On the reduction of 4d $ \mathcal{N}=1 $ theories on $ {\mathbb{S}}^2

Here, we discuss reductions of general $ \mathcal{N}=1 $ four dimensional gauge theories on $ {\mathbb{S}}^2 $. The effective two dimensional theory one obtains depends on the details of the coupling of the theory to background fields, which can be translated to a choice of R-symmetry. We argue that...

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Bibliographic Details
Published in:The journal of high energy physics 2015-11, Vol.2015 (11)
Main Authors: Gadde, Abhijit, Razamat, Shlomo S., Willett, Brian
Format: Article
Language:English
Subjects:
Duality in Gauge Field Theories
PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
Supersymmetric gauge theory
Supersymmetry and Duality
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Summary:Here, we discuss reductions of general $ \mathcal{N}=1 $ four dimensional gauge theories on $ {\mathbb{S}}^2 $. The effective two dimensional theory one obtains depends on the details of the coupling of the theory to background fields, which can be translated to a choice of R-symmetry. We argue that, for special choices of R-symmetry, the resulting two dimensional theory has a natural interpretation as an $ \mathcal{N}(0,2) $ gauge theory. As an application of our general observations, we discuss reductions of $ \mathcal{N}=1 $ and $ \mathcal{N}=2 $ dualities and argue that they imply certain two dimensional dualities.
ISSN:1029-8479
1029-8479