School of Mathematics
http://hdl.handle.net/2262/1
School of Mathematics2017-12-13T11:13:38ZThe Ads/CFT spectrum via Integrability-based algorithms
http://hdl.handle.net/2262/82011
The Ads/CFT spectrum via Integrability-based algorithms
MARBOE, CHRISTIAN
The spectral problem of the AdS/CFT correspondence is believed to be integrable in the planar limit. The Quantum Spectral Curve captures the underlying mathematical structure in a relatively simple Riemann-Hilbert problem. To get physical results from this structure, one needs to solve it explicitly. The main goal of this thesis is the development of efficient algorithms to do this perturbatively for general states in the spectrum. The first step in this procedure is to find a leading solution for each multiplet in the spectrum. This is traditionally done by solving Bethe equations, which is notoriously hard. This thesis outlines a new and more powerful technique, which is also applicable more generally to rational spin chains. It then explains how perturbative corrections can be generated through recursive procedures, and describes a conceptually simple and practically powerful algorithm to do this for general states. This opens the door to a vast range of new spectral data, including 10-loop anomalous dimensions for a variety of multiplets. This data is used to reconstruct the six- and seven-loop contributions to the anomalous dimension of twist-two operators with arbitrary spin. Finally, the thesis discusses the evaluation of Q-operators for non-compact spin chains with the future aim of generating perturbative corrections to these from the Quantum Spectral Curve in mind.
APPROVED
2017-01-01T00:00:00ZCuts from residues: the one-loop case
http://hdl.handle.net/2262/81893
Cuts from residues: the one-loop case
BRITTO, RUTH
PUBLISHED
2017-01-01T00:00:00ZCₒ(X)-structure in C*-algebras, multiplier algebras and tensor products
http://hdl.handle.net/2262/80336
Cₒ(X)-structure in C*-algebras, multiplier algebras and tensor products
McConnell, David
We begin in Chapter 2 with an introduction to the various notions of a bundle of C*-algebras that have appeared throughout the literature, and clarify the definitions of upper- and lower-semicontinuous C*-bundles not explicitly defined in a formal way elsewhere. The definition of C0(X)-algebra, introduced by Kasparov [38], and its relation to C*-bundles is discussed in this chapter also. The purpose of this chapter is to bring together concepts that we will refer to in subsequent sections and which are described using various notations by different authors. Most of this is implicitly understood elsewhere, though Theorem 2.3.12, relating sub-modules of C0(X)-modules and subbundles of C*-bundles, is a new result.
2015-01-01T00:00:00ZPeturbative study of the Chirally Rotated Schrödinger Functionality in Lattice QCD
http://hdl.handle.net/2262/80311
Peturbative study of the Chirally Rotated Schrödinger Functionality in Lattice QCD
Mainar, Pol Vilascea
In this thesis we study the renormalisation and O(a) improvement of the Chirally Rotated Schrödinger Functional (xSF) in perturbation theory. The xSF was originally proposed in [1] as a way of rehabiliting the mechanism of automatic O(a) improvement in the Schrödinger Functional formulation. In order to achieve this in the interacting theory, the finite coefficient of a dimension 3 boundary counterterm has to be tuned. After this, O(a) effects originating from the bulk action or from insertions of composite operators in the bulk will be absent in physical quantities. As in any lattice regularization with SF boundary conditions, extra O(a) effects arise from the boundaries and are cancelled by tuning two dimension 4 boundary coefficients.
2014-01-01T00:00:00Z