Construction of the emergent Yang-Mills theory

Date
2020
Authors
De Carvalho, Shaun
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Abstract
In this thesis, we focus on the construction of the emergent Yang-Mills theory that is expected to arise at low energy on the world volume of a giant graviton. Our basic approach is to study the operators in N = 4 super Yang-Mills theory dual to excited giant graviton states. The system we work with consists of giant gravitons and open strings connecting between them. They are described in the language of both restricted Schur polynomials and Gauss graph operators, and we study the action of the one loop dilatation operator at large N, including the leading and rst subleading terms, in the SU(3) sector. The construction of these operators and computations with them requires sophisticated methods from group representation theory, as well as basic ideas from quantum eld theory. Consequently the thesis begins with a careful review of exactly the background that is required. We will consider operators that are a small deformation of a 1 2-BPS multi-giant graviton state. Our rst novel result proves that the subleading matrix elements of the dilatation operator can be interpreted in terms of bosons hopping on a lattice. In this way, we are able to diagonalize the dilatation operator at subleading order. The description and computations are technically challenging, which motivated us to pursue a symmetry based approach to the problem. The second novel result achieved in this thesis, enables us to decompose the state space of excited gaint graviton branes (the Gauss graph operators) into irreducible representations of the su(2j2) global symmetry. As explained by Beisert, this algebra admits central extensions. We argue that in our non-planar setting the global symmetry again is centrally extended, with the charges naturally describing gauge transformations of the emergent gauge theory. Gauge invariance forces these charges to vanish so that we end up with the physically expected result: the full global su(2j2) symmetry is not centrally extended.
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Thesis submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Doctor of Philosophy, Johannesburg, 2020
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