Oliver J. Rosten

Manifestly gauge-invariant QCD

We uncover a method of calculation that proceeds at every step without fixing the gauge or specifying details of the regularisation scheme. Results are obtained by iterated use of integration by parts and gauge invariance identities. Calculations can be performed almost entirely diagrammatically. The method is formulated within the framework of an exact renormalisation group for QED. We demonstrate the technique with a calculation of the one-loop beta function, achieving a manifestly universal result, and without gauge fixing.

A generalised manifestly gauge invariant exact renormalisation group for SU(N) Yang–Mills

We take the manifestly gauge invariant exact renormalisation group previously used to compute the one-loop β function in SU(N) Yang–Mills without gauge fixing, and generalise it so that it can be renormalised straightforwardly at any loop order. The diagrammatic computational method is developed to cope with general group theory structures, and new methods are introduced to increase its power, so that much more can be done simply by manipulating diagrams. The new methods allow the standard two-loop β function coefficient for SU(N) Yang–Mills to be computed, for the first time without fixing the gauge or specifying the details of the regularisation scheme.

A manifestly gauge invariant, continuum calculation of the SU(N) Yang-Mills two-loop beta function

The manifestly gauge invariant exact renormalization group provides a framework for performing continuum computations in

Manifestly gauge invariant QED

SU(N)

Exact scheme independence at two loops

Yang-Mills theory, without fixing the gauge. We use this formalism to compute the two-loop

A MANIFESTLY GAUGE INVARIANT AND UNIVERSAL CALCULUS FOR SU(N) YANG–MILLS

\ensuremath{\beta}

General Computations Without Fixing the Gauge

function in a manifestly gauge invariant way, and without specifying the details of the regularization scheme.

A primer for manifestly gauge invariant computations in SU(N) Yang-Mills

We uncover a method of calculation that proceeds at every step without fixing the gauge or specifying details of the regularisation scheme. Results are obtained by iterated use of integration by parts and gauge invariance identities. Calculations can be performed almost entirely diagrammatically. The method is formulated within the framework of an exact renormalisation group for QED. We demonstrate the technique with a calculation of the one-loop beta function, achieving a manifestly universal result, and without gauge fixing.

Scheme independence to all loops

We further develop an algorithmic and diagrammatic computational framework for very general exact renormalization groups, where the embedded regularisation scheme, parametrised by a general cutoff function and infinitely many higher point vertices, is left unspecified. Calculations proceed iteratively,by integrating by parts with respect to the effective cutoff, thus introducing effective propagators, and differentials of vertices that can be expanded using the flow equations; many cancellations occur on using the fact that the effective propagator is the inverse of the classical Wilsonian two-point vertex. We demonstrate the power of these methods by computing the beta function up to two loops in massless four dimensional scalar field theory, obtaining the expected universal coefficients, independent of the details of the regularisation scheme.

Gauge invariant regularization in the AdS/CFT correspondence and ghost D-branes

Within the framework of the Exact Renormalization Group, a manifestly gauge invariant calculus is constructed for SU(N) Yang–Mills. The methodology is comprehensively illustrated with a proof, to all orders in perturbation theory, that the β function has no explicit dependence on either the seed action or details of the covariantization of the cutoff. The cancellation of these nonuniversal contributions is done in an entirely diagrammatic fashion.