Boundary-Boundary Duality on Regular Black Holes, Supersymmetric Solitons and Holographic Spinning Plasma Disks

Technical Summary: Boundary-Boundary Duality on Regular Black Holes, Supersymmetric Solitons and Holographic Spinning Plasma Disks

Problem Statement
The paper addresses the theoretical challenge of describing the equilibrium properties of strongly coupled, rotating relativistic fluids, specifically the quark–gluon plasma (QGP) observed in heavy-ion collisions. While hydrodynamics successfully describes the bulk evolution of such plasmas, there is currently no first-principles framework for their equilibrium states at large vorticity. Holography (AdS/CFT) offers a tool for modeling these systems at strong coupling, but constructing exact solutions that describe a finite, spinning plasma disk with a boundary reaching the speed of light has remained difficult. Furthermore, standard holographic setups typically involve a single conformal boundary, whereas the physical limit of a spinning fluid (where tangential velocity $v \to c$) suggests the emergence of a new causal structure.

Methodology
The authors construct a new family of exact, rotating solutions to four-dimensional Einstein–Maxwell theory with a negative cosmological constant. The construction is guided by:

1. Geometric Constraints: The requirement that the conformal boundary at $r \to \infty$ be Minkowski spacetime supporting a spinning perfect fluid with angular velocity $\Omega_0$.
2. Supersymmetry: Utilizing the integrability conditions of Rarita-Schwinger field transformations to identify supersymmetric limits.
3. Coordinate Analysis: Employing a specific coordinate system $(t, \phi, r, y)$ where $r$ acts as the holographic radial coordinate and $y$ parameterizes the Lorentzian energy scale.

The authors perform a rigorous analysis of the global geometry, checking for curvature singularities, the existence of event horizons, and the presence of closed timelike curves (CTCs). They apply standard holographic renormalization to compute the expectation value of the energy-momentum tensor ($\langle T_{\mu\nu} \rangle$) and conserved currents at the boundaries.

Key Contributions and Results

• Exact Rotating Solutions: The paper presents a new exact solution (Eq. 3.1) describing regular spinning AdS black holes and smooth solitons. These geometries are free of curvature singularities.
• Absence of Closed Timelike Curves (CTCs): The authors identify open regions in the parameter space where the solutions are free of CTCs, both outside and inside horizons. Super-extremal configurations in these regions correspond to smooth, horizonless solitons.
• Dual Conformal Boundaries: A central finding is that the bulk geometry possesses two distinct codimension-one conformal boundaries:
  1. The Minkowski Boundary ($r \to \infty$): Here, the expectation value of the energy-momentum tensor describes a finite spinning disk of strongly coupled conformal plasma. The edge of this disk rotates at the speed of light ($\gamma \to \infty$).
  2. The Rotating Boundary ($y \to \infty$): This boundary corresponds to a rotating black-hole geometry (or soliton) where the standard energy-momentum tensor vanishes ($\langle T_{\mu\nu} \rangle = 0$). However, the Cotton tensor is non-vanishing, defining a "dual graviton" configuration.
• Boundary-Boundary Duality: The paper establishes a duality between these two boundaries. Through a double Wick rotation ($t \to it, \phi \to i\phi$) and the identification of the holographic renormalization scale $r$ with the Lorentz factor $\gamma$ of the fluid ($r \leftrightarrow \gamma$), the geometry at $y=\infty$ is shown to be the dual graviton of the spinning plasma at $r=\infty$.
  • The energy density of the dual graviton exactly reproduces the energy density of the plasma.
  • Electromagnetic duality exchanges the electric and magnetic currents between the two boundaries, providing a generalized mirror symmetry.
  • Consequently, the Lorentz factor of the rotating fluid is identified with the electromagnetic dual of the renormalization scale.
• Supersymmetric Ground States: The authors demonstrate that both the "electric" and "magnetic" branches of the solution admit supersymmetric configurations (BPS solitons). These solutions are everywhere regular and horizonless, suggesting they represent stable ground states.
• Static Limit: In an appropriate limit, the rotating solutions reduce to the planar Reissner–Nordström–AdS black hole. However, the supersymmetric solitons do not possess a regular static limit; they require rotation to remain non-singular.

Significance and Claims
The paper claims to provide a consistent holographic formulation for strongly coupled rotating fluids in Minkowski spacetime, resolving the issue of the "light surface" by introducing a second conformal boundary.

• Resolution of Instability: The authors propose that the existence of everywhere regular supersymmetric rotating solitons resolves a longstanding problem regarding the stability of electrically charged black branes in supergravity. Previous work indicated that the supersymmetric limit of static charged black holes leads to naked singularities or instability. This paper suggests that rotation provides a natural endpoint for this instability, yielding stable, regular ground states.
• New Duality: The work introduces a "boundary-boundary duality" where the Lorentz scale of a physical fluid is dual to the renormalization group scale of a dual theory. This extends the concept of mirror symmetry to systems with finite angular velocity.
• Vacuum Structure: The paper notes that the vacuum state (vanishing $\langle T_{\mu\nu} \rangle$) of a strongly coupled QFT coupled to a global $U(1)$ current in Minkowski spacetime is non-trivial if the state is rotating, corresponding to an $AdS_3$ geometry with a radius proportional to the inverse of the charge.

The authors conclude that these results open new avenues for analyzing condensed matter phenomena in the presence of rotation and provide a framework for understanding the microscopic origin of entropy for spinning black holes via horizonless solitons.