Fivebrane Deconfinement Transition

• The fivebrane deconfinement transition is a process where horizonless NS5-brane configurations shift to a phase with a black hole horizon, liberating non-abelian little string degrees of freedom.
• Key dynamics are controlled by the fivebrane ring radius reaching the non-abelian scale, leading to light D2-brane excitations and breakdown of the semiclassical supergravity description.
• The duality with AdS3/CFT2 relates this transition to the Hawking–Page phase change, providing a calculable model of black hole emergence and deconfinement in gravity.

The fivebrane deconfinement transition refers to a nonperturbative process in string theory and supergravity in which a system of NS5-branes, initially in a “confined” regime described by horizonless BPS supergravity solutions (“fivebrane stars”), undergoes a transition to a “deconfined” phase characterized by the dynamical liberation of non-abelian little string degrees of freedom and the formation of a black hole horizon. This transition provides a direct, calculable realization of deconfinement and black hole emergence in the gravity description and has been identified as the bulk dual of the Hawking–Page transition in $\mathrm{AdS}_3/\mathrm{CFT}_2$ correspondence (Martinec et al., 9 Dec 2025, Martinec et al., 25 Nov 2024).

1. Supergravity and Brane Setup

Fivebrane deconfinement is formulated within type II string theory compactified as $\mathbb{R}^{1,1}\times S^1_y \times T^4$, with $n_5$ NS5-branes and $n_1$ fundamental strings wrapped on $S^1_y$ (the “P” charge is momentum along $S^1_y$). The BPS supergravity ansatz employs chiral wave profiles $X^i_{\text{NS5}}(v)$ and $X^i_{\text{F1}}(v)$ in the common transverse $\mathbb{R}^4$. The bosonic fields and their couplings arise from an effective ten-dimensional action coupling the bulk NS–NS plus R–R supergravity sector to the brane worldvolume effective actions. The BPS solutions are constructed by solving for harmonic functions with delta-function sources localized on the wave profiles, yielding smooth, horizonless “supertube” backgrounds parameterized by collective brane profiles (Martinec et al., 9 Dec 2025, Martinec et al., 25 Nov 2024).

The six-dimensional string frame metric (NS–NS sector) is

$$ds^2 = -\frac{2}{Z_1}(dv+\beta)\biggl[du+\omega+\frac12\,\mathcal F\,(dv+\beta)\biggr] + Z_2\,d\mathbf x^2 + ds^2(T^4),$$

with harmonic functions $Z_1$, $Z_2$, and one-forms determined via layered Poisson equations sourced by the constituent branes’ trajectories. Circular configurations yield explicit solutions where the key control parameters are the fivebrane ring radius $a$, string ring radius $b$, charges $Q_5$, $Q_1$, and $Q_p$, and the string coupling $g_s$.

2. Order Parameters and the Deconfinement Scale

The transition is controlled by the radius of gyration $a$ of the fivebrane configuration. As $a$ is reduced, the separation between individual NS5-brane strands approaches a fundamental “non-abelian scale”,

$$\ell_{\rm na} = \sqrt{\alpha'}\left(\frac{V_4}{(\alpha')^2}\right)^{1/2} \sim \sqrt{\alpha'} \times \mathcal{O}(1),$$

where $V_4$ is the volume of the compact $T^4$. At $a \simeq \ell_{\rm na}$, D2-brane excitations stretched between the NS5-branes become light, and the low-energy abelianized (Coulomb branch) description in terms of horizonless supergravity solutions becomes invalid. The physical implications are that the system becomes sensitive to non-abelian dynamics corresponding to “deconfined” little string degrees of freedom—analogous to the liberation of color degrees of freedom in gauge theory deconfinement (Martinec et al., 9 Dec 2025).

3. Microphysics, Worldvolume Dynamics, and Collective Modes

The effective description of the brane ensemble is a 1+1-dimensional sigma model for the mutually BPS brane sources on the supergravity background, encoding both transverse (geometric) and internal (gauge and 2-form) sector fluctuations. A collective rescaling mode (the “breathing mode” associated with the relative scale of the ring radii) controls the depth of the emergent $AdS_2$ throat region for ultracompact configurations; its effective dynamics, after integrating out other fluctuations, is governed by a Schwarzian action,

$$S_{\rm Sch}[f] = -C \int dt\, \biggl\{\tan\frac{\pi}{\beta}f(t)\,,\, t \biggr\} + \cdots,$$

characteristic of $AdS_2$ near-extremal gravitational systems. This indicates a direct connection to SYK-type/Schwarzian quantum mechanics at the boundary of the black-hole-like throat (Martinec et al., 9 Dec 2025).

4. Thermodynamics: Star and Black Hole Phases

The entropy in the horizonless (star) phase is

$$S_{\rm star} \simeq 2\pi \sqrt{\frac{c_\perp}{6} N_\perp}, \qquad (c_\perp = 4),$$

with $N_\perp$ denoting excitation quanta in transverse modes. The black hole phase is described by a little string Hagedorn density of states,

$$S_{\rm BH}(E) \simeq \beta_H E, \qquad \beta_H = 2\pi \sqrt{n_5\alpha'},$$

where excitation energy $E$ is primarily accommodated by internal degrees of freedom.

The phase transition is first-order in the thermodynamic sense: as energy or excitation partition varies, there is a critical point where the free energies of both phases coincide,

$F_{\rm star} = F_{\rm BH},$

defining the transition. For $N_\perp$ above a critical value, the star phase is entropically favored; below, the black hole (deconfined) phase dominates. At the transition, the free energy is continuous but non-analytic. The heat capacity is positive in the star phase and diverges (Hagedorn) in the deconfined regime (Martinec et al., 25 Nov 2024).

5. Breakdown of Semiclassics and Black Hole Formation

As the fivebranes coalesce ($a\to\ell_{\rm na}$), the mass of stretched D2-branes vanishes. The semiclassical gravity description ceases to be accurate, as the low-energy non-abelian little string dynamics becomes dominant. The system then enters the black hole phase, exhibiting a deep $AdS_2$ throat, and the entropy approaches that of extremal BTZ black holes,

$$S_{\rm BTZ} = \frac{A_{\rm hor}}{4 G_6} = 2\pi\sqrt{n_5 n_1 n_p} = 2\pi \sqrt{\frac{c}{6} L_0},$$

with $A_{\rm hor}$ the horizon area, $G_6$ the six-dimensional Newton constant, and $L_0$ the left-moving oscillator number in the dual CFT. This matching confirms the identification of the deconfined phase with black hole microstates and Hagedorn little string thermodynamics (Martinec et al., 9 Dec 2025).

6. AdS/CFT Interpretation and the Hawking–Page Transition

In $\mathrm{AdS}_3/\mathrm{CFT}_2$ duality, the bulk fivebrane deconfinement transition precisely corresponds to the Hawking–Page transition, or the deconfinement transition in the dual boundary CFT, at the critical temperature $T_c = 1/(2\pi R_y)$. In the bulk, the confined phase consists of horizonless fivebrane stars with free energy $F_{\rm star} \sim -N^0 T^0$ ($N=n_1 n_5$ large), while the black hole phase features a BTZ horizon with $F_{\rm BH} \sim -N T^2$. The sign change in $F_{\rm BH} - F_{\rm star}$ at $T_c$ traces the location of the phase transition, corroborating the correspondence between semiclassical deconfinement in gravity and large-$N$ phase structure in the boundary theory (Martinec et al., 9 Dec 2025).

7. Fluctuations, Probes, and Onset of Deconfinement

The onset of deconfinement is traceable via two-point functions. In the star phase, the normalized fivebrane density operator $\rho(v,\vec x)$ and its correlator exhibit large fluctuations for separations less than the blob radius $r_b$. For bulk graviton probes, the absorption cross section is enhanced for momentum transfers $\sim 1/r_b$ and grows as $r_b$ shrinks, indicating the system’s approach to black hole-like absorption/graybody behavior. Near-BPS perturbations around the background yield an effective quantum mechanics on the moduli space of BPS configurations, with high-energy ergodicity underlying the slow thermalization and collapse to the BTZ deconfined regime (Martinec et al., 25 Nov 2024).

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The fivebrane deconfinement transition provides a concrete and calculable framework for studying the emergence of black holes from brane collective dynamics, establishing deep connections between bulk string dynamics, worldvolume gauge theory, and boundary CFT phenomenology (Martinec et al., 9 Dec 2025, Martinec et al., 25 Nov 2024).