Axion monodromy in a model of holographic gluodynamics

TL;DR

The paper studies axion monodromy in a holographic model of gluodynamics using Witten's D4-brane construction, focusing on how the vacuum energy $E(\theta)$ depends on the theta angle and the emergence of metastable branches. It constructs the full backreacted supergravity solution in Type IIA (and its M-theory lift) to analyze large $\theta$ behavior, showing that the energy flattens and the mass gap shrinks below the UV KK scale. The authors identify two classes of domain walls interpolating between adjacent vacua, derive their tensions, and map out perturbative and nonperturbative instabilities that eventually end the metastable branches. They also explore the dynamical axion regime, discussing axion-driven inflation and axion strings, and discuss implications for embedding into full string compactifications and broader monodromy scenarios.

Abstract

The low energy field theory for N type IIA D4-branes at strong 't Hooft coupling, wrapped on a circle with antiperiodic boundary conditions for fermions, is known to have a vacuum energy which depends on the $θ$ angle for the gauge fields, and which is a multivalued function of this angle. This gives a field-theoretic realization of "axion monodromy" for a nondynamical axion. We construct the supergravity solution dual to the field theory in the metastable state which is the adiabatic continuation of the vacuum to large values of $θ$. We compute the energy of this state and show that it initially rises quadratically and then flattens out. We show that the glueball mass decreases with $θ$, becoming much lower than the 5d KK scale governing the UV completion of this model. We construct two different classes of domain walls interpolating between adjacent vacua. We identify a number of instability modes -- nucleation of domain walls, bulk Casimir forces, and condensation of tachyonic winding modes in the bulk -- which indicate that the metastable branch eventually becomes unstable. Finally, we discuss two phenomena which can arise when the axion is dynamical; axion-driven inflation, and axion strings.

Figures (10)

• Figure 1: The monodromy potential. The spectrum is invariant under shifts of $\theta$ by $2\pi$; a given state, under adiabatic evolution of $\theta$ rises in energy, becoming metastable when $\theta$ shifts by $\pi$ away from its value at zero energy.
• Figure 2: A plot of $E(\theta)$. The three branches corresponds to shifting $\theta$ by $2\pi$.
• Figure 3: The vacuum energy of the theory. On the left we have the vacuum structure when $\lambda/N \ll 1$ and so the energy behaves quadratically. This is the regime where the IIA description is valid. On the right we have the structure when $\lambda/N \gg 1$, and there is strong departure from the quadratic behavior. This corresponds to the M theory description being appropriate.
• Figure 4: A plot of the lightest glueball and lightest KK mode mass as a function of $x$. The lower solid curve is the lightest glueball mass, and the upper curve is the lightest KK mode ($n=1$.) Note that the glueball mass becomes parametrically smaller than the KK scale as we increase $x$.
• Figure 5: A plot of the potential energy density of a D6-brane at $u = u_0$ wrapping the $S^3\subset S^4$ labeled by $\varphi$.