Papers

Understanding quantum phases and phase transitions in the presence of symmetries is a central objective of quantum many-body physics. A powerful modern paradigm for investigating this problem is topological holography, which relates symmetries in $k$ dimensions to "bulk" topological orders in $(k+1)$ dimensions. While conceptually profound, most existing bulk construction methods rely on sophisticated mathematical formalisms and can be difficult to apply to certain symmetry types. In this work, we propose a physically intuitive and versatile method, termed the layered gauging construction, to systematically generate $(k+1)$-dimensional (liquid or fracton) topological orders from $k$-dimensional generalized symmetries. Roughly speaking, the prescription is to stack many layers of $k$-dimensional quantum systems with certain symmetries into a $(k+1)$-dimensional pile, and then sequentially gauge a diagonal symmetry acting on each nearest-neighbor pair of layers. The detailed procedure depends on the specific symmetry types. We have successfully implemented the method in a number of examples in different spatial dimensions, with symmetries that are conventional, higher-form, subsystem, anomalous, nonabelian, or noninvertible. We hence conjecture the method to be very general. For example, from the subsystem symmetry of the $2d$ plaquette Ising model, we derive the X-cube model and also an anisotropic fracton topological order. Additionally, starting from an anomalous $\mathbb Z_2$ symmetry in $1d$, we construct a new square lattice model realizing the double semion topological order.

The death of massive stars produces central accreting compact objects and sometimes relativistic jets. Not all jets escape the stellar envelope: unsuccessful, or choked, jets dissipate their energy into a pressurized cocoon, which expands and may break out as a mildly relativistic outflow. We investigate the plasma physics of collapsing massive stars hosting choked jets through relativistic, non-resistive magnetohydrodynamical simulations. We delineate the parameter space for jet choking and quantify the acceleration rate and efficiency of charged particles at strong shocks, which are potential sources of high-energy neutrinos and electromagnetic transients. Our study focuses on blue and red supergiant progenitors, both promising candidates for jet choking.

Species-resolved azimuthal anisotropy scaling functions are constructed from identified particle $v_2$ and $v_3$ obtained from event-by-event iEBE-VISHNU simulations for Pb+Pb collisions at $\sqrt{s_{NN}}=2.76$ and $5.02$~TeV. The scaling functions exhibit a robust collapse across transverse momentum, centrality, particle species, and beam energy, indicating a common and tightly constrained scaling structure. High scaling fidelity yields quantitative agreement with the data-defined reference through an energy-dependent attenuation baseline $\beta_0$ in central to mid-central collisions and a centrality-dependent modification of the effective attenuation in more peripheral collisions, with only a weak dependence on $\sqrt{s_{NN}}$. The multiplicity dependence of the extracted scaling parameters reflects the interplay of EOS-driven collective expansion, finite system lifetime, and hadronic re-scattering. These results demonstrate that the scaling framework provides a quantitative, constraint-driven probe of the hydrodynamic response, enabling the disentanglement and constraint of the coupled contributions to azimuthal anisotropy.

Quantum integrable spin chains are known to possess a large family of long-range deformations generated by the local, boost and bilocal operators. Although these deformations are well-understood on the level of the pairwise commuting charges, the underlying quantum group structures had not yet been recognised. In this paper, we provide a quantum group-theoretical description for the family of long-range deformations of arbitrary homogeneous Yang-Baxter integrable spin chains up to first order in the deformation parameter. In particular, we show that the deformations are obtained via a twist of the algebraic structure of the underlying quantum group. This twisting results in a generally non-associative algebra that has a non-trivial Drinfeld associator. The Drinfeld associator is then shown to encode the information about the long-range interaction terms for the integrable spin chain. Moreover, the deformed quantum group is shown to contain a large perturbatively associative substructure, thus ensuring the perturbative integrability of the long-range model. The deformed quantum group provides explicit expressions for the Lax operators and R-matrices of the long-range deformed models, which manifestly satisfy the RLL relation and the Yang-Baxter equation up to first order in the deformation parameter. In order to derive the results, we introduce algebra elements that we call the algebraic charge densities. As a side result, we provide a conjecture for the explicit expressions of the undeformed charge densities in terms of these algebra elements.

Rotating calorons were introduced in the context of rotating quark-gluon plasmas. They are anti-self-dual gauge fields on $\mathbb{R}^4$ that are invariant under a glide rotation. We formulate a Nahm transform which identifies rotating calorons with solutions of a delayed-differential equation. Using this transform, we prove existence of an eight-parameter family of charge 1 rotating calorons with nontrivial holonomy and rotational angle $\pi$, which we construct and visualise using a numerical implementation of the Nahm transform.

We study the BPS cohomology and Hamiltonian of a model built from an $N\times N$ matrix $\Psi$ of complex fermions, with supercharge $Q_p={\rm Tr}(\Psi^p)$ for odd $p\ge3$. Numerical calculations give the BPS multiplicity at every fermion number for $(p,N)=(5,3),(5,4),(5,5),(7,4)$, and through fermion number six at $(7,5)$. In $Z_{BPS}^{(p,N)}(x)=\sum_Rh_Rx^R$, $x$ records fermion number and $h_R$ counts BPS states in sector $R$. In each of the four cases computed at every fermion number, factoring out the lowest power of $x$ leaves a polynomial divisible by a positive power of $p$ and by $(1+x)^N$. The quotient by these factors has nonnegative integer coefficients. Exact decoupling of ${\rm Tr}\Psi$ and the Euler characteristic prove divisibility by $(1+x)^2$. Pairing sectors of complementary fermion number gives a third factor when $N$ is odd. For odd $p\le2N-1$, the only range in which $Q_p$ can be nonzero, the same pairing proves the corresponding rank symmetry for $Q_p$. The additional factors required to reach $(1+x)^N$ remain conjectural in general. Evaluating at $x=1$ gives the total BPS count $Z_{BPS}^{(p,N)}(1)$. For each fixed odd $p$, the Witten indices imply that, for any sequence of matrix sizes $N_j\to\infty$ along which $N_j^{-2}\log Z_{BPS}^{(p,N_j)}(1)$ converges, its limit lies in $[\log(2\cos\frac{\pi}{2p}),\log 2]$. After dividing the Hamiltonian by $p^2$, normal ordering gives an alternating sum of operators $K_k$, with $K_k$ containing $k$ creation and $k$ annihilation operators. We obtain exact formulas for $K_0,K_1,K_2$ when $p=5$ and $N\ge3$. Only $K_3,K_4$ can contain spectral information beyond the number of traceless fermions and the quadratic Casimir. At $N=3$, the Hodge star maps the invariant cubic form to the quintic form up to scale, so all five terms commute. Calculations with integer matrices give nonzero commutators in the reported $N=4$ sectors.

We present quantitative evidence that high-quality internucleon forces derived from $\chi$EFT exhibit a striking dominance of Wigner's supermultiplet symmetry, without invoking the large-$N_c$ limit of QCD or assumptions about specific nuclei. We trace the manifestation of this symmetry in nuclear structure using the ab initio Symmetry Adapted Model (SAM) and identify suppressed spin-isospin polarizability. Our calculations show that a majority of $\rm ^4He$, $\rm ^6Li$, and $\rm ^6He$ wave functions is concentrated in a few $\rm U(4)$ irreducible representations, without imposing any a priori constraints on the model space. This emergent feature points to a strategy for reducing explosive many-body bases of the NCSM while retaining physically important configurations needed to compute observables.

The early universe need not be described by an incomplete inflationary phase connected to a separate, more exotic prehistory. Recent results show that, within non-static FRW cosmology, only positive spatial curvature permits a nonsingular, geodesically complete universe with ANEC-respecting matter. We construct a geodesically complete closed $k=+1$ bounce-plus-inflation cosmology in ordinary general relativity, sourced by a single canonical scalar field with a positive vacuum offset. The bounce is supported by curvature rather than exotic stress energy: the matter content satisfies the NEC throughout and violates only the strong energy condition, as in any accelerated expansion. The solved branch remains sub-Planckian and evolves onto a curvature-diluted slow-roll phase with inflationary observables consistent with current constraints. The pivot-scale predictions are $n_s=0.9617$, $r=0.0045$ at $N_*=55$ and $n_s=0.9650$, $r=0.0037$ at $N_*=60$. Direct evolution of closed-universe infrared perturbations shows regular tensor and scalar propagation through the bounce and inflationary era, with the physical curvature perturbation freezing in the standard way. This gives a minimal explicit realization of a complete early-universe cosmology in the closed FRW branch selected by completeness and ANEC compatibility.

The walled Brauer algebras $B_N(m,n)$ govern Schur–Weyl duality for unitary groups $U(N)$ acting on mixed tensor spaces $V_N^{\otimes m}\otimes \overline{V}_N^{\otimes n}$ and play an important role in applications ranging from AdS/CFT to quantum information theory. In the stable regime $N\ge m+n$ the algebra is semisimple and its representation theory is well understood. For $N<m+n$, however, $B_N(m,n)$ becomes non-semisimple. The representation of the algebra on tensor space has a non-trivial kernel and the corresponding quotient algebra is semisimple, with representation dimensions differing from those in the stable regime. We introduce restricted Bratteli diagrams, obtained by modifying the standard Bratteli diagrams for $B_N(m,n)$. This construction provides a systematic way to use representation-theoretic data from the stable regime to compute the dimension modifications arising in the non-semisimple regime. In the regime $N=m+n-l$, with $l$ small compared to $m,n$, we show that the restricted diagrams exhibit a stability property and enable an efficient counting of the paths responsible for these dimension corrections. Remarkably, the resulting generating functions are governed by the partition function of an infinite tower of simple harmonic oscillators. We briefly discuss implications for the construction of orthogonal bases of matrix invariants in gauge theory and related applications in quantum information theory.

We develop a framework to describe how quantum coherences between distinct charge sectors evolve under generic charge-conserving dynamics. Our framework captures the nonperturbative interactions between quantum coherences and hydrodynamic large deviations—i.e., rare “voids” of low charge entropy. Conditional on surviving, the quantum coherence and its surrounding void form a collective polaron-like object. In one dimension, even at infinite temperature, we show that the lifetime of coherences is parametrically enhanced because they bind to voids. We use our framework to address two fundamental questions about generic quantum dynamics with a conserved charge. First, we argue that gapped Ruelle-Pollicott resonances are absent in the weak-noise limit, even in sectors of operator space that contain no hydrodynamic slow modes: instead, the spectral gap in all sectors vanishes nonperturbatively in the noise strength. Second, we compute the spacetime asymptotics of the dynamical single-particle Green's function, both in the weak-noise regime and in the absence of noise. In the noiseless case, we find that the void–coherence polaron undergoes subdiffusion, with an exponent we calculate. We support our general arguments with a microscopic derivation for random charge-conserving circuits, as well as numerical evidence from tensor-network simulations.

We provide a holographic bulk realization of Carrollian free-field structures arising in three-dimensional asymptotically flat (higher-spin) gravity. We construct a class of boundary conditions that generalizes the diagonal gauge of Anti-de Sitter to flat spacetimes. We show that the associated asymptotic symmetries decompose into genuine physical transformations and pure gauge redundancies, the latter being generated by Carrollian screening charges. This structure leads to a bulk-born realization of Carrollian Miura transformations, expressing physical observables in terms of celestial free scalars. Our results establish a concrete link between flat space (higher-spin) gravity and a Carrollian Coulomb gas description, thereby providing a promising route toward the quantization of flat holography.

We find the perturbative potential on the 3d $\mathcal{N}\!=\!2$ Coulomb branch arising from a chiral 4d $\mathcal{N}\!=\!1$ gauge theory on $\mathbb{R}^3 \times S^1$, zeta-regularizing the D-term couplings generated by the Kaluza-Klein modes. This fills a significant gap in the literature on circle-compactified SUSY gauge theories. Unlike earlier indirect approaches to the circle reduction of chiral theories, our formula provides a global view of the Coulomb branch, necessary for capturing holonomy saddles and for systematic implementation. The zero locus of the potential identifies perturbative SUSY vacua, and we show how data-analysis techniques (such as RANSAC hyperplane detection) numerically extract the structure of the moduli space when this locus is extended. Our formula yields new results even in abelian theories, and offers a new perspective on several earlier observations in the context of the Cardy limit of the superconformal index. In particular, circle reductions (of interest in the SCFT/VOA correspondence) found earlier from limits of the index can now be reproduced on $\mathbb{R}^3 \times S^1$. An appendix shows how our 3d $\mathcal{N}\!=\!2$ potential is related to a function arising in the Cardy limit of the index analogously to how the 4d $\mathcal{N}\!=\!2$ prepotential arises in a limit of the Nekrasov partition function.

Recent proposals suggest that a notion of generalized complexity, analogous to generalized entropy, may be necessary for understanding the dynamics of holographic complexity in settings where quantum effects are non-negligible, such as evaporating black holes. Beginning with a notion of generalized complexity, we introduce a complexity-based quantum expansion for timelike geodesic congruences, and investigate the consequence of a timelike quantum focusing conjecture. We find that for a suitable class of codimension-0 field theory complexity measures the timelike focusing condition implies a complexity-based quantum strong energy condition as well as a complexity bound which is analogous to the covariant entropy bound.

Neural network field theory (NNFT) represents fields as neural networks and samples field configurations by drawing network parameters from a probability distribution. We identify a previously unexplored architectural freedom in NNFT, parameterized by $\alpha$, that leaves the infinite-width theory invariant but dramatically affects finite-width errors in the calculation of correlation functions. For a massive scalar field, we show that $\alpha=0$, corresponding to propagator-weighted neuron momenta and constant neuron amplitudes, is optimal: it minimizes finite-width variance and uniquely removes IR-sensitive corrections in the interacting theory. Even at $\alpha=0$, relative errors from both bias and variance grow exponentially with distance beyond the correlation length. The bias can be removed by extrapolating to infinite width, which we demonstrate numerically, while the variance imposes a fundamental bound on the achievable signal-to-noise ratio as in lattice field theory. These results chart a path toward developing NNFT into a practical tool for the numerical study of field theories.

In this work, we revisit black hole Love numbers from two complementary perspectives. First, we develop a manifestly gauge-invariant framework that directly integrates out the short-distance degrees of freedom of a static black hole in arbitrary spacetime dimensions. This approach yields the effective point-particle action and its associated Love numbers without relying on the standard matching procedure or on the Regge-Wheeler equation and its associated master field. Second, we investigate the role of Love numbers in black hole thermodynamics by analyzing a Schwarzschild black hole subjected to various types of external perturbations. We show that Love numbers govern the induced polarization of the black hole and control the leading corrections to its thermodynamic properties, thereby clarifying their physical significance in black hole thermodynamics.

In this work, we construct a double O(3)-sigma model minimally coupled to a Maxwell field in (2+1)-dimensional spacetime and investigate the existence of self-dual magnetic vortex solutions. An analysis of the Bogomol'nyi-Prasad-Sommerfield (BPS) property reveals that both sigma fields belong to the same topological sector and that the potential assumes a periodic cosine-like form. Furthermore, the theory supports the emergence of magnetic vortices with quantized flux, described by two nonlinear O(3)-sigma sectors that effectively combine into a single topological sector in the BPS regime. In addition, we analytically verify the consistency of the BPS structure and its asymptotic behavior. Within this framework, numerical vortex solutions confirm that the field profiles are smooth and spatially localized, with both the magnetic field and the energy density remaining regular and localized.

We consider a holographic Einstein-Maxwell model in five dimensions with pure gauge and mixed gauge-gravitational Chern-Simons terms to study anomaly-induced transport in the presence of explicit symmetry breaking. We include the full backreaction of the scalar field and gauge fields on the metric and compute the anomalous transport coefficients using Kubo formulae involving charge and energy current correlators. Our findings reveal that, in the presence of explicit symmetry breaking, anomaly-induced transport phenomena can extend beyond anomalous currents and affect the non-anomalous sector as well. The transport coefficients exhibit a clear dependence on the symmetry-breaking mass parameter, highlighting the interplay between quantum anomalies and explicit symmetry breaking in holographic systems.

We develop the Schwinger-Keldysh path-integral formalism for open non-Abelian gauge theories that are gauge-fixed via the BRST method in covariant gauges. We focus on generic initial states, pure and mixed, specified at finite times suitable for non-equilibrium processes. We pay particular attention to the handling of the indefinite Hilbert space, the construction of BRST-invariant Schrodinger picture wavefunctionals, density matrices and inner product, the implementation of the Hata-Kugo prescription, and the role of boundary terms at both the initial and final times. We highlight the advantages of the Nakanishi-Lautrup field representation in dealing with initial/final conditions. The resulting Schwinger-Keldysh path integral is manifestly invariant under a diagonal (retarded) BRST symmetry for arbitrary physical initial states, whether pure or mixed. From this, we obtain the corresponding Ward-Takahashi-Slavnov-Taylor identities, valid perturbatively. Non-perturbatively the Gribov ambiguity is expected to break or modify the BRST symmetry. The naive advanced BRST symmetry is shown to be explicitly violated by the in-in boundary conditions. We show that the Feynman-Vernon influence functional derived by integrating out charged matter and/or hard gluon modes remains (perturbatively) BRST invariant. When the Open EFT action is expanded to second order in advanced fields it exhibits an exact symmetry under a contraction of the original BRST symmetry. This Keldysh BRST symmetry is equivalent to the BRST associated with the retarded gauge transformations together with a linearly realized BRST transformation of the advanced fields. These govern the structure of the leading terms in an Open EFT. We illustrate this with the explicit example of Hard Thermal Loop Effective Theory, and construct the general form of the Open EFT in a Higgs phase when all gauge symmetries are spontaneously broken.

We discuss some new results on the construction of supersymmetric solutions of Type IIB supergravity of the form ${\rm WAdS}_3\times{\rm WS}^3\times T^4$, ${\rm WAdS}_3$ and ${\rm WS}^3$ denoting warped anti-de Sitter spacetime and sphere, respectively. The distinctive feature of these backgrounds is that, in spite of them being supersymmetric, the warpings of the two factors are described by independent parameters. We illustrate how some of these geometries, characterised by a lightlike warping of the anti-de Sitter factor, arise in the near-horizon limit of a regular, asymptotically locally flat configuration of D-branes and fluxes. Central to the construction of the latter solutions is the use of two independent TsT transformations. We also give a new class of supersymmetric solutions of the general form ${\rm WAdS}_3\times{\rm WS}^3\times T^4$, which has not been published yet. They feature warpings of the anti-de Sitter factor of the lightlike, spacelike and timelike types. We discuss their properties.

We establish the rate at which the renormalized stress–energy tensor of a massless minimally coupled scalar field in the in-vacuum state of a collapsing null-shell spacetime approaches the corresponding Unruh-state value. At finite exterior radius, we establish the upper bound \[ |\Delta\langle T_{\mu\nu}\rangle|\leq C(r)\,t_s^{-3} \] from the Cauchy-surface decomposition of the Hadamard difference and the branch-cut structure of the retarded Green function. At future null infinity, we show that the leading coefficient in the late-time expansion \[ \Delta\langle T_{uu}\rangle\sim C_{uu}\,u_s^{-3} \] is nonzero, by computing the branch-cut residue explicitly at small frequency and using the Planck suppression of the thermal spectrum at large frequency to show that the dominant contribution to $C_{uu}$ has a definite sign. The result gives \[ \Delta\langle T_{uu}\rangle\big|_{\Iscr^+}(u_s) \sim C_{uu}\,u_s^{-3}, \qquad u_s\to\infty, \] with $C_{uu}\neq 0$. The exponent is determined by the $\omega^2\ln\omega$ branch-point singularity in the Wronskian of the $\ell=0$ radial wave equation, the same structure responsible for Price's law. The sign $C_{uu}<0$ is supported by a physical argument and by the numerical mode data of Gholizadeh Siahmazgi, Anderson, and Fabbri. The result confirms their conjecture that the approach is a power law. We conjecture that the same mechanism gives an analogous $t_s^{-7}$ bound for gravitational perturbations ($\ell_{\min}=2$), though the extension to the spin-2 case involves gauge issues not addressed here.

The Euclidean bounce for vacuum decay enjoys an $O(4)$ symmetry that is lost in the presence of impurities than can catalyze the decay. We present a formulation for the calculation of the tunneling decay action, that is explicitly positive definite, for impurities whose effects are spherically symmetric so that the bounce symmetry is reduced to $O(3)$. The action constructed can be regarded as a generalization of the tunneling potential method, which implicitly assumed $O(4)$ symmetry. We show that the action obtained reduces to the tunneling potential for $O(4)$-symmetric cases and provide analytic examples with $O(3)$ symmetry and arbitrary wall thickness.

We introduce equivariant localization as a method for computing the action of probe branes in supergravity backgrounds. We apply it to supersymmetric probe D3-branes in type IIB supersymmetric spacetimes obtained by uplifting the Kerr-Newman-AdS$_5$ black hole on a toric Sasaki-Einstein space. Depending on the cycles they wrap, such branes represent non-perturbative corrections to or defect operator insertions in the superconformal index of a large family of four-dimensional $\mathcal{N}=1$ quiver superconformal field theories. The resulting action reduces to equivariant integrals and can be evaluated entirely from toric data.

We propose the first examples of scale-separated vacua with extended supersymmetry. They arise as circle compactifications of four-dimensional vacua of massive type IIA supergravity with scale separation, upon introducing additional fluxes and sources. We provide both the ten-dimensional solutions and the three-dimensional effective descriptions in terms of Kähler potential and superpotential. The conformal dimensions of the putative dual two-dimensional field theory appear not to be integers. The superpotential for the additional fluxes of one of our models was guessed by ChatGPT and, to the best of our knowledge, it does not appear in existing literature. Should these vacua be solutions of string theory, they would allow to address the open problem of scale separation from the vantage point of extended supersymmetry.

Using a fully gauge-invariant approach, we compute for the first time in the literature relativistic effects on the redshift drift up to second order in cosmological perturbation theory. This is achieved by employing a set of light-cone coordinates that simplify the description of light propagation in an inhomogeneous and anisotropic universe. We show that redshift-space distortion occurs only as a second-order effect whereas, as known, it is not present among the linear perturbations. We then derive analytical expressions of the bispectrum for the leading-order perturbative contributions on sub-Hubble scales, providing some numerical evaluations. Our finding is that, at low redshift and for large momenta, the non-linearities in the bispectrum are enhanced more than the squared power spectrum.

We study two-point correlation functions of heavy scalar fields in the Nariai geometry. Utilizing the heat kernel formalism, we obtain this result from a geodesic approximation to the two-point function on a product of spheres. By analytically continuing one of the spheres, we obtain the correlation function in the Nariai geometry. This result involves a sum over complex geodesics, extending previous results in pure de Sitter space. We emphasize the important role of the phase of each geodesic contribution, which needs to be taken into account to avoid spurious singularities in the correlator.

We present a genuinely non-radial quantum-mechanical route by which $\pi$ emerges from equatorial localization on the sphere. For the highest-weight branch of spherical harmonics, this localization is captured by a natural geometric rigidity index, whose exact finite-quantum-number value is a Wallis partial product. The mechanism is realized in two settings: the standard rigid rotor and the surface sector of a thin spherical shell, where radial freezing reduces the dynamics to the same angular problem. In the large-quantum-number limit, the probability cloud collapses toward the equator, the rigidity index approaches its classical value, and the Wallis formula is recovered through the correspondence principle. The result shows that Wallis-type structures in quantum mechanics can arise as exact signatures of semiclassical localization encoded by a simple geometric observable.

We investigate the spreading of entanglement, and entanglement memory effects, in two-dimensional conformal field theory (CFT) propagating on evaporating black hole backgrounds. Memory effects leading to late-time spikes in mutual information for widely separated intervals are well known in CFTs admitting a quasiparticle description. In this work we examine the effect of black hole scrambling on late time mutual information spikes for disjoint intervals in free fermion CFT prepared in a thermofield double state. Late-time entanglement revival is driven by island-induced purification of modes in the union of the intervals. We show across two distinct 2d gravity models, Jackiw-Teitelboim (JT) gravity and the Russo-Susskind-Thorlacius (RST) model, that parametrically dialing up black hole scrambling time smooths out and suppresses entanglement spikes until they disappear at a critical scale, interpolating between free quasiparticle and maximal scrambling pictures. At the critical point, the interval lengths are exponential in black hole scrambling time. We further find a very closely related effect manifest as an entanglement dip for a single interval in a single-sided evaporating RST black hole.

In the background of a Kerr-Newman black hole, the motion of a scalar particle is integrable by virtue of an extra conserved charge known as Carter charge. When the particle is endowed with spin, it is known that another conserved charge, the Rüdiger charge, maintains the integrability at least at low orders in the spin magnitude. We explore the extent of this integrability in a simpler model where both the source and the probe are root-Kerr particles, the non-gravitating limit of the Kerr-Newman black hole. At the leading order in the probe charge, the integrability holds to all orders in the spin magnitude if the interaction vertices of the probe are dictated by the Newman-Janis shift. At the second order in the probe charge, the integrability can be extended to the spin-squared order but begins to fail at the spin-cubic order. An argument based on asymptotic conservation suggests that it is impossible to restore the conservation at the spin-cubic order by a further deformation of the probe action. We compare our results with related observations for Kerr black holes with gravitational interactions.

We point out that constraints on $\Delta N_\mathrm{eff}$ reported by the ACT collaboration in their DR6 data release are surprisingly sensitive to the assumptions made about the initial power spectrum from inflation. The ACT collaboration reports no evidence of new light degrees of freedom alongside a low value of the expansion rate, thus confirming the Hubble tension. However, as we show here, when considering self-interacting dark radiation and including running, $\alpha_s$, and running of the running, $\beta_s$, of the spectral index $n_s$, the picture changes significantly. Confronting this extended model with Planck, ACT DR6, DESI DR2, and uncalibrated Pantheon+ data, we find the significantly relaxed bound $\Delta N_\text{eff}< 0.58$ at 95$\%$ CL, together with a $2.9 \sigma$ ($2.6 \sigma$) preference for $\alpha_s>0$ ($\beta_s>0$), while the Hubble tension is reduced to $2.2 \sigma$ with only three more parameters compared to $\Lambda$CDM. If the dark radiation fluid is initially coupled to dark matter, and undergoes dark radiation-matter decoupling (DRMD) around matter-radiation equality, predicting dark acoustic oscillations with drag horizon $r_{d,\mathrm{DAO}} \approx 60 \,\mathrm{Mpc}/h$, the bound is further relaxed to $\Delta N_\text{eff}< 0.68$ at 95$\%$ CL, reducing the Hubble tension below $2\sigma$. We also discuss how $\alpha_s$ and $\beta_s$ could naturally appear in inflationary scenarios, possibly connected to the end of a first act of inflation. In this case dark radiation is mostly probed by scales covered by Planck and DESI, while smaller scales carry information on inflationary dynamics.

We study the dynamics of circular cosmic string loops in a spatially flat Friedmann Lemaître Robertson Walker universe within a fractional Polyakov framework that incorporates nonlocal memory effects. Allowing both the loop radius and polar angle to evolve, we obtain a coupled non-autonomous system governed by string tension, cosmological expansion, and an emergent centrifugal contribution. We show that angular dynamics plays a crucial role in determining the loop evolution. In contrast to standard scenarios where loops collapse, we identify a class of solutions exhibiting sustained expansion driven by dynamically generated angular motion. The system also displays nonlinear behavior with signatures of chaos, with the onset of chaotic dynamics closely correlated with expanding solutions. Our results demonstrate that fractional memory effects and angular degrees of freedom qualitatively modify cosmic string loop dynamics, providing new mechanisms for stability in cosmological backgrounds.