Abstract
We find a new supersymmetric solution of type IIB supergravity which is holographically dual to the planar limit of the four-dimensional mathcal{N}={2}^{ast } supersymmetric Yang-Mills theory on S4. We study a probe fundamental string in this background which is dual to a supersymmetric Wilson loop in the mathcal{N}={2}^{ast } theory. Using holography we calculate the expectation value of this line operator to leading order in the ’t Hooft coupling. The result is a non-trivial function of the mass parameter of the mathcal{N}={2}^{ast } theory that precisely matches the result from supersymmetric localization.
Highlights
Integral of the N = 2∗ SYM theory to a finite-dimensional matrix integral
We find a new supersymmetric solution of type IIB supergravity which is holographically dual to the planar limit of the four-dimensional N = 2∗ supersymmetric Yang-Mills theory on S4
Our main interest here is to study probe fundamental strings which are holographically dual to Wilson lines in the fundamental representation in the gauge theory [30, 31]
Summary
We note that since we are in Euclidean signature the complex conjugated fields should be treated as independent variables We emphasize this by denoting the conjugate of Zi by Zi, we still use |Zi|2 to denote the combination ZiZi. The second term in (2.3) denotes the conformal coupling of the scalars in the theory to the curvature of S4. We conclude that the Lagrangian of the N = 2∗ theory on S4 preserves U(1)V × U(1)H global symmetry It was noted in [20] that N = 4 SYM has an extra continuous symmetry in the planar limit, namely the compact U(1)s subgroup of the SL(2, R) S-duality group.
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