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Dissertation zugänglich unter
URN: urn:nbn:de:gbv:18-90731
URL: http://ediss.sub.uni-hamburg.de/volltexte/2018/9073/

Quantum Spectral Curve for the η-deformed AdS_5 × S^5 superstring

Quantenspektralkurve der η-deformierten AdS_5 × S^5-Superstringtheorie

Klabbers, Rob

 Dokument 1.pdf (1.838 KB) 

SWD-Schlagwörter: Quantenfeldtheorie
Freie Schlagwörter (Deutsch): Spektralproblem , Integrabilität
Freie Schlagwörter (Englisch): Physics , Integrability , Spectral problem , String theory , Quantum Field theory
Basisklassifikation: 33.24
Institut: Physik
DDC-Sachgruppe: Physik
Dokumentart: Dissertation
Hauptberichter: Arutyunov, Gleb (Prof. Dr.)
Sprache: Englisch
Tag der mündlichen Prüfung: 24.01.2018
Erstellungsjahr: 2017
Publikationsdatum: 11.04.2018
Kurzfassung auf Englisch: Being able to solve an interacting quantum field theory exactly is by itself an exciting
prospect, as having full control allows for the precise study of phenomena described by
the theory. In the context of the AdS/CFT correspondence, which hypothesises a duality
between certain string and gauge theories, planar N = 4 super Yang-Mills theory shows
signs of great tractability due to integrability. The spectral problem of finding the scaling
dimensions of local operators or equivalently of the string energies of string states of its
AdS/CFT-dual superstring theory on the AdS_5 × S^5 background turned out to be very
tractable. After over a decade of research it was found that the spectral problem can
be solved very efficiently through a set of functional equations known as the quantum
spectral curve. Although it allowed for a detailed study of the aforementioned theory,
many open questions regarding the wider applicability and underlying mechanisms of the
quantum spectral curve exist and are worth studying.
In this thesis we discuss how one can derive the quantum spectral curve for the η-
deformed AdS_5 × S^5 superstring, an integrable deformation of the AdS_5 × S^5 superstring with quantum group symmetry. This model can be viewed as a trigonometric version of the AdS_5 × S^5 superstring, like the xxz spin chain is a trigonometric version of the xxx spin chain. Our derivation starts from the ground-state thermodynamic Bethe ansatz
equations and discusses the construction of both the undeformed and the η-deformed
quantum spectral curve. We reformulate it first as an analytic Y -system, and map this
to an analytic T -system which upon suitable gauge fixing leads to a Pμ system – the
quantum spectral curve. We then discuss constraints on the asymptotics of this system
to single out particular excited states. At the spectral level the η-deformed string and its
quantum spectral curve interpolate between the AdS_5 × S^5 superstring and a superstring
on “mirror” AdS_5 × S^5 , reflecting a more general relationship between the spectral and
thermodynamic data of the η-deformed string.


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