Topologically twisted renormalization group flow and its holographic dual

TL;DR

This paper explores a holographic dual description of topologically twisted renormalization group flows in Euclidean field theories, revealing conditions for non-trivial fixed points and their gravitational duals within the AdS/CFT framework.

Contribution

It develops a holographic model for topologically twisted RG flows, showing that certain bulk theories support non-trivial fixed points with Euclidean AdS metrics.

Findings

Non-trivial fixed points require fine-tuning in the bulk theory.

O(3) Yang-Mills coupled with Einstein gravity supports such fixed points.

The model provides a gravitational dual for scale-invariant but non-conformal Euclidean field theories.

Abstract

Euclidean field theories admit more general deformations than usually discussed in quantum field theories because of mixing between rotational symmetry and internal symmetry (a.k.a topological twist). Such deformations may be relevant, and if the subsequent renormalization group flow leads to a non-trivial fixed point, it generically gives rise to a scale invariant Euclidean field theory without conformal invariance. Motivated by an ansatz studied in cosmological models some time ago, we develop a holographic dual description of such renormalization group flows in the context of AdS/CFT. We argue that the non-trivial fixed points require fine-tuning of the bulk theory in general, but remarkably we find that the $O(3)$ Yang-Mills theory coupled with the four-dimensional Einstein gravity in the minimal manner supports such a background with the Euclidean AdS metric.