Abstract
We present the superspace formulation of the local RG equation, a framework for the study of supersymmetric RG flows in which the constraints of holomorphy and R-symmetry are manifest. We derive the consistency conditions associated with super-Weyl symmetry off-criticality and initiate the study of their implications. As examples, we derive an expression for the a-function, and present an analog of the a-maximization equation, which is valid off-criticality. We also apply this machinery to the study of conformal manifolds and give a simple proof that the metric on such manifolds is Kahler.
Highlights
Renormalization group (RG) flows describe a trajectory in the space of theories, induced by a change of scale
We present the superspace formulation of the local RG equation, a framework for the study of supersymmetric RG flows in which the constraints of holomorphy and Rsymmetry are manifest
In the original formulation of the local RG (LRG) equation, there are just three consistency condition which can not be used to eliminate some anomaly coefficients as an algebraic function of the others (see eqs. (2.66) and (2.68) of [5]); these three equations are similar in form to eqs. (3.55), (3.62), and (3.52); in the superspace formalism we find many more consistency conditions
Summary
Renormalization group (RG) flows describe a trajectory in the space of theories, induced by a change of scale. Supersymmetric RG flows are known to have a rich structure and non-trivial properties, such as the non-renormalization theorems for the superpotential [7] and the exact formula for the β-function in gauge theories [8, 9] The derivation of these results is based on two properties of supersymmetric theories — R-symmetry and holomorphy. As in the framework of the LRG equation, we define a function a, which is a continuation off-criticality of the a coefficient in the Weyl anomaly, and find a relation between its derivative with respect to the coupling λI and the β function:. The paper is organized as follows: In section 2 we define the basic ingredients used in our formalism, namely the background fields and the generating functional W, and present the generalized super-Weyl (SW) symmetry. Throughout this paper we use the notations of [22]
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