The Enhancon and N=2 Gauge Theory/Gravity RG Flows

TL;DR

This work analyzes ten-dimensional type IIB supergravity solutions that realize RG flows from ${\mathcal N}=4$ to ${\mathcal N}=2$ supersymmetric Yang–Mills theories and uses a D3-brane probe to diagnose the Coulomb-branch dynamics. A ring-shaped enhançon locus emerges where the probe tension vanishes, signaling the appearance of new massless degrees of freedom and suggesting interior excision of the supergravity solution. The IR running of the gauge coupling is captured by a logarithmic behavior near the enhançon, with a precise analytic expression for the running in terms of the IR variable $v$ and the parameter $v_e$. An SL(2,${\mathbb Z}$) duality acts on the enhançon vacua, permuting the $(p,q)$ dyons, and the work provides a concrete, geometrical realization of how gauge theory phenomena on the Coulomb branch are encoded in the dual gravity description, including a proposed consistency condition that the region inside the enhançon be excised to obtain a physical solution.

Abstract

We study the family of ten dimensional type IIB supergravity solutions corresponding to renormalisation group flows from N=4 to N=2 supersymmetric Yang-Mills theory. Part of the solution set corresponds to a submanifold of the Coulomb branch of the gauge theory, and we use a D3-brane probe to uncover details of this physics. At generic places where supergravity is singular, the smooth physics of the probe yields the correct one-loop form of the effective low energy gauge coupling. The probe becomes tensionless on a ring at finite radius. Supergravity flows which end on this ``enhancon'' ring correspond to the vacua where extra massless degrees of freedom appear in the gauge theory, and the gauge coupling diverges there. We identify an SL(2,Z) duality action on the enhancon ring which relates the special vacua, and comment on the massless dyons within them. We propose that the supergravity solution inside the enhancon ring should be excised, since the probe's tension is unphysical there.

Figures (3)

• Figure 1: The metric function $G_{vv}$ representing the moduli space probe result for the D3--brane. It is proportional to the probe's tension. The enhançon is at $v_e=1$ here. This is also the result for the running of the inverse squared Yang--Mills gauge coupling as a function of energy scale $v$. It stops running in the UV. On the right is a closeup, showing the logarithmic running near $v_e$, in the IR.
• Figure 2: The families of $(\chi,\alpha)$ curves for differing $\gamma$, given by equation (\ref{['partialresult']}). There are three classes of curves. The blue (middle) curve is $\gamma=0$, the $\gamma<0$ curves are below it, and the $\gamma>0$ curves are above. The flow from UV to IR along each curve is to the right. Recall that $\rho=e^\alpha$, and refer to the text for further physical interpretation of each curve.
• Figure 3: The functional dependence of the tension of $(1,0)$, $(0,1)$, and $(1,1)$ strings as one goes around a generic circle. At the enhançon, any point on the circle will have a lightest string/dyonic state.