Abstract
We discuss an SL(2,R) family of deformed N=2 four-dimensional gauge theories which we derive from a flux background in M-theory. In addition to the Omega-deformation this family includes a new deformation, which we call the Alpha-deformation, which can be viewed as an S-dual to the Omega-deformation. We study these gauge theories in two ways: by constructing a non-Abelian (but UV-complete) Lagrangian, and by their strong coupling lift to M-theory where their low-energy dynamics can be determined by examining the equation of motion of a single M5-brane wrapped on a Riemann surface.
Highlights
Of of deformed 4d non-Abelian gauge theories can be obtained in this way
In addition to the Omegadeformation this family includes a new deformation, which we call the Alpha-deformation, which can be viewed as an S-dual to the Omega-deformation. We study these gauge theories in two ways: by constructing a non-Abelian Lagrangian, and by their strong coupling lift to M-theory where their low-energy dynamics can be determined by examining the equation of motion of a single M5-brane wrapped on a Riemann surface
The second approach is to remain in M-theory where the branes are given by an M -brane wrapped on a Riemann surface
Summary
The Omega-deformation of a gauge theory was originally constructed via a twisted compactification. In [14, 18] this twisted compactification was reinterpreted in String Theory as a flux background by first finding coordinates that diagonalize the action and performing a T-duality along x9 This leads to a purely geometrical background, the fluxtrap, which can be lifted to M-theory if the original theory is type iib. The original construction of this metric started with the Omega-deformation in type iib string theory followed by T-duality along x9 and an M-theory lift on x10 [14, 19] Given this solution we can ignore this connection and explore M5-branes in this background. This allows us in particular to construct the Alpha-deformation, which can be viewed as an S-dual to the Omega-deformation
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