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Exact results in supersymmetric field theory. / Thomas Kingaby
Swansea University Author: Thomas, Kingaby
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This thesis examines N = 2 Super-Yang-Mills theory where the low-energy effective action of the theory is governed by a holomorphic function called the prepotential. The Seiberg-Witten solution of the theory determines the prepotential in terms of an complex curve and, once we compactify the theory...
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This thesis examines N = 2 Super-Yang-Mills theory where the low-energy effective action of the theory is governed by a holomorphic function called the prepotential. The Seiberg-Witten solution of the theory determines the prepotential in terms of an complex curve and, once we compactify the theory on a circle, we will examine the identification of this complex curve with the spectral curve of the Calogero-Moser integrable system. Since the supersymmetry restricts the perturbative contributions to the prepotential, the results we gain are exact. Further, they are independent of the compactification radius. The generalization to the quiver models, with gauge group SU(N)k, is introduced along with the spin generalization of the integrable system. The massive vacua of these theories have been determined previously, here we examine the case of a specific gauge group in order to determine the complete phase structure, including the massless vacua. We then move on to determining contributions coming from instantons to the prepotential of the theory with gauge group SU(N). We see how by lifting the theory onto 5 dimensions the functional integral on the instanton moduli space is realized as a quantum mechanical sigma-model with the moduli space as a target. However, just such a model is shown to calculate a particular index of the manifold, in this case a particular equivariant index since the space has isometries. We account for the non-compact nature of the moduli space by removing boundary terms and then calculate explicit results in the case of SU(2).
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