Perturbative and non-perturbative approaches to string sigma-models in AdS/CFT
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Mathematisch-Naturwissenschaftliche Fakultät
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Abstract
Diese Doktorarbeit behandelt quantentheoretische Aspekte von Typ II Superstringtheorien in AdS5xS5- und AdS4xCP3-Hintergründen für die AdS/CFT Korrespondenz. Dabei werden perturbative Methoden und Verfahren der Gitterfeldtheorie benutzt. Die Konstruktion des Supercoset-Sigma-Modell für Strings im AdS5xS5wird skizziert, während die generelle Quantendynamik des Superstring in AdS4xCP3 mit Hilfe einer dimensionaler Reduktion der Supermembrane-Wirkung in AdS4xS7 beschrieben wird. Ein manifest kovarianter Formalismus zur semi-klassischen Quantisierung von Strings um beliebige Minimalflächen in AdS5xS5 wird präsentiert, der durch die Darstellung der Fluktuationsoperatoren in Form von intrinsischen und extrinsischen Varianten der Hintergrundgeometrie erreicht wird. Eine Verallgemeinerung der Lame-Differentialgleichung zur 4. Ordnungwird mit Hilfe der Spektralmethode exakt gelöst. Dadurch konnten in 1-Schleifennäherung die Energie des String im SU(2)-Sektor, im Grenzfall beschrieben durch ein Quantum-Landau-Lifshitz-Modell, und der bosonische Beitrag zur Energie des in AdS5 und S5 rotierenden String bestimmt werden. In ähnlicher Weise erhält man in 1-Schleifennäherung den ¼-BPS-Latitude Wilson-Loop in N=4-SYM-Theorie normiert durch den ½-BPS-Loop. Das Regularisierungsschema reproduziert die Vorhersage aus supersymmetrischer Lokalisierung bis auf einen Rest, welcher diskutiert wird. Außerdem wird die Wirkung des AdS4xCP3-String, entwickelt um den null-cusp Hintergrund, studiert und die Cusp-Anomalie in 2-Schleifennäherung berechnet. Das Ergebnis stimmt mit dem vermuteten exakten Ausdruck, der ABJM-Interpolationsfunktion, überein. Schließlich wird die AdS5xS5-Superstringtheorie in AdS-Lichtkegel-Eichung diskretisiert und mit Monte-Carlo-Algorithmen Gittersimulationen bei endlicher Kopplung durchgeführt. Dabei werden die Stringwirkung, aus der mit Hilfe von AdS/CFT die null-cusp anomale Dimension von N=4 SYM extrahiert werden kann, und die Masse einer AdS Anregung bestimmt.
This thesis discusses quantum aspects of type II superstring theories in AdS5xS5 and AdS4xCP3 backgrounds relevant for the AdS/CFT correspondence, using perturbative methods at large string tension and lattice field theory techniques inspired by a work of Roiban and McKeown. We review the construction of the supercoset sigma-model for strings in the AdS5xS5 background, whereas the general quantum dynamics of the superstring in AdS4xCP3 is described by a double dimensional reduction of the supermembrane action in AdS4xS7. We present a manifestly covariant formalism for semiclassical quantization of strings around arbitrary minimal-area surfaces in AdS5xS5, expressing the fluctuation operators in terms of intrinsic and extrinsic invariants of the background geometry. We exactly solve the spectral problem for a fourth-order generalization of the Lame'' differential equation with doubly periodic coefficients in a complex variable. This calculates the one-loop energy of the (J1,J2)-string in the SU(2) sector in the limit described by a quantum Landau-Lifshitz model and the bosonic contribution to the energy of the (S,J)-string rotating in AdS5 and S5. Similar techniques calculate the 1/4-BPS latitude Wilson loops in N=4 SYM theory at one loop, normalized to the 1/2-BPS circular loop. Our regularization scheme reproduces the next-to-leading order predicted by supersymmetric localization, up to a remainder function that we discuss upon. We also study the AdS4xCP3 string action expanded around the null cusp background and compute the cusp anomaly up to two loops. This agrees with an all-loop conjectured expression of the ABJM interpolating function. We finally discretize the AdS5xS5 superstring theory in the AdS light-cone gauge and perform lattice simulations at finite coupling with a Monte Carlo algorithm. We measure the string action, from which we extract the null cusp anomalous dimension of N=4 SYM as derived from AdS/CFT, as well as the mass of an AdS excitation.
This thesis discusses quantum aspects of type II superstring theories in AdS5xS5 and AdS4xCP3 backgrounds relevant for the AdS/CFT correspondence, using perturbative methods at large string tension and lattice field theory techniques inspired by a work of Roiban and McKeown. We review the construction of the supercoset sigma-model for strings in the AdS5xS5 background, whereas the general quantum dynamics of the superstring in AdS4xCP3 is described by a double dimensional reduction of the supermembrane action in AdS4xS7. We present a manifestly covariant formalism for semiclassical quantization of strings around arbitrary minimal-area surfaces in AdS5xS5, expressing the fluctuation operators in terms of intrinsic and extrinsic invariants of the background geometry. We exactly solve the spectral problem for a fourth-order generalization of the Lame'' differential equation with doubly periodic coefficients in a complex variable. This calculates the one-loop energy of the (J1,J2)-string in the SU(2) sector in the limit described by a quantum Landau-Lifshitz model and the bosonic contribution to the energy of the (S,J)-string rotating in AdS5 and S5. Similar techniques calculate the 1/4-BPS latitude Wilson loops in N=4 SYM theory at one loop, normalized to the 1/2-BPS circular loop. Our regularization scheme reproduces the next-to-leading order predicted by supersymmetric localization, up to a remainder function that we discuss upon. We also study the AdS4xCP3 string action expanded around the null cusp background and compute the cusp anomaly up to two loops. This agrees with an all-loop conjectured expression of the ABJM interpolating function. We finally discretize the AdS5xS5 superstring theory in the AdS light-cone gauge and perform lattice simulations at finite coupling with a Monte Carlo algorithm. We measure the string action, from which we extract the null cusp anomalous dimension of N=4 SYM as derived from AdS/CFT, as well as the mass of an AdS excitation.
Description
Keywords
Gitter, AdS/CFT Korrespondenz, Superstringtheorie, perturbative, starker, Determinante, lattice, AdS/CFT correspondence, perturbative, strong, Superstring theory, determinant
Dewey Decimal Classification
530 Physik
Citation
Vescovi, Edoardo.(2016). Perturbative and non-perturbative approaches to string sigma-models in AdS/CFT. 10.18452/17612