`Aspects of RG flow: the A-theorem for gauge theories'
Abstract:
Renormalization Group (RG) flow describes the behaviour of Quantum Field
Theories under changes in the energy scale. If one treats the couplings
${g^{I}}$ of the theory as points on a manifold, then there exists a function
$A(g)$ satisfying $\\mathop{d_{g}}A(g)=dg^{I}T_{IJ}(g)\\beta^{J}(g)$; this
function also satisfies $A(g_{*})=4a$ and $\beta^{I}(g_{*})=0$ for any RG
fixed point $g_{*}$, where a is the Euler Density coefficient in the Trace
Anomaly. The symmetric part $G_{IJ}$ of the matrix $T_{IJ}$ acts as a metric
on the coupling space, and the extent to which this metric constrains changes
in a QFT under RG flow will provide a resolution to Cardy\'s conjecture (the
A-theorem). I will present an explicit calculation of A at four loops,
generalising some recent results obtained for a theory with Yukawa and scalar
couplings to a theory that also includes a gauge coupling.