Gauge and Gravity Amplitudes from Trees to Loops

TY - BOOK

T1 - Gauge and Gravity Amplitudes from Trees to Loops

AU - Huang, Rijun

PY - 2013

Y1 - 2013

N2 - This thesis describes two subjects that I mainly work on during my PhD study. They are both about scattering amplitudes, covering gravity and gauge theories, tree and loop level, with or without supersymmetry. The rst subject is Kawai-Lewellen-Tye(KLT) relation in field theory, which mysteriously relates Yang-Mills amplitudes to gravity amplitudes. Based on many known works about KLT and super-KLT relations, we provide a complete map between super-gravity amplitudes and super-Yang-Mills amplitudes for any number of supersymmetry that allowed in 4-dimensional theory. We also provide an explanation for vanishing identities of Yang-Mills amplitudes as violation of linear symmetry groups based on KLT relation argument. The second subject is integrand reduction of multi-loop amplitude. The recent methods based on computational algebraic geometry make it possible to systematically study multi-loop amplitude with generalized unitarity cut. Using Grobner basis and primary decomposition, we thoroughly study integrand basis and solution space of equations from maximal unitarity cut for all 4-dimensional two-loop topologies. Algorithm and examples of this computation are illustrated in this thesis. We also study a special type of two-loop and three-loop diagrams where equations of maximal unitarity cut de ne complex curve. Geometry genus of complex curve is a topological invariant, and characterizes the property of curve. Wecompute the genus of complex curve for some two-loop and three-loop diagrams from information of degree and singular points of that curve using algebraic geometry method. Information of integrand basis, structure of solution space as well as geometric genus is useful for future multi-loop amplitude computation.

AB - This thesis describes two subjects that I mainly work on during my PhD study. They are both about scattering amplitudes, covering gravity and gauge theories, tree and loop level, with or without supersymmetry. The rst subject is Kawai-Lewellen-Tye(KLT) relation in field theory, which mysteriously relates Yang-Mills amplitudes to gravity amplitudes. Based on many known works about KLT and super-KLT relations, we provide a complete map between super-gravity amplitudes and super-Yang-Mills amplitudes for any number of supersymmetry that allowed in 4-dimensional theory. We also provide an explanation for vanishing identities of Yang-Mills amplitudes as violation of linear symmetry groups based on KLT relation argument. The second subject is integrand reduction of multi-loop amplitude. The recent methods based on computational algebraic geometry make it possible to systematically study multi-loop amplitude with generalized unitarity cut. Using Grobner basis and primary decomposition, we thoroughly study integrand basis and solution space of equations from maximal unitarity cut for all 4-dimensional two-loop topologies. Algorithm and examples of this computation are illustrated in this thesis. We also study a special type of two-loop and three-loop diagrams where equations of maximal unitarity cut de ne complex curve. Geometry genus of complex curve is a topological invariant, and characterizes the property of curve. Wecompute the genus of complex curve for some two-loop and three-loop diagrams from information of degree and singular points of that curve using algebraic geometry method. Information of integrand basis, structure of solution space as well as geometric genus is useful for future multi-loop amplitude computation.

UR - https://rex.kb.dk/primo-explore/fulldisplay?docid=KGL01009082305&context=L&vid=NUI&search_scope=KGL&isFrbr=true&tab=default_tab&lang=da_DK

M3 - Ph.D. thesis

BT - Gauge and Gravity Amplitudes from Trees to Loops

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

ER -