On renormalization group flows in four dimensions

Dftt 17/98 a Proof of the Irreversibility of Renormalization Group Flows in Four Dimensions

We present a proof of the irreversibility of renormalization group flows, i.e. the c–theorem for unitary, renormalizable theories in four (or generally even) dimensions. Using Ward identities for scale transformations and spectral representation arguments, we show that the c–function based on the trace of the energy-momentum tensor (originally suggested by Cardy) decreases monotonically along r...

Holographic Renormalization Group Flows: The View from Ten Dimensions †

The holographic description of supersymmetric RG flows in supergravity is considered from both the five-dimensional and ten-dimensional perspectives. An N = 1∗ flow of N = 4 super-Yang Mills is considered in detail, and the infra-red limit is studied in terms of IIB supergravity in ten dimensions. Depending on the vevs and the direction of approach to the core, the supergravity solution can be ...

Optimized renormalization group flows

We study the optimization of exact renormalization group ~ERG! flows. We explain why the convergence of approximate solutions towards the physical theory is optimized by appropriate choices of the regularization. We consider specific optimized regulators for bosonic and fermionic fields and compare the optimized ERG flows with generic ones. This is done up to second order in the derivative expa...

On Renormalization Group Flows and Exactly Marginal Operators in Three Dimensions

As in two and four dimensions, supersymmetric conformal field theories in three dimensions can have exactly marginal operators. These are illustrated in a number of examples with N = 4 and N = 2 supersymmetry. The N = 2 theory of three chiral multiplets X,Y,Z and superpotential W = XY Z has an exactly marginal operator; N = 2 U(1) with one electron, which is mirror to this theory, has one also....

Aspects of Renormalization Group Flows