Papers

Defects are both physically rich objects and powerful tools in modern quantum field theory. They are extended operators, such as boundaries, impurities, and probe particles, embedded in many-body systems. In this dissertation, we study the universal aspects of defect dynamics from the perspective of symmetry principles. We bring together several themes, including defect renormalization group flows, effective string theory, and impurities in atomic quantum gases.

The relation $M_H^2\simeq M_ZM_t$, previously proposed as a non-trivial Higgs mass coincidence, is reconsidered with present electroweak inputs and with a scheme-consistent matching analysis. With the 2025 PDG values for $M_Z$, $M_W$ and $M_H$, and the ATLAS-CMS direct top-mass combination, the pole-level ratio is $\rho_{Zt}=M_ZM_t/M_H^2=1.00362\pm0.00261$. Thus an exact pole-level geometric relation predicts either $M_H=125.426\pm0.120\,\mathrm{GeV}$ or $M_t=171.898\pm0.302\,\mathrm{GeV}$, which is still a $1.4\sigma$ test rather than an exclusion. By contrast, the companion arithmetic relation gives $\rho_{Wt}=(M_W+M_t)/(2M_H)=1.00994\pm0.00159$ and is not a viable exact mass sum rule. We then evaluate the complete NNLO weak-scale $\overline{\mathrm{MS}}$ matching formulae at $\mu=M_t$. In the standard convention one obtains $\widehat\rho_{Zt}(M_t)=\sqrt{g_2^2+g_Y^2}\,y_t/(4\sqrt2\lambda)=0.96714\pm0.00361$. Consequently, the exact running-coupling boundary condition $\lambda=g_Zy_t/(4\sqrt2)$ at the top scale would predict $M_H=123.19\pm0.20\,\mathrm{GeV}$, or equivalently $M_t=177.81\pm0.50\,\mathrm{GeV}$ when $M_H$ is held fixed. This is incompatible with the measured point. A possible symmetry explanation must therefore act on pole-level threshold quantities, or provide a finite matching factor $\kappa_{\rm th}=1.0340\pm0.0039$ at the electroweak scale. We formulate this requirement as a target for custodial/top-Higgs or triality-like symmetry extensions.

In this work, we investigate higher-derivative quantum field theories and the problem of Ostrogradsky instability within an open-system Keldysh-Lindblad framework. Coupling the ghost sector to dissipative baths generates non-perturbative effective masses and dissipative widths through self-consistent gap equations. Above a critical coupling, the nonequilibrium dynamics develops bifurcated dissipative branches, signaling the emergence of a dissipative phase transition and a nontrivial critical structure in parameter space. We find that the resulting dissipative dynamics can suppress ghost excitations through two distinct mechanisms: in one branch, a large dynamically generated effective mass preserves a quasiparticle-like excitation, while in the second branch, strong dissipative broadening destroys the quasiparticle character through overdamped dynamics. Our results suggest that dissipative effects may provide a nonequilibrium mechanism for the spectral suppression of Ostrogradsky ghosts. The comparison with the healthy sector indicates that the stabilization mechanism is intrinsically tied to the ghost-like spectral structure.

We study algebraic locality principles on a 2+1D closed lattice in the presence of a Gauss law for a non-invertible symmetry. Prior work in arXiv:2509.03589 showed that when enforcing the Gauss law of an invertible symmetry, the principle of "Haag duality" is preserved exactly, and "disjoint additivity" is preserved after appropriate treatment of discreteness artifacts. Here we show that for a large class of non-invertible on-site symmetries, Haag duality is preserved exactly only for sufficiently nice, "cuspless" regions. For cusped regions, we instead have a weak form of Haag duality that requires adding a collar. Our results apply to double models with a purely magnetic constraint, and to the more general framework of constraints induced by the on-site action of a Hopf algebra. In particular, we treat a class of extended string-net models explicitly. We also demonstrate disjoint additivity for double models based on a group, and a weakened form of disjoint additivity in the setting of a general Hopf algebra.

We initiate the study of gravitational-wave lensing in the wave-optics regime within modified gravity. We consider a phenomenological setup in which the gravitational-wave amplitude obeys a curvature-coupled propagation equation. This framework reproduces the standard GR behaviour in the geometric-optics regime, while leading to qualitatively different infrared dynamics. In particular, the usual argument implying that the amplification factor approaches unity in the zero-frequency limit no longer applies. This is due to the persistence of curvature-induced interactions in the infrared, which modify the natural propagation basis itself. As a result, the standard Fresnel treatment ceases to be valid at sufficiently low frequency. The correct infrared regime is instead controlled by an interacting static Green function, with a finite-frequency completion provided by a partial-wave formulation. We show that this structure admits an equivalent distorted-wave interpretation, in which the curvature interaction is absorbed into a dressed reference propagation basis, while the residual lensing effect is encoded in finite-frequency phase shifts. We further demonstrate that these phenomena admit a natural interpretation in the language of scattering amplitudes. Wave-optics lensing can therefore probe propagation-level departures from GR that remain entirely invisible in geometric optics.

The chiral Lagrangian is a cornerstone of modern particle physics, offering a systematic and quantitative description of low-energy pions. Using tools from the modern scattering amplitudes program, we show that consistent multiparticle dynamics impose novel constraints on the coupling constants of this theory. In the planar limit, these constraints imply that certain Wilson coefficients of the chiral Lagrangian are bounded from below by the chiral anomaly. Our results reveal a subtle connection between the anomalous and nonanomalous sectors of the underlying strong interactions, while introducing a novel formulation of multipositivity bounds that holds for any planar tree-level theory.

We revisit the computation of four-point wavefunction coefficients and correlators for external conformally coupled scalars exchanging a particle of generic mass and spin. Much of the phenomenology of cosmological collider physics in the near-de Sitter limit follows from these functions. Computing them in detail is a central challenge in the cosmological bootstrap. Using the cosmological Grassmannian, we write these objects in closed form using hypergeometric functions and Legendre polynomials. We achieve this by writing the standard bootstrap differential equation using the Plücker coordinates of the Grassmannian, and using the basis of Mandelstam invariants. The exchange in the s-channel can be written in terms of a hypergeometric function of the S Mandelstam, while the spin information appears as an overall Legendre polynomial factor that also depends on the other Mandelstams. We fix the boundary conditions by first demanding the absence of unphysical singularities, and, for correlators, by further matching to a kinematic limit in momentum space. Our formulae in Grassmannian space are much simpler than their counterparts in momentum space, demonstrating another useful application of the Grassmannian as a kinematic space for cosmology.

We show that Maxwell theory with a codimension-$1$ Chern-Simons interface supports chiral electromagnetic surface waves on the interface, even when the bulk theory on both sides is conventional vacuum electrodynamics in infinite space. Solving the exact boundary value problem we find that the Chern-Simons interaction acts with opposite sign on the two helicities oriented along the interface, giving rise to one normalizable mode localized on the interface. This mode is a gapless chiral surface photon with linear dispersion and a frequency-independent index of refraction set by the Chern-Simons coefficient. This mode exists despite the absence of ambient material response or geometric confinement.

In this work, we investigate the physics of charged black holes modified by Weyl corrections, which emerge from the non-minimal coupling between spacetime curvature and electromagnetism. We begin by revisiting the thermodynamics of these systems, deriving the Hawking temperature, Wald entropy, and heat capacity to examine how the Weyl correction parameter reshapes the landscape of thermal stability and phase transitions. Then, we apply a topological method to classify the thermodynamic states and reveal the impact of the Weyl modifications on this classification. To explore astrophysical signatures, we analyze the null trajectories and shadow cast by photons under two-photon polarization modes, deriving observational constraints on the black hole parameters. Finally, we model the accretion disk around these black holes. By calculating the energy flux, spectral luminosity, and differential luminosity, we show how these corrections leave a detectable trace on the emitted radiation.

The previously formulated the mass gap approach to QCD, based on a new insights into its ground state(vacuum), makes it possible to exactly define the dynamically generated gluon pole mass. We developed a non-perturbative multiplicative renormalization program for the corresponding massive full gluon propagator. Its asymptotic properties have been analyzed, including the perturbation theory limit to the free gluon state, i.e., no asymptotic freedom effect. The peculiarities of the mass-shell structure of the massive full gluon propagator has been discussed. The inconsistency of the canonical gauge in QCD is fixed. Our approach does not allow the massive gluons to be mass-shell objects. This prevents them to appear in the physical spectrum (confinement of the massive gluon states). The massive gluons may exist in the vacuum or inside hadrons only. Expression for massive full gluon propagator in Euclidean metric for the lattice simulations is present. It is also shown that the massive solution has a correct limit to the massless full gluon propagator, when the gluon pole mass is to be formally put zero.

We study cosmological collider (CC) signatures generated by right-handed neutrino loops in the setup of inflation combined with the neutrino seesaw mechanism. We formulate the inflaton interaction with the right-handed neutrinos through a unique dimension-5 operator respecting shift symmetry, which induces an effective chemical potential in the slow-roll background, leading to helicity-dependent production of right-handed neutrinos and enhancing the CC signatures. The right-handed neutrino is described by a two-component Weyl spinor with a Majorana mass term. Using the Schwinger-Keldysh formalism, we derive a set of seed integrals for fermion propagators of the right-handed Majorana neutrino. With these, we compute the factorized nonlocal contributions to the three-point inflaton correlator generated by the triangle loop of right-handed neutrinos. We show that the chemical potential can substantially soften the heavy-mass Boltzmann suppression and amplify the oscillatory non-Gaussianity signatures associated with the dominant helicity mode. We systematically analyze the spinor structure, the factorization of fermion triangle loop, the loop-momentum integrals and the time seed integrals, which give a controlled computation of the nonlocal contributions to the CC signals of the right-handed neutrinos.

Relativistic hydrodynamics successfully provides an effective field theory description for the low energy regime of many out-of-equilibrium systems. On the other hand, in this paper we prove that any stand-alone hydrodynamic EFT is inherently acausal and therefore requires the addition of transient UV modes in order to restore causality. This is made possible by the exponential decay of dissipative hydrodynamics in a majority of the lightcone, allowing the possibility of a causal description that still reduces to the hydrodynamic one at late timescales. We then investigate the emergence and possible restrictions of the non-hydrodynamic modes in these causal UV completions.

We show that anyon chains, after stabilizing with infinite-dimensional ancilla spaces, factorize locally as tensor products of infinite-dimensional Hilbert spaces. This implies that any unitary fusion category can be realized as symmetries on a tensor product of infinite-dimensional Hilbert spaces. We then show that any two anyon chains with the same symmetry category are related by a symmetry-compatible locality-preserving unitary after stabilizing with infinite-dimensional ancilla, showing that for a fixed fusion category, there is a single stable equivalence class of symmetry realizations on the lattice via anyon chains. As a corollary of our proof, we show that the physical boundary algebras of Levin-Wen type models are bounded spread isomorphic after stabilization if and only if they have the same bulk topological order.

Irreversibility theorems – such as the $A$-theorem – establish a hierarchy among fixed points of the renormalization group flow. The strongest thesis of this type of theorems would be that there exists a scalar function $A$ (generally suggested by the topological Weyl anomaly) and a positive definite metric $G_{IJ}$ in the space of couplings such that the renormalization group flow satisfies a gradient equation, $\partial_I A= G_{IJ}\beta^J$, in which case $A$ is locally monotonic along the flow. In this paper we consider the long-range multiscalar $\phi^4$ theory, a theory without a local energy-momentum tensor that is unitary in $d=2,3$ and that is believed to be conformally invariant at fixed points, and show that its renormalization group flow satisfies the gradient structure up to the third loop order in the coupling. We also show that $A$ and $G_{IJ}$ can be matched to the leading nontrivial order with the sphere free-energy $\tilde{F}$ and Zamolodchikov's metric $C_{IJ}$ of the corresponding conformal theory concentrating on the examples of the long-range vector $O(N)$ and hypercubic $H_N$ models. Our results imply a perturbative proof of the $\tilde{F}$-theorem at the leading nontrivial order. We conclude the paper discussing briefly whether this result should hold to the next orders in perturbation theory.

We propose that holography contains an exact kinematic sector distinct from holographic dynamics. The appropriate setting for this sector is a CFT on an open solid torus in the Weyl frame. The open solid torus introduces an intrinsic scale, and the Weyl frame makes this scale manifest as an extra bulk direction. The resulting bulk-boundary pairs are exact and finite: no cutoff, large-$N$ limit, strong-coupling assumption, or heavy-operator approximation is required. The AdS geometry appearing in this sector should be understood as a kinematic geometry; only in special CFTs and appropriate limits is it promoted to a dynamical semiclassical bulk. The standard boundary-anchored dictionary entries are recovered only as singular limits. As a striking demonstration, we show that Weyl-frame two-point functions provide a replica-free definition of entanglement entropy.

We investigate the elliptic-flow splitting between prompt $D^0$ and $D_s^+$ mesons within a heavy-quark transport framework with sequential hadronization, in which $D_s^+$ forms at $1.2\,T_c$ and $D^0$ at $T_c$. We present predictions for the $p_T$-differential $v_2$ and $D_s^+/D^0$ yield ratio in O–O $0$–$20\%$ collisions at $\sqrt{s_{NN}} = 5.36$~TeV, where preliminary ALICE data are available. The sequential scenario reproduces the observed $v_2(D^0) > v_2(D_s^+)$ ordering and predicts an enhanced $D_s^+/D^0$ ratio at low $p_T$, whereas a simultaneous baseline yields the opposite ordering. Decomposing the hadronic splitting into its partonic components, we show that the $v_2$ ordering is driven by the late-stage flow accumulated by $D^0$-parent charm quarks during the $1.2\,T_c \to T_c$ interval, with hadronic rescattering essential to preserve the signal in small systems. A systematic scan across nine collision configurations spanning O–O and Pb–Pb centralities reveals a universal linear scaling between the hadronic splitting and the partonic flow increment accumulated during this window. This establishes the $D^0$–$D_s^+$ flow splitting as a hadronization chronometer of the QGP at $\sqrt{s_{NN}} = 5.36$~TeV.

We find that the effective dimension of the Wasserstein space of energy eigenstates decreases as a quantum system becomes more chaotic. To demonstrate this, we study a quantum coupled harmonic oscillator system using Husimi Q-representations, to which Sinkhorn-regularized optimal transport is applied to construct an embedding geometry via the Gram-spectrum method. We also demonstrate that exponential OTOC growth, referred to here as quantum scrambling even in the absence of chaos, induces a folding structure in the emergent Wasserstein space, which may underlie the chaotic reduction of the Wasserstein dimension. At the separatrix (the scrambling point) of the inverted harmonic oscillator, the Wasserstein distance correctly captures the Lyapunov exponent. Furthermore, we discover that a branching structure in the Wasserstein space signals quantum scar states within the chaotic sea of phase space. Our optimal transport approach thus provides a new diagnostic for quantum chaos, quantum scrambling, quantum scars, and quantum Lyapunov exponents. The observed chaotic dimensional reduction also supports the recent conjecture [arXiv:2604.17649] that the Wasserstein space serves as an emergent holographic space through the manifold hypothesis, since chaoticity is a characteristic signature of black holes in holography.

We study chaos-integrability transition purely within a BPS subspace of a specific supersymmetric model that interpolates between the chaotic $\mathcal{N}=2$ SYK model and an integrable $\mathcal{N}=2$ "commuting" SYK model. Using the framework of BPS chaos, we analyze the spectrum of an operator projected onto the BPS subspace. We numerically find that its spectral statistics exhibit random-matrix behavior near the SYK limit and smoothly transitions to Poisson statistics near the integrable limit. Our results provide a direct example of a chaos-integrability crossover diagnosed solely from BPS states.

By solving algebraic relations for the conditions of Haantjes structure on a Lie algebra ${\G}$ and by using the corresponding automorphism group we proceed to classify all inequivalent algebraic Haantjes structures on ${\G}$. In this manner, we obtain 34 inequivalent algebraic Haantjes structures on the ${h_{4}}$ Lie algebra. We deform the chiral sigma model on a Lie group by using Haantjes structure on it. Then we try to obtain conditions on this structure such that the deformed sigma model remains to be integrable. Finally, using the ${h_{4}}$ Haantjes structures and solving this conditions three new integrable sigma models on the ${H_{4}}$ Lie group are obtained.

We report the first rigorous evaluation of the physical mass of electroweak vortex rings, establishing precise values of 18.01 and 26.80 TeV for solutions characterized by different winding numbers. Analysis of the internal structure reveals that repulsive interactions shape the geometry of these configurations, while complex current distributions lead to a neutral analogue of Ampere's circuital law, suggesting a corresponding self-stabilizing pinch mechanism. These findings set the energy scales for the potential observation of such configurations at future colliders and offer a framework for understanding topological structures in the Standard Model.

We study exact defect $g$-functions for integrable line defects in two-dimensional integrable quantum field theory and use them to probe defect fusion. We consider three settings: fusion of purely transmitting topological defects, fusion of non-topological defects with reflection and transmission, and fusion of a defect with an integrable boundary. For topological defects, the separated logarithmic $g$-function is additive, and the fusion limit is controlled by the multiplicative composition of transmission factors. For non-topological defects, separation-dependent phases in the Bethe-Yang equations produce oscillatory finite-size effects, while the fused defect is described by effective reflection and transmission amplitudes. In the Ising examples studied here, fusion involving non-topological defects lowers the finite localized contribution to the entropy, whereas topological defect-boundary fusion leaves it unchanged.

The entangling power of a unitary operator quantifies its ability to generate entanglement from product states and provides a natural probe of quantum many-body dynamics. Entanglement extremization at points of enhanced symmetry has previously been observed in high-energy scattering. In this work we compute the time-averaged entangling power of anisotropic Heisenberg spin chains across two-site models and finite-size systems, as well as the entangling power of the two-magnon $S$-matrix in the thermodynamic limit. For two-site models we establish a monotonic hierarchy: the entangling power decreases as the symmetry group grows, reaching its minimum at the $SU(2)$ XXX point. Finite-size XXZ chains exhibit sharp dips at the $SU(2)$ points $\Delta=\pm 1$ and the free-fermion point $\Delta=0$, with the free-fermion dip decaying much more slowly with system size. In the thermodynamic limit, we decompose the two-magnon $S$-matrix into quantum logic gates – Identity, SWAP, and $\sigma_z\otimes\sigma_z$ – and show that the entangling power vanishes for all scattering energies at the $SU(2)$ points, where the $S$-matrix reduces to the Identity gate, while the free-fermion point achieves the maximum – the opposite of the finite-size many-body behavior. The entangling power can serve as an operator diagnostic for symmetry and selected aspects of integrability in quantum simulations of spin-chain dynamics.

Motivated by string theory, we constrain non-commutative black hole parameters through shadow behaviors using machine learning techniques combined by CUDA computations. To do so, we first investigate the structure of the event horizon of non-commutative black holes in the presence of string clouds and dark energy sectors by exploiting CUDA-based methods. We numerically approach the shadow properties and the energy emission rate of rotating and charged black holes in non-commutative geometry via such high-performance parallel computings. To bridge these findings with observational data, we implement a CUDA-based framework in order to constrain the involved black hole parameters including the non-commutative one. Using the resulting numerical data, we build a robust training datasets for a fully connected neural network to determine whether a given set of parameters matches with the observational data provided by Event Horizon Telescope collaborations. As a result, we find that the non-commutative model under study is consistent with the observations of $SgrA^*_{\mathrm{Keck}}$ black holes.

This work introduces the causal bootstrap, a framework for bounding smeared spectral observables from finite non-perturbative Euclidean data. The method optimizes over the convex set of positive spectral densities compatible with the data to compute rigorous upper and lower bounds on the target observable. Statistical uncertainties, including correlations, are incorporated through compatibility regions using the covariance matrix. The bounds are equivalent, via Lagrange duality, to certified bounds on the target smearing kernel. For polynomial, rational, and piecewise rational kernels, the resulting dual problems can be reduced to finite-dimensional semidefinite programs using techniques familiar, e.g., in the numerical conformal bootstrap. The present formulation clarifies the relation to moment problems, Nevanlinna–Pick interpolation, and linear kernel-reconstruction methods. Numerical examples demonstrate the method.

Electromagnetic duality is a symmetry of the source-free Einstein-Maxwell equations that rotates electric and magnetic fields while leaving the stress-energy tensor invariant. We present the first fully nonlinear realization of this symmetry in dynamical strong-gravity regimes by performing numerical relativity simulations of charged black hole mergers across a continuous duality family. Starting from electrically charged binaries, we generate dyonic and magnetically charged configurations via duality rotations and evolve them within a common numerical framework. We find that all dual configurations exhibit identical spacetime dynamics, while the emitted electromagnetic radiation is related by a rotation of its polarization equal to the duality angle. Our results demonstrate a degeneracy of gravitational observables under electromagnetic duality and provide a concrete mapping between dual configurations at the level of radiation, establishing electromagnetic duality as an organizing principle for dynamical Einstein-Maxwell solutions.

The conformal anomaly has well-known ambiguities related to the possible schemes of regularization and renormalization. In case of dimensional regularization, one of the options is to formulate the theory as conformal in the dimension $D \neq 4$. For a gauge vector field this can be done in several ways and one of the options is to introduce an auxiliary scalar playing the role of a compensator. The advantage of this approach is that it preserves gauge symmetry and avoids problems with possible violation of unitarity. We explore the consequences of introducing such an auxiliary field for the anomaly and anomaly-induced action. It is shown that the new scalar degree of freedom gains an independent dynamics after taking the $4D$ limit. The remnant scalar, also, demonstrates some interesting properties.

Holographic superfluids/superconductors are one of the most studied systems in the AdS/CFT duality. In the low-energy, in the long-wavelength limit, they should be described by a Ginzburg-Landau theory. For critical dynamics, one expects that they belong to "model F" universality class. We consider a bulk 5-dimensional holographic superfluid/superconductor in the probe limit. For the holographic superconductor, we impose the boundary Maxwell equation to make the boundary Maxwell field dynamical. We identify the dual model F equations where numerical coefficients are obtained exactly.

Asymptotically flat balanced configurations of two spinning black holes with synchronised scalar hair (2sBHs) are possible (arXiv:2305.15467). These are constructed within a generalized Bach-Weyl framework and arise from two spinning boson stars (2sBSs) by placing a horizon at the center of each component. Here, we investigate the effects of quartic scalar self-interactions on this family of solutions, comprising the 2sBSs, the 2sBHs, and an intermediate configuration–single spinning black hole with quadrupolar scalar hair (1sBHs). For 2sBSs, the additional repulsive force introduced by the self-interactions drives a topological transition of the ergoregion, from a single torus to a double torus, in the strong-gravity regime. For 1sBHs, as the self-interaction coupling strength increases, the solutions become "hairier" but their horizons cannot become heavier; moreover, the self-interactions broaden the regime in which an analytical effective model accurately describes these solutions. For 2sBHs, increasing the coupling reshapes the bifurcation structure of the solution sequences and, as in the 1sBH case, repulsive self-interactions cannot make the horizons heavier; horizons carrying a larger mass fraction are obtained only when attractive self-interactions are considered.

We construct an impact-parameter-resolved transfer framework for null acoustic rays in the rotating draining-bathtub spacetime. The formalism separates the source-independent ray geometry from the source and detector model by keeping explicit the acoustic redshift, transfer convention, emissivity, emitter velocity field, and source-to-screen mapping. The geometric capture interval provides two clean observables: a shadow centroid that shifts linearly with circulation and a shadow width that grows monotonically with circulation. Observable profiles are obtained from direct ray-source intersections, finite source width or extended-disk integration, detector convolution, and convergence checks, rather than from an approximate semi-analytic ring map. The transfer calculation shows that rotation produces a left-right redshift tilt and a branch-dependent flux imbalance, while the total flux alone remains a degenerate circulation diagnostic. The most useful diagnostics are differential quantities: the shadow centroid, branch-integrated flux asymmetry, peak asymmetry, left-right redshift asymmetry, and global redshift contrast. We also discuss how these observables respond to the transfer convention, intrinsic azimuthal emissivity, the choice of left-right split, finite resolution, and physical limitations such as dispersion, viscosity, and finite-depth corrections.

We develop a semiclassical description of Reissner–Nordström–de Sitter (RN–dS) evaporation by combining a spherically reduced two-dimensional dilaton gravity model with Polyakov anomaly backreaction. The framework captures the causal and thermodynamic structure of the static patch and yields closed adiabatic evolution equations for the mass and charge. With an outward-oriented flux convention, the anomaly-induced Killing-energy flux is $\mathcal F=(N_{\rm eff}/48\pi)(\kappa_b^2-\kappa_c^2)$, while the full mass evolution is $\dot M=-\mathcal F+\Phi_b\dot Q$, with $\Phi_b=Q/r_b$. We prove analytically that along the entire sub-Nariai neutral Schwarzschild–de Sitter branch $\kappa_b>\kappa_c$, so neutral black holes lose mass monotonically. Schwinger pair production provides the discharge channel. In the rapid-discharge regime, controlled charged trajectories become effectively neutral on a timescale short compared with the anomaly-driven Hawking mass-loss time and then follow the neutral SdS channel toward empty de Sitter space. The classical lukewarm locus $T_b=T_c$ is only the nullcline of the anomaly-induced heat flux: the electromagnetic work term tilts the full semiclassical vector field away from this curve, so it is not an invariant trajectory. When sufficiently light charged species provide a rapid-discharge channel, the classical cold/extremal, charged Nariai, ultracold, and lukewarm loci are not semiclassical attractors for controlled nondegenerate trajectories. These results give an adiabatically backreacted derivation of the RN–dS evaporation endpoint in the regime controlled by anomaly-induced flux and rapid charge discharge, and provide the semiclassical background for generalized-second-law monotonicity and conservative quantum-extremal-surface/island estimates.