Quantum Wormholes in UV-Complete Gravity

• Quantum wormholes are defined as nontrivial spacetime structures incorporating UV completions, quantum corrections, and entanglement-based phenomena.
• They employ methodologies like renormalization group improvements, thin-shell constructions, and Euclidean path integrals to ensure stable and traversable solutions.
• Applications include experimental proposals using quantum interferometry and nonlinear optics to detect throat parameters and probe gravitational quantum effects.

A quantum wormhole is a topologically nontrivial configuration in a gravitational or quantum field theoretic setting that is intrinsically governed by quantum effects—such as ultraviolet (UV) completions, semiclassical back-reaction, quantum state entanglement, or quantum superposition—rather than purely classical geometry or exotic matter. Quantum wormholes span a range of formulations: from spacetime metrics incorporating quantum corrections (e.g., UV-regularized or renormalization-group-improved actions) to Euclidean spacetime instantons mediating tunneling, to hypothetical connections induced by entanglement (ER=EPR paradigm), as well as exact quantum solutions in phase space or quantum cosmology. This article reviews the principal frameworks, mathematical features, and physical implications of quantum wormholes as represented in state-of-the-art research on arXiv.

1. UV Completion, T-Duality, and Regularized Wormhole Geometries

String-theoretic corrections, especially T-duality, induce a fundamental minimal length scale, the zero-point length $\ell_0$, interpreted as a natural UV cutoff regulating short-distance divergences in gravitational backgrounds. The zero-point length originates from the mapping between relativistic path integral duality (Padmanabhan’s invariance $ds \to L_P^2/ds$) and closed-string T-duality, leading to a nonlocal deformation of the Green’s function, effectively replacing $(x-y)^2$ by $(x-y)^2 + \ell_0^2$ (Lobo et al., 22 Jun 2025).

The quantum-inspired wormhole solutions generated under such UV completions utilize a modified Morris–Thorne ansatz,

$$ds^2 = -e^{2\Phi(r)}dt^2 + \frac{dr^2}{1-b(r)/r} + r^2\,d\Omega^2,$$

where the shape function $b(r)$ is sourced from a smeared (non-singular) energy density,

$$\rho(r) = \frac{3\ell_0^2M}{4\pi(r^2+\ell_0^2)^{5/2}},$$

to obtain nonsingular, stable metrics free of curvature pathologies at $r\lesssim\ell_0$. Despite such regularity, the null energy condition (NEC) is generically violated everywhere in the bulk, i.e., $\rho + p_r < 0$ (Lobo et al., 22 Jun 2025).

To minimize and localize NEC violation, thin-shell constructions are employed:

• Type I, interior-exterior matching: The wormhole interior is joined to an exterior Schwarzschild solution at $r=a>2M$ via Israel–Lanczos junction conditions. The surface energy $\sigma$ and pressure $\mathcal{P}$ on the shell can be tuned such that NEC violation is confined to the shell, with $\sigma+\mathcal{P}\ge0$ for $a$ just outside the throat.
• Type II, cut-and-paste across the horizon: Two identical regular quantum-corrected black hole spacetimes are glued at $r=a>r_h$ (with $r_h$ the horizon radius), leading again to NEC violation strictly on the shell.

In both cases, all exotic matter content is pushed into an infinitesimal layer, preserving regular geometry and rendering the solution traversable for finite proper-time trajectories (Lobo et al., 22 Jun 2025).

2. Quantum Gravitational Corrections and Renormalization Group Improved Wormholes

Asymptotically Safe Gravity (ASG) incorporates renormalization group running of Newton’s constant $G(k)$, which becomes scale-dependent,

$G(r) = \frac{G_0 r^2}{r^2 + \xi^2},$

where $\xi$ is a quantum scale parameter. This directly modifies the field equations and the matter-gravity coupling (Rebouças et al., 21 Oct 2025).

When a wormhole is sourced by a realistic dark matter halo, e.g., the Dekel–Zhao profile,

$$\rho(r) = \rho_0\left(\frac{r}{r_c}\right)^{-a}[1 + (r/r_c)]^{a-3},$$

the scale-dependent $G(r)$ amplifies curvature near the throat and NEC violation at $r_0$ by a factor $1 + (\xi/r_0)^2$. Stability criteria based on the adiabatic sound speed $\langle v_s^2\rangle$ and a modified Tolman–Oppenheimer–Volkoff equation reveal an additional repulsive “quantum force,” absent when $\xi=0$, that can stabilize high-curvature throats.

Phenomenologically, the wormhole shadow radius scales almost linearly with $\xi$, and parameter regimes exist where the shadow agrees with Event Horizon Telescope measurements of Sgr A* for $\xi/M \simeq 0.8$–$0.9$ (Rebouças et al., 21 Oct 2025).

3. Quantum Wormholes from Euclidean Path Integrals and Canonical Quantization

Quantum wormholes in the sense of Euclidean quantum gravity are realized as normalizable, exponentially damped solutions to the Wheeler–DeWitt (WdW) equation in minisuperspace, typically under Hawking–Page boundary conditions (Rahaman et al., 16 Nov 2025, Darabi, 2011). For a closed Friedmann–Robertson–Walker model with minimally coupled scalars or perfect fluids,

$$\left\{ \frac{\hbar^2}{2M}\left[\frac{\partial^2}{\partial a^2} + \frac{p}{a}\frac{\partial}{\partial a}\right] - \frac{M}{2}k a^2 - \frac{\hbar^2}{2a^2}\left[\partial_\phi^2 + \frac{q}{\phi}\partial_\phi\right] + a^4V(\phi) \right\} \Psi(a,\phi) = 0,$$

with solutions regular at $a\to0$ and exponentially damped at large $a$. In such contexts, the wavefunction $\Psi(a,\phi)$ corresponds to a “handle” (wormhole) attached to the universe. In Kaluza–Klein extensions, wormhole wavefunctions admit either the external ($R$) or internal ($a$) scale as the throat variable, forming quantum bridges between topologically distinct regions (Rahaman et al., 16 Nov 2025, Darabi, 2011).

The path-integral approach for wormhole amplitudes, especially in the context of 1D quantum systems or 2D CFT, interprets the $n$-fold wormhole partition function as an $n$th Rényi trace of a special “thermo-mixed double” state, encoding classical and quantum correlations. This construction in 2D CFT via geometric path integrals reproduces gravitational Euclidean wormhole amplitudes in AdS$_3$ (Verlinde, 2021).

4. Quantum Field Theory Support and Traversability

Quantum field-theoretic back-reaction can provide NEC-violating stress-energy necessary for wormhole maintenance without invoking negative energy fluids:

• Einstein–Dirac–Maxwell wormholes: Solutions with minimally coupled Dirac and Maxwell fields exist where the quantum Dirac vacuum polarization supplies the requisite NEC violation, with well-defined throat radius, ADM mass, and net charge. Such wormholes are asymptotically flat and free of classical exotic matter sources, although their static forms are generically unstable under perturbations (Kain, 2023).
• Bohmian quantum corrections: Quantum Raychaudhuri equations incorporating a Bohmian “quantum potential” modify the effective stress–energy and the lensing properties of the geometry, formally paralleling the role of electric charge but with an origin in quantum anisotropies (Jusufi et al., 2018).
• Euclidean wormhole gases: In the Euclidean section, a dilute or degenerate gas of pointlike wormholes acts as a spacetime foam. At large scales, this renormalizes mass and couplings; at high energies, suitably engineered distributions eliminate UV divergences, yielding finite field theory Green’s functions (Savelova, 2012).

Quantum tunneling through wormhole throats of generalized Ellis–Bronnikov type is governed by the geometry-induced effective potential, with analytical solutions available for $n=2$ via confluent Heun functions and explicit delta-barrier approximations for transmission and reflection. Quantum mechanical tunneling renders the geometry traversable even when classical passage is forbidden (Furtado et al., 2022).

5. Quantum Energy Inequalities and Constraints

Negative energy densities required for traversability are severely restricted by quantum energy inequalities (QEIs):

• Timelike-averaged and null-averaged QEIs provide rigorous lower bounds on the smeared stress–energy tensor, e.g., $$\int f^2(t) \langle T_{\mu\nu} t^\mu t^\nu \rangle \gtrsim -C/\tau^4$$ for sampling time $\tau$ (Kontou, 2024).
• Short wormholes (with travel time shorter than the spatial geodesic) are generically ruled out in semiclassical gravity by the achronal averaged null energy condition (ANEC) and by QEIs unless the throat is Planckian or $b'(r_0) \to 1$ to extreme precision.
• Long wormholes (with travel time longer than the exterior path) evade the achronal ANEC but are tightly constrained by finite-segment null QEIs such as the double-smeared null energy condition (DSNEC). For instance, the Maldacena–Milekhin–Popov wormhole saturates the SNEC, essentially forbidding macroscopic throats under standard assumptions (Kontou, 2024).

A consequence is that, without modifications to QEIs or introduction of new negative-energy sources, semiclassical traversable wormholes appear physically admissible only at the Planck scale or with extreme parameter fine-tuning.

6. Entanglement, Electric-Flux Threading, and ER=EPR

The ER=EPR correspondence posits that entangled quantum systems can be interpreted as being connected by a “quantum wormhole.” In this framework, the “wormhole susceptibility” $\chi_\Delta$ quantifies the capacity for gauge flux threading:

• Classical Einstein–Rosen bridges have $\chi_\Delta^{(ER)} \sim 1/g_F^2$ for a $U(1)$ gauge theory.
• Quantum EPR wormholes exhibit $\chi_\Delta^{(EPR)} = q^2 f(m\beta, ma)$, which is suppressed by $(g_F q)^2$ relative to the classical case, but can be enhanced by increasing the number of entangled charges or the temperature (Engelhardt et al., 2015).

In both cases, the existence of a nonzero wormhole susceptibility signals the ability for an electric field to thread the wormhole, mimicking the classical observable even for Planck-scale, “quantum” wormholes.

7. Detection, Simulation, and Physical Implementation

Quantum metrology protocols have been proposed for detecting or constraining quantum/regularized wormhole properties:

• Quantum interferometric detection: Propagation of a coherent electromagnetic field through the modified metric of a distant wormhole imparts a phase shift sensitive to the throat radius. With current long-baseline interferometers, sensitivity to $b_0$ in the meter-to-kilometer range is, in principle, possible at parsec scales (Sabín, 2017).
• Nonlinear quantum optics: Kerr-nonlinear Mach–Zehnder interferometers can, in principle, estimate throat parameters with super-Heisenberg ($1/N^{3/2}$) scaling of the quantum Fisher information, surpassing the canonical $1/N$ scaling of linear metrology. This requires extremely high photon numbers and low optical loss (Sabín et al., 2018).
• Analog quantum simulation: Transmission lines based on dc-SQUID arrays can mimic 1D traversable wormhole spacetimes for sub-millimeter throat radii. Finite array impedance and quantum phase fluctuations analogize chronology protection, limiting the attainable geometries and possibly preventing the formation of closed timelike curves (Sabín, 2016).

These approaches are theoretical proposals; practical obstacles include noise, decoherence, and technological limits in realizing the requisite geometric or quantum-state control.

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Quantum wormholes represent the confluence of quantum field theory, semiclassical and modified gravity, global spacetime topology, and quantum information. Their physical relevance is circumscribed by strict quantum energy constraints, but they provide vital laboratories for exploring UV-complete gravity, the fate of topology, and the operational meanings of entanglement in gravitational theories. Active research continues on the viability, detectability, and implications of quantum wormholes in both fundamental theory and candidate observational channels.