of the product of copies of the K-theoretic Nekrasov's partition function, summed over gauge magnetic fluxes. The formula generalizes to five dimensions the topologically twisted index of three-and four-dimensional field theories. We analyze the large N limit of the partition function and some related quantities for two theories: N = 2 SYM and the USp(2N ) theory with N f flavors and an antisymmetric matter field. For P 1 × P 1 × S 1 , which can be easily generalized to Σ g 2 × Σ g 1 × S 1 , we conjecture the form of the relevant saddle point at large N . The resulting partition function for N = 2 SYM scales as N 3 and is in perfect agreement with the holographic results for domain walls in AdS 7 × S 4 . The large N partition function for the USp(2N ) theory scales as N 5/2 and gives a prediction for the entropy of a class of magnetically charged black holes in massive type IIA supergravity. arXiv:1808.06626v3 [hep-th] 27 Nov 2018 14 See [87, sect. 4.2] for a more complete explanation..(3.96) 26 The free energy on Σ g2 × S 3 as a function of ∆ was explicitly computed in field theory in [67] after the completion of this work. The result in [67] perfectly agrees with (3.95).

Section: B Metric and Spinor Conventionsmentioning

confidence: 99%

Topologically twisted indices in five dimensions and holography

Hosseini

Yaakov

Zaffaroni

2018

168

“…If this is the case, a relationship similar to the one described here should hold for the partition functions on four-manifolds and five-manifolds of the type described in e.g. [65,66].…”

Section: Discussionmentioning

confidence: 74%

Supersymmetric Rényi entropy and defect operators

Nishioka

Yaakov

2017

We describe the defect operator interpretation of the supersymmetric Rényi entropies of superconformal field theories in three, four and five dimensions. The operators involved are supersymmetric codimension-two defects in an auxiliary Z n gauge theory coupled to n copies of the SCFT. We compute the exact expectation values of such operators using localization, and compare the results to the supersymmetric Rényi entropy. The agreement between the two implies a relationship between the partition function on a squashed sphere and the one on a round sphere in the presence of defects. 4 Discussion 34 A Conventions 35 B Special functions 35 -1 -C The instanton partition function 37

“…Furthermore, we employ localization techniques to compute the partition function of the cohomological theories we constructed. Computations of path integrals via a purely cohomological formulation of supersymmetry appeared for theories defined on specific manifolds in 3d [33][34][35], 4d [25,32,[36][37][38][39], 5d [40][41][42][43][44], and 7d [45][46][47]. We refer to [31] and to references therein for an exhaustive bibliography.…”

Section: Jhep09(2020)133mentioning

confidence: 99%

“…The latter requires regularization, which is a delicate matter. For instance, in cases linked to five-dimensional manifolds, the regularization was established in [37,[42][43][44]59]. Here, we will examine diverse regularizations.…”

Section: Jhep09(2020)133mentioning

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.