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We calculate the exact eigenvalues of the adjoint scalar fields in the massive vacua of N=1* SUSY Yang-Mills with gauge group SU(N). This provides a field theory prediction for the distribution of D3 brane charge in the AdS dual. We verify the proposal of Polchinski and Strassler that the D3-branes lie on a fuzzy sphere in the supergravity limit and determine the corrections to this distribution due to worldsheet and quantum effects. The calculation also provides several new results concerning the equilibrium configurations of the N-body Calogero-Moser Hamiltonian.
We continue our study of the N=1* supersymmetric gauge theory and its relation to elliptic integrable systems. Upon compactification on a circle, we show that the semi-classical analysis of the massless and massive vacua depends on the classification
We study and analyse the questions regarding breakdown of global symmetry on noncommutative sphere. We demonstrate this by considering a complex scalar field on a fuzzy sphere and isolating Goldstone modes. We discuss the role of nonlocal interaction
The behaviour of matrix string theory in the background of a type IIA pp wave at small string coupling, g_s << 1, is determined by the combination M g_s where M is a dimensionless parameter proportional to the strength of the Ramond-Ramond background
E. Cartan proved that conformally flat hypersurfaces in S^{n+1} for n>3 have at most two distinct principal curvatures and locally envelop a one-parameter family of (n-1)-spheres. We prove that the Gauss-Codazzi equation for conformally flat hypersur
We use Higgs bundles to study the 3d $mathcal{N} = 1$ vacua obtained from M-theory compactified on a local $Spin(7)$ space given as a four-manifold $M_4$ of ADE singularities with further generic enhancements in the singularity type along one-dimensi