Perturbative and non-perturbative approaches to string sigma-models in AdS/CFT

Description

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. Read more... Abstract: 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 Front Matter ....Pages i-xiii Introduction (Edoardo Vescovi)....Pages 1-32 Superstring Actions in \(AdS_5\times S^5\) and \(AdS_4\times \mathbb {CP}^3\) Spaces (Edoardo Vescovi)....Pages 33-50 Geometric Properties of Semiclassically Quantized Strings (Edoardo Vescovi)....Pages 51-76 “Exact” Semiclassical Quantization of Folded Spinning Strings (Edoardo Vescovi)....Pages 77-94 Towards Precision Holography for Latitude Wilson Loops (Edoardo Vescovi)....Pages 95-128 Light-Like Cusp Anomaly and the Interpolating Function in ABJM (Edoardo Vescovi)....Pages 129-145 \(AdS_5\times S^5\) Superstring on the Lattice (Edoardo Vescovi)....Pages 147-175 Conclusion and Outlook (Edoardo Vescovi)....Pages 177-183 Back Matter ....Pages 185-239