Holography for coset spaces and noncommutative solitons
2002115 pages
Supervisor:
Thesis: PhD - Andrew Strominger()
- Harvard U.
Report number:
- UMI-30-51317
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Abstract:
M/string theory on noncompact, negatively curved, cosets which generalize AdSD+1 = SO(D, 2)/SO(D, 1) is considered. Holographic descriptions in terms of a conformal field theory on the boundary of the spacetime are proposed. Examples include SU (2, 1)/U(2), which is a Euclidean signature (4, 0) space with no supersymmetry, and SO(2, 2)/SO(2) and SO(3, 2)/SO(3), which are Lorentzian signature (4, 1) and (6, 1) spaces with eight supersymmetries. Qualitatively new features arise due to the degenerate nature of the conformal boundary metric. We propose a definition of dS/CFT correlation functions by equating them to S-matrix elements for scattering particles from I- to I+ . In planar coordinates, which cover half of de Sitter space, we consider instead the S-vector obtained by specifying a fixed state on the horizon. We construct the one-parameter family of de Sitter invariant vacuum states for a massive scalar field in these coordinates, and show that the vacuum obtained by analytic continuation from the sphere has no particles on the past horizon. We use this formalism to provide evidence that the one-parameter family of vacua corresponds to marginal deformations of the CFT by computing a three-point function. The quantum mechanics of N slowly-moving BPS black holes in five dimensions is considered. A divergent continuum of states describing arbitrarily closely bound black holes with arbitrarily small excitation energies is found. A superconformal structure appears at low energies and can be used to define an index counting the weighted number of supersymmetric bound states. It is shown that the index is determined from the dimensions of certain cohomology classes on the symmetric product of N copies of R4 . An explicit computation for the case of N = 2 with no angular momentum yields a finite nonzero result. We construct a new class of scalar noncommutative multi-solitons on an arbitrary Kahler manifold by using Berezin's geometric approach to quantization and its generalization to deformation quantization. We analyze the stability condition which arises from the leading 1/h correction to the soliton energy and for homogeneous Kahler manifolds obtain that the stable solitons are given in terms of generalized coherent states. We apply this general formalism to a number of examples, which include the sphere, hyperbolic plane, torus and general symmetric bounded domains. As a general feature we notice that on homogeneous manifolds of positive curvature, solitons tend to attract each other, while if the curvature is negative they will repel each other. Applications of these results are discussed.- Thesis
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