Perturbative and Non-perturbative Approaches to String Sigma-Models in AdS/CFT

Authors: Vescovi, Edoardo

Nominated as an outstanding Ph.D. thesis by the Humboldt University Berlin, Berlin,Germany
Provides a clear introduction to the superstring models relevant for the N=4 super Yang-Mills (N=4 SYM) and ABJM theory, complemented by appendices and references for further reading
Offers pedagogical explanations of typical string perturbative calculations at one- (functional determinants) and two loops (Feynman diagrams)
Presents an innovative approach to 2d worldsheet theory via lattice field theory

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About this book: This thesis introduces readers to the type II superstring theories in the AdS5×S5 and AdS4×CP3 backgrounds. Each chapter exemplifies a different computational approach to measuring observables (conformal dimensions of single-trace operators and expectation values of Wilson loop operators) relevant for two supersymmetric theories: the N=4 super Yang-Mills theory and the N=6 Chern-Simons-matter (ABJM) theory.
Perturbative techniques have traditionally been used to make quantitative predictions in quantum field theories, but they are only reliable as long as the interaction strengths are weak. The anti-de Sitter/conformal field theory (AdS/CFT) correspondence realizes physicists’ dream of studying strongly coupled quantum field theories with “enhanced” symmetries, using the methods provided by string theory.

The first part of the thesis sets up the semiclassical quantization of worldsheet sigma-model actions around string solutions of least area in AdS space. This machinery is used to capture quantum corrections at large coupling to next-to-leading and next-to-next-to-leading order by solving the determinants of partial differential operators and by computing Feynman diagrams, respectively. In turn, the second part presents an innovative approach based on Monte Carlo simulations to finite coupling for a lattice-discretized model of the AdS5×S5 superstring action.

The thesis focuses on fundamental aspects, as well as on applications previously published by the author, and offers a valuable reference work for anyone interested in the most recent developments in this field.

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About the authors: Edoardo Vescovi received the B.Sc. and the M.Sc. in Physics at Parma University (Italy) in the groups of Prof. Raffaella Burioni and Prof. Luca Griguolo respectively. He completed his Ph.D. in Theoretical Physics at Humboldt University Berlin (Germany) in 2016 in the Independent Emmy Noether Research Group "Gauge Fields from Strings" led by Prof. Dr. Valentina Forini.

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