Perturbative And Non-perturbative Approaches To String Sigma-models In Ads/cft (springer Theses)
by Edoardo Vescovi /
2017 / English / PDF
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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.
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.
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 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.
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.