Thermodynamic Stability and Phases of General Spinning Branes

TL;DR

The paper analyzes thermodynamic stability and phase structure for near-extremal spinning D3-, M5-, and M2-branes with multiple angular momenta, deriving stability domains in grand-canonical and canonical ensembles via supergravity and contrasting with a multi-R-charge field-theory model. It uncovers explicit boundary polynomials in angular-momentum ratios that bound stable configurations and shows that near these boundaries the system exhibits nonanalytic critical behavior with generic exponents γ ≈ 1/2, modified by degeneracies. Phase mixing between stable and unstable phases can entropically favor inhomogeneous angular-momentum distributions, effectively softening the boundary and indicating a first-order-like transition near χ ≈ 0.325. In Euclidean setups, large spin induces twists by R-symmetry in the partition function, partially restoring supersymmetry, and the holographic analysis yields confinement-scale relations such as M_gap ∼ T ε^{1−n/2}, with implications for QCD-like models and their limitations.

Abstract

We determine the thermodynamic stability conditions for near-extreme rotating D3, M5, and M2-branes with multiple angular momenta. Critical exponents near the boundary of stability are discussed and compared with a naive field theory model. From a partially numerical computation we conclude that outside the boundary of stability, the angular momentum density tends to become spatially inhomogeneous. Periodic Euclidean spinning brane solutions have been studied as models of QCD. We explain how supersymmetry is restored in the world-volume field theory in the limit of large spin and discuss the hierarchy of energy scales that develops as this limit is approached.

Figures (4)

• Figure 1: The solid black lines are contours of constant $\chi_{av}$ with $\chi_{av} < 1/3$. The grey lines are contours of constant $\chi_{av}$ with $\chi_{av} > 1/3$. The dashed line is the solution set of (\ref{['EntExt']}). The region below the dashed line is where entropy along a contour increases as one moves to larger $\chi$. If a contour intersects the dashed line, then the maximum of the entropy function along that contour is at the first intersection with the dashed line; otherwise the maximum is at the lower border $\lambda = 0$.
• Figure 2: The dimensionless ratio $\sigma_{av} = s_{av}^4/e_{av}^3$ is plotted against $\chi$ for two values of $\chi_{av}$ on either side of the phase transition: in a) $\chi_{av} = 0.324$ while in b) $\chi_{av} = 0.326$. In a) we see that the $\chi = 0.324$, $\lambda = 1$ solid phase wins out entropically; in b) the mixed phase with $\chi \approx 0.075$ and $\lambda \approx 0.46$ is entropically favored.
• Figure 3: The spectrum of momenta in the compactified $S^1$ direction of the D4-brane world volume. The larger ticks indicate bosons; the smaller ticks indicate fermions. The first line follows from standard thermal boundary conditions. The second and third lines show what happens when one approaches the boundary of the phase space (large angular momentum for fixed energy), either at an edge ($n=1$) or a corner ($n=2$). The splittings in these cases are on the order $\epsilon T$. In the close groupings of ticks in the second and third lines, the degeneracies follow the ratios $1:4:6:4:1$ and $1:2:1$, respectively.
• Figure 4: Energies scales in various attempts to find a supergravity dual to confining gauge theories. Also included for purposes of comparison is a cartoon sketch of real-world QCD and a generic lattice model. The quark masses shown are the parameters that enter into the lagrangian: constituent masses.