Deconstructing Little Strings with $\mathcal{N}=1$ Gauge Theories on Ellipsoids

Abstract

A formula was recently proposed for the perturbative partition function of certain $\mathcal{N}=1$ gauge theories on the round four-sphere, using an analytic-continuation argument in the number of dimensions. These partition functions are not currently accessible via the usual supersymmetric-localisation technique. We provide a natural refinement of this result to the case of the ellipsoid. We then use it to write down the perturbative partition function of an $\mathcal{N}=1$ toroidal-quiver theory (a double orbifold of $\mathcal{N}=4$ super Yang-Mills) and show that, in the deconstruction limit, it reproduces the zero-winding contributions to the BPS partition function of (1,1) Little String Theory wrapping an emergent torus. We therefore successfully test both the expressions for the $\mathcal{N}=1$ partition functions, as well as the relationship between the toroidal-quiver theory and Little String Theory through dimensional deconstruction.

arXiv comment6 pages; v2: typos corrected and references added; v3: minor clarifications added; v4 typo corrected and references added

References in corpus (23)

• Liouville Correlation Functions from Four-dimensional Gauge Theories
• N=2 dualities
• Localization of gauge theory on a four-sphere and supersymmetric Wilson loops
• (De)Constructing Dimensions
• The Refined Topological Vertex
• Localization techniques in quantum field theories
• M-Strings
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• Deconstructing (2,0) and Little String Theories
• Localization on Hopf surfaces
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• Supersymmetric partition functions on Riemann surfaces
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• Instanton-Monopole Correspondence from M-Branes on ${\mathbb{S}}^1$ and Little String Theory
• Little strings and T-duality
• Exact Deconstruction of the 6D (2,0) Theory
• 2D CFT blocks for the 4D class ${\mathcal{S}}_k$ theories
• Analytic continuation of dimensions in supersymmetric localization
• One-loop tests of supersymmetric gauge theories on spheres
• Localizing gauge theories on $S^d$
• Deconstructing S-Duality
• Towards Deconstruction of the Type D (2,0) Theory

Cited by in corpus (7)

• Universal Features of BPS Strings in Six-dimensional SCFTs
• A slow review of the AGT correspondence
• Type-B Anomaly Matching and the 6D (2,0) Theory
• The Coulomb and Higgs Branches of $\mathcal{N}=1$ Theories of Class ${\mathcal{S}}_k$
• Comments on Quivers and Fractons
• Deconstructing Defects
• Quivers, Lattice Gauge Theories and Fractons