The goal of this project is to invent new mathematical and physical methods of integrable systems and use them to compute the non-local observables of gauge theory and string theory exactly with respect to the coupling constant. It is believed that a special type of gauge theory and string theory are two equivalent descriptions of the same physical phenomena. This idea is called the Gauge/String Duality or AdS/CFT correspondence. This research thereby tests the AdS/CFT correspondence via the exact computation of non-local objects based on integrability methods.
The integrability method called the Thermodynamic Bethe Ansatz (TBA) equations is the basis of our method. This set of equations is expected to give the spectrum of the conformal dimension of local operators in N=4 supersymmetric Yang-Mills theory, and the energy of closed string states on the AdS_5 x S^5 space-time, for any operators/states and at any value of the coupling constant. This project aims at generalizing this powerful formulation, and developing novel methods to solve nonlinear integral equations of TBA-type in analytic and numerical manners.
The theory of integrable systems has rich mathematical structure, and is one of the major research fields in the modern mathematical physics. The integrable systems have a long history of its own since the discovery of quantum mechanics, and their exact solutions have provided important physical insights with the researchers of low-dimensional lattice models, quantum field theories, string theory and the AdS/CFT correspondence.
The applicant will undertake the research at the Mathematical Institute in Oxford under the supervision of Prof. Luis-Fernando Alday. The applicant will also participate in the Oxford String Theory Group, which is one of the largest string theory research groups in UK with 9 faculty members from the Mathematical Institute and the Rudolf Peierls Centre for Theoretical Physics.
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