TY - BOOK

T1 - Aspects of Quantum Field Theory

AU - Volk, Matthias

PY - 2021

Y1 - 2021

N2 - This PhD thesis consists of two parts:The topic of the first part is defect conformal field theories that arise as modifications of the well-known AdS5/CFT4 correspondence between type IIB superstring theory and N = 4 super-symmetric Yang-Mills theory. We review the supersymmetric D3-D5 probe brane intersection and then study two D3-D7 brane intersections in which supersymmetry is completely broken. We obtain the mass spectrum of the field theories by diagonalizing the quadratic part of the action and derive the propagators, thereby allowing for perturbative computations of correlation functions. The procedure closely follows previous work in the field theory dual of a 1/2-BPS D3-D5 brane intersection. We compute the one-point function of a scalar single-trace operator and the expectation value of a straight Wilson line and compare the results to a computation on the string theory side of the correspondence.The second part deals with the special functions that arise as integrals over loop momenta in Feynman diagrams in the perturbative computation of scattering amplitudes. Using direct integration techniques we study both integrals that can be computed in terms of multiple polylogarithms as well as others that require new classes of functions. To the latter class of integrals we associate a Calabi-Yau geometry and study its properties. For a class of conformal integrals we are able to obtain this geometry more directly as the leading singularity locus in momentum twistor space. It is generally unknown whether different parameterizations of a given integral lead to different geometries, but we are able to confirm this for the sunrise integrals and the two-loop elliptic double box integral.

AB - This PhD thesis consists of two parts:The topic of the first part is defect conformal field theories that arise as modifications of the well-known AdS5/CFT4 correspondence between type IIB superstring theory and N = 4 super-symmetric Yang-Mills theory. We review the supersymmetric D3-D5 probe brane intersection and then study two D3-D7 brane intersections in which supersymmetry is completely broken. We obtain the mass spectrum of the field theories by diagonalizing the quadratic part of the action and derive the propagators, thereby allowing for perturbative computations of correlation functions. The procedure closely follows previous work in the field theory dual of a 1/2-BPS D3-D5 brane intersection. We compute the one-point function of a scalar single-trace operator and the expectation value of a straight Wilson line and compare the results to a computation on the string theory side of the correspondence.The second part deals with the special functions that arise as integrals over loop momenta in Feynman diagrams in the perturbative computation of scattering amplitudes. Using direct integration techniques we study both integrals that can be computed in terms of multiple polylogarithms as well as others that require new classes of functions. To the latter class of integrals we associate a Calabi-Yau geometry and study its properties. For a class of conformal integrals we are able to obtain this geometry more directly as the leading singularity locus in momentum twistor space. It is generally unknown whether different parameterizations of a given integral lead to different geometries, but we are able to confirm this for the sunrise integrals and the two-loop elliptic double box integral.

M3 - Ph.D. thesis

BT - Aspects of Quantum Field Theory

PB - Niels Bohr Institute, Faculty of Science, University of Copenhagen

ER -