ETD Collection

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    Gravitational description of the conformally invariant quantum mechanics of large matrices
    (2017) Hanmer, Jeffrey Thomas
    We study the collective field theory of a free multi-matrix model in the radial sector, which has an emergent 1/r2 term, and take the large N limit. We show that it is possible to generate 2−d metrics with generic dependence on the collective field Lagrange multiplier (μ) and potential and which are distinguished by the choice of the potential. The Lagrange multiplier is shown to depend on an induced scale parameter after an I.R. regularization and breaks scale invariance. The collective field sl(2, R) algebras of the free Hamiltonian and a related alternative compact operator only close in the absence of μ. We point out that the broken conformal symmetry is contained in the associated metrics which suggests that they are related to a Near-AdS2 geometry. We also comment on the resemblance of these metrics to black hole solutions.
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    Large N conformal field theory from gauge/gravity duality
    (2017) Hasina Tahiridimbisoa, Nirina Maurice
    In this dissertation we exploit the Ads slash CFT correspondence to describe a system of strings suspended between giant gravitons. The strings can be in an excited state. The excitations of the strings can be given a particle-like description and are known as magnons. The proposed gauge invariant operators used to construct a complete description of this system belong to the su(2) sector of the N = 4 SYM. Using an open spin chain description of the suspended strings, the states of the system we consider enjoy an SU 2j2)2 symmetry. By making use of this symmetry, we compute the all loop anomalous dimensions of these operators. The spectrum of the dilatation operator in the su(2) sector of the theory is reproduced in the dual gravity description. In the dual theory, the energies of the magnons are computed using strings in a background LLM geometry and the results are in complete agreement with the anomalous dimensions of the operators we have considered. Using the symmetries enjoyed by our system we achieve a complete determination - up to an overall phase - of the reection/scattering matrix between a boundary magnon and a bulk magnon. Thus, although the open boundary conditions of the spin chain spoil integrability. The two-loop subleading correction to the dilatation operator is also explored. This subleading term corresponds to a correction of the magnon energies. The computation of this subleading term requires consideration of the giant's backreaction on their excitations. We nd that this backreaction implies a nontrivial mixing of the dual operators and this mixing is characterized completely.
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    Spectra of the excited giant gravitons from the two loop dilatation operator
    (2016-09-19) Ali, Abdelhamid Mohamed Adam
    The AdS/CFT correspondence is a conjectured exact duality between type IIB string theory on the AdS5 S5 background and N = 4 Super Yang-Mills theory, a conformal eld theory (CFT), on the boundary of the AdS space. A speci c observable of the CFT, which can be read from the two point correlation function, is the anomalous dimension. In this dissertation we will compute spectra of anomalous dimensions of excited giant gravitons up to two loops in a speci c limit. We are interested in the anomalous dimensions because the AdS/CFT correspondence associates them with energies of states in quantum gravity. We study operators constructed using n Z elds and m Y elds with n << m: In this case m n is a small parameter. At the leading order in m n and at large N, the problem of determining the anomalous dimensions can be mapped into the dynamics of m non-interacting magnons. The subleading terms at two loops, computed for the rst time in this dissertation, induce interactions between the magnons. Even after including this new correction, we nd the BPS operators remain BPS.