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Non-anticommutative N=2 super-Yang-Mills theory with singlet deformation

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 Added by Emery Sokatchev
 Publication date 2003
  fields
and research's language is English




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We consider a non-anticommutative N=2 superspace with an SU(2) singlet and Lorentz scalar deformation parameter, ${theta^{alpha i},theta^{beta j}}_star = -2iP e^{alphabeta}e^{ij}$. We exploit this unique feature of the N=2 case to construct a deformation of the non-Abelian super-Yang-Mills theory which preserves the full N=2 supersymmetry together with the SU(2) R symmetry and Lorentz invariance. The resulting action describes a kind of heterotic special geometry with antiholomorphic prepotential $bar f(barphi) = Tr (barphi^2 (1+Pbarphi)^{-2})$.



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We find a formulation of $mathcal{N}=2$ supersymmetric Yang-Mills theory in Projective superspace. In particular we find an expression for the field strength in terms of an unconstrained prepotential which is desirable when quantizing the theory. We use this to write the action in terms of the prepotential and show that it reduces to the known result in the abelian limit.
The N=2* Super-Yang-Mills theory (SYM*) undergoes an infinite sequence of large-N quantum phase transitions. We compute expectation values of Wilson loops in k-symmetric and antisymmetric representations of the SU(N) gauge group in this theory and show that the same phenomenon that causes the phase transitions at finite coupling leads to a non-analytic dependence of Wilson loops on k/N when the coupling is strictly infinite, thus making the higher-representation Wilson loops ideal holographic probes of the non-trivial phase structure of SYM*.
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We construct the D3-brane solution in the holographic dual of the N = 2* theory that describes Wilson lines in symmetric representations of the gauge group. The results perfectly agree with the direct field-theory predictions based on localization.
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