Papers

We study the evaluation of Rényi multi-entropies $S^{(q)}_n$ in Random Tensor Network (RTN) states in the large bond-dimension limit. For the case of Rényi index $n=2$ and arbitrary number of parties $q$, we prove that that multi-entropies are determined by minimal multiway cuts through the network. When the minimal multiway cut is degenerate, we characterize the full minimizer set via compatible families of minimal cuts and give a criterion for all minimizers to come from ordinary cut partitions. For $n=2$, this gives a natural generalization of the minimal cut description of bipartite entanglement to multipartite systems with arbitrarily many parties. For the case of integer $n>2$, we show that the minimal multiway cut conjecture is in general not true by providing explicit counter examples for both the single random tensor and for the network built from isometric tilings. We discuss the implication for our results on the multipartite entanglement structures in RTN and holography.

We rederive the Cosmological Supersymmetry Breaking Relation $m_{3/2} = \frac{C}{\sqrt{R_{dS} L_P}}$ from a deformation of the Awada-Gibbons-Shaw local supersymmetry algebra.

The $\mathsf{O}(N)$ $\mathsf{BCFT}$ is analyzed in the large $N$ expansion in a generic bulk dimension $2<d+1<4$. Focus is on boundary conditions corresponding to the ordinary transition, however techniques used can be generalized to special or extraordinary transitions. We study the system of bulk $2$-pt functions $\langle \phi\phi\rangle$, $\langle \phi^2 \phi^2\rangle$ and $\langle \sigma\sigma \rangle$, where $\sigma$ is the Hubbard–Stratonovich field. They are expanded in bulk/boundary conformal partial waves. The coefficient functions of this expansion – the spectral functions – encode $\mathsf{BCFT}$ data and determine bulk/boundary conformal block expansions. We prove conjectures about boundary spectral functions in Dujava et al. [arXiv:2503.16345] and reproduce the bulk expansion of $\langle \phi\phi \rangle$ in Giombi et al. [arXiv:2007.04955]. The bulk expansion of $\langle\sigma\sigma\rangle$ is new and allows to extract the leading large $N$ expression for an unknown OPE coefficient $C_{\sigma\sigma\sigma^3}$ (the computation outputs as a byproduct also a mixing coefficient, which matches an existing result by Derkachov et al. [arXiv:hep-th/9705020], providing further support for the main result). Besides these derived data infinitely many constraints are produced, though due to operator mixing growing in complexity as degeneracy increases, they cannot be disentangled without further input.

We formulate the gravitationally induced quantum decoherence of a massive object prepared in a spatial superposition. Starting from linearized gravity coupled to a massive system particle and an environmental scalar field, we derive a closed-time-path influence functional governing the reduced system dynamics. In the nonrelativistic and quasi-static regime, the decoherence exponent can be written as a bilinear functional of the difference of the system stress-energy tensors and an effective noise kernel obtained by dressing the environmental stress-energy tensor correlator with graviton propagators. We then apply this framework to the Newtonian long-range gravitational interaction and evaluate the resulting decoherence function for a dilute nonrelativistic gas modeled by finite wave packets and coarse-grained in time and space. By performing controlled approximations, we obtain analytic expressions for the cumulative decoherence function and show that the dominant contribution is accumulated logarithmically over a broad range of distances, while remaining subdominant to conventional collisional decoherence under realistic conditions.

Based on an efficient technology for the excavation of entire open string trajectories of physical states, we propose an algorithmic method of constructing the largely unknown closed string trajectories. Due to combinatorial complexity, the "double copy" of open strings is limited in efficiency as a means of building closed string trajectories. We bypass this technical difficulty by employing one open string as the fundamental seed and then dressing it by a suitable selection of generators of a symplectic algebra that acts on both the left and the right sector. By applying Howe duality, the dressed seeds amount to closed string trajectory candidates, finding the physical subset of which is possible by solving systems of equations involving Diophantine-like recursion relations, which we also illustrate with examples.

Wilsonian renormalization is usually formulated in momentum space, but on curved backgrounds momentum shells have no invariant meaning. We replace them by an intrinsic spectral cutoff, ordering modes by the covariant Laplacian and setting the cutoff resolution by the system size in renormalization group (RG) units. For a scalar field on $S^3$, this yields a covariant, momentum-free RG flow whose trace is an exact sum over spherical harmonics. The standard flat-space flow is recovered when the sphere is large compared with the coarse-graining scale. As a nontrivial test, the compact spectral flow realizes Wilson-Fisher universality without momentum shells: the interacting fixed point survives at finite resolution, has one relevant direction, and approaches its flat-space counterpart smoothly, with critical exponents only weakly affected by the compact spectrum.

We introduce noncommutative geometry techniques in order to reinterpret the Penrose–Sparling non-Hausdorff twistor space of the anti-self-dual Coulomb field by means of an explicit etale gluing groupoid and its convolution algebra. This algebraic model keeps track of both the identified open part and the two non-separated copies of the source quadric. We compute two kinds of Chern–Connes pairings. The strict tangent-module analogue, obtained from \([T_{\mathbb R}\CP^3\otimes\C]\), vanishes because \[ \operatorname{ch}_3(T^{1,0}\CP^3)+ \operatorname{ch}_3(T^{0,1}\CP^3)=0. \] By contrast, the Penrose–Sparling Coulomb line bundle \(\calC_n\) defines a \(K_0(A_Q)\)-class, and the relative cyclic cocycle supported on the two non-separated copies of a ruling line \(L\subset Q\) gives \[ \mathcal Q(\calC_n)= \frac12\left\langle \varphi_L^+-\varphi_L^-,[\calC_n]\right\rangle=n. \] Thus the source-adapted cyclic pairing recovers the Coulomb charge. We also formulate the non-abelian version in principal-bundle language. For a connected complex reductive group \(G\), a maximal torus \(T\subset G\), and a cocharacter \(\lambda:\C^*\to T\), the source is a principal \(G\)-bundle modification of type \(\lambda\) along \(Q\).

It is proposed that spatial subregions in quantum gravity can be assigned pure states, rather than mixed reduced density matrices. The state is prepared by a partially frozen gravitational path integral, in which a spacetime subregion containing the spatial subregion is fixed while the field configurations and ambient geometry are summed over. In the semiclassical regime, we further propose a holographic prescription for the entanglement entropy of bipartitions of this state, with a frozen-region analogue of the homology constraint. The prescription satisfies nontrivial self-consistency conditions, including strong subadditivity, complementarity, and entanglement wedge nesting, and reproduces several known entropy formulas in holography and gravity as special cases. The construction suggests an observer-dependent entanglement wedge labeled by the frozen subregion.

Defect conformal field theories have special operators of protected dimension known as displacements and tilts. They arise due to the breaking of global symmetries by the defect and the normalisations of their two-point functions are characteristics of the defect. In the case of surface defects, these normalisations are related to some of the anomaly coefficients in the surface effective action. To study these operators and their flows between different defect renormalization group fixed points we present an elegant approach using conformal perturbation theory that easily reproduces the known examples from the critical Wilson-Fisher $O(N)$ model in $4-\varepsilon$ dimensions and allows us to construct new ones in other multiscalar theories. In all the systems that we study the flows are short and under full control, as is the change of the displacement and tilt normalizations. We point out some novel features like the existence of vortices when the defect conformal manifold is not simply connected. In addition to regular human labour, this work relied heavily on generative AI; see full disclosure in methodology section.

In this paper, we develop a multihair thermodynamic description of Lorentzian Kerr-Newman-NUT-AdS$_4$ spacetime in which rotation, electric charge, AdS pressure and polar conical tensions enter a homogeneous Christodoulou-Ruffini-type squared-mass formula. The NUT contribution is described by a rotation-like secondary hair $J_n=mn/K^2$ and a charge-like secondary hair $N=n/\sqrt K$. Both depend on the metric parameters of the physical solution family but are varied independently in the enlarged thermodynamic state space. The mass formula yields the first law and Smarr relation in a single enthalpy representation, with the area entropy and Hawking temperature. The Kerr-Newman-AdS, asymptotically flat Kerr-Newman-NUT and nonrotating RN-NUT-AdS limits check the angular normalization and the NUT and pressure contributions. We also consider alternative NUT variables, including the conformal dual mass, and derive the corresponding changes in thermodynamic volume and conical-defect lengths. This description applies to the chosen homogeneous state space and does not require the secondary hairs to be independent asymptotic or Misner-string surface charges.

The space of solutions to the free equations of motion for massless fields of arbitrary integer spin in Minkowski spacetime is recovered as a smooth limit of the anti-de Sitter solution space for any even spacetime dimension. The infinite set of boundary data near null infinity that characterise solutions in Minkowski spacetime is obtained from an expansion of the anti-de Sitter source and vev in powers of the cosmological constant. In particular, the source gives rise to the analogue of the gravitational shear tensor, while the vev yields the analogues of the mass and angular-momentum aspects, as well as the subleading infinite tower of boundary data. These identifications are further supported by the branching of the source and vev into representations of the Lorentz algebra identified with the conformal algebra of the celestial sphere.

The quantum-computing speedup theory considers the symmetric structures and properties of quantum systems as the fundamental Quantum-Computing-Speedup (QCS) resources which are responsible for exponentially speeding up quantum computing and simulating. At present a large and important problem is how to make use of the fundamental QCS resources to speed up essentially quantum computing and simulating. Here the author makes a great effort toward solving this important problem. The theoretical research work in this paper is mainly divided into the two Parts I and II. The Part I investigates mainly the multiple-quantum operator algebra spaces. And the relationships are analyzed among the multiple-quantum operator algebra spaces, quantum simulating for the unitary time-evolutional processes, and the fundamental QCS resources which exist in the different kinds of basic quantum spaces: the multiple-quantum operator algebra spaces, the density operator spaces, and the Hilbert spaces. It concludes that the multiple-quantum operator algebra space must be positioned as the central place where the fundamental QCS resources are exploited to speed up quantum computing and simulating. The Part II investigates mainly the subspace-selective unitary manipulation based on the Hilbert-space symmetric structures. Recognize that the multiple-quantum operator algebra space is the central place. Then those fundamental QCS resources original from the Hilbert space (a quantum-state space) must be explicitly taken into account in the multiple-quantum operator algebra space (a linear operator space). This is an important problem. The subspace-selective unitary manipulation is able to solve this problem. It aims to harness the fundamental QCS resources original from the Hilbert space to speed up quantum computing and simulating in the multiple-quantum operator algebra space.

We show that the remaining diagonal Einstein equations in the Carter-projective sector of stationary axisymmetric spacetimes are equivalent to a single sourced master equation. The projective structure is taken as the input fixed by the off-diagonal Einstein equations. In the anti-aligned exponential branch, which contains the Kerr–Carter and Plebański–Demiański real section, the remaining diagonal Einstein system reduces to \[ \mathcal L_{\rm CP}[\Delta,Y] =16\pi\Sigma \left( T_{\hat0\hat0}+T_{\hat3\hat3} \right), \] where \(\Delta(r)\) and \(Y(x)\) are the radial and angular structure functions. The reduction is accompanied by two geometric diagonal identities of the Einstein tensor, which become algebraic compatibility conditions on admissible matter sources. In the homogeneous limit, the vacuum–\(\Lambda\) Kerr–Carter and Plebański–Demiański families are recovered as solutions of the same master operator. We also show the projective covariance of the construction and discuss compatible sources, including the aligned Maxwell field and separable anisotropic examples.

In gravitational physics, matter does not merely move within spacetime; it also determines the light cones that define causal relations. What happens when the matter that determines these light cones is itself in a quantum state? We address this question in a controlled low-energy setting: a massless scalar field propagating in the spacetime with the Newtonian gravitational potential sourced by a non-relativistic quantum particle. We show that the light cones are affected by an operator-valued Shapiro delay, with the three consequences: (i) causal-boundary shifts are promoted to noncommuting observables, giving the causal structure an irreducible quantum uncertainty; (ii) the causal relation between two fixed spacetime points can become a superposition of timelike and spacelike configurations; and (iii) tracing out the source smears the Wightman light-cone singularity, producing an effective UV cutoff. Thus, quantum matter does not merely fluctuate within spacetime; it makes the causal structure itself quantum, even without including propagating graviton modes.

We study the $b$-$6j$ symbols – an analytic extension of the $6j$-symbols for the principal series of the modular double of $\mathrm U_q\mathfrak{sl}(2;\mathbb R)$ – with complex index $b,$ refereed to as the \emph{complex $b$-$6j$ symbols}. Then we relate their asymptotics, when the six parameters scale according to the dihedral angles of a hyperideal hyperbolic tetrahedron, to the volume and the determinant of the Gram matrix of the tetrahedron. In the case $\arg b=\pm \frac{\pi}{4},$ we believe that this work is closely related to the complex Liouville string\,\cite{CEMR}.

The chiral anomaly famously manifests in a rich variety of forms, from abelian and singlet to consistent or covariant. In this paper, all these realizations are described in detail, along with their properties and phenomenological applications. Central to this presentation is a novel expression for the fully generic chiral anomaly, derived with either massive or massless fermions, that incorporates not only the standard triangle but also the box and pentagon diagrams. From this master expression, the various traditional forms of the anomaly are then transparently derived. This provides a powerful tool, technically and conceptually, driving two further objectives. First, the topological aspects of each form are dutifully described while bypassing the differential language entirely, save for Stokes' theorem. Second, to make sure anyone interested can truly reproduce all the results in a reasonable amount of time, a FeynCalc implementation of the relevant calculations is provided. Ultimately, this simplified and unified description of all the forms of the chiral anomaly highlights the underlying conceptual beauty, and offers a comprehensive grasp of the physics at play.

Topological holography (TH), or SymTFT, realizes symmetries and dualities of a quantum system as boundary data of a topological bulk in one higher dimension. We formulate fracton topological holography (FTH), extending this mechanism from liquid topological orders to fracton stabilizer codes. The construction is organized as a general four-stage framework: prepare the bulk model and compute its excitations, determine boundary data and admissible gapped top boundaries, identify the low-energy preserving operator algebra together with its symmetry, relation, and twist data, and then switch among top boundaries to compare the induced boundary descriptions. As a type-I example, we develop FTH for the X-cube model with smooth and rough top boundaries; for a minimal effective Hamiltonian, both yield transverse-field plaquette Ising models, with exchanged subsystem symmetry and twist data, and the boundary switch is implemented by a linear-depth local unitary sequential quantum circuit (SQC). As a type-II example, we formulate FTH for Haah's cubic code in the Laurent-polynomial stabilizer formalism and analyze the natural $(Z)$ and $(X)$ top boundaries, which induce two two-dimensional qubit systems related locally by exchanging generalized plaquette Ising and transverse-field terms and nonlocally by a symmetry–relation duality. These results show that FTH is a genuine extension of TH to both type-I and type-II fracton orders. FTH therefore provides a concrete framework for organizing and understanding duality, with the prospect of offering a systematic route to new dualities.

The Lorentzian IIB matrix model provides a non-perturbative framework for emergent spacetime from matrix degrees of freedom. We study whether algebraic consistency constrains such structures by imposing restricted off-shell supersymmetry closure, modulo gauge transformations and explicitly identified trivial symmetries, on a CPT-even low-order effective-action ansatz with anisotropic background fields, without imposing their equations of motion. The zeroth-order Ward identity forces the scalar ansatz to be constant. At order two, retaining distinct macroscopic and internal transformation normalizations leads to a closure-compatible block-diagonal branch. On the nontrivial internal branch, Clifford-algebra identities force the internal non-Abelian flux to vanish. In four dimensions, a distinct dual-flux remainder can be absorbed into a Lorentz-type rotation when the macroscopic matrices form a non-degenerate coordinate sector. Within a linear absorption ansatz, the rank-three coefficient tensor is the Hodge dual of a vector. Macroscopic spatial isotropy selects its timelike orientation, yielding a $\kappa$-Minkowski-like algebra. Finite-dimensional Hermitian representations make the spatial sector trivial, so a nontrivial realization requires an infinite-dimensional limit with unbounded coordinate operators. The different weights of the spatial and internal generators under the adjoint action of $B_0$ are purely algebraic and are not interpreted as physical time evolution or dynamical compactification.

The paper discusses renormalization aspects of the quantum four-dimensional Yang-Mills theory with a cutoff regularization in the coordinate representation. The background field method is used to formulate a generating functional, and the regularization is introduced through quasi-local probabilistic averaging. Two main types of regularization are proposed: strong deformation, which consists in averaging fluctuation fields, and weak deformation, which is a covariant generalization of the first case with respect to gauge transformations of the background field. We study singular contributions for the first two quantum corrections in this paper and compare them in detail with the case of dimensional regularization. The consistency of the action and the equation of motion after introducing the regularization and making a renormalization procedure is analyzed. New counter-vertices are studied, in particular their locality properties and dependence on the regularization parameter.

The gravitino is a prominent example of a freeze-in dark matter candidate. Its relic abundance depends on the reheating temperature and on supersymmetry-breaking parameters, that is the universal gaugino mass, $M_{1/2}$, and the gravitino mass, $m_{3/2}$. As a consequence, the reheating temperature consistent with the observed dark matter abundance exhibits a maximum value, $T_{\rm reh}^{\rm reak}$, which decreases as $M_{1/2}$ increases. This behavior gives rise to a tension between prospective lower bounds on the gluino mass from future collider searches and the high reheating temperatures required for successful thermal leptogenesis. In this work, we investigate a nonstandard cosmological scenario in which the thermal bath is supplemented by an additional scalar field. We show that, for a matter-like equation of state, this component can induce a substantial dilution of the gravitino abundance, thereby allowing significantly larger values of the reheating temperature. In contrast, for a kination-like equation of state, the gravitino abundance is enhanced rather than diluted, leading to a reduction of the maximum allowed reheating temperature.

Building on the recently discovered origami-amplituhedron correspondence, we prove that the BCFW (Britto-Cachazo-Feng-Witten) cells triangulate the $m=4$ amplituhedron in full generality at all loop orders, both in momentum and momentum-twistor space. Along the way, we develop two natural "$L$-punctured" extensions of the positive Grassmannian and relate them via T-duality.

The earliest massive black holes are often discussed in terms of heavy baryonic seeds, primordial black holes, or super-Eddington accretion. We develop a different possibility: a compact object on a hidden donor brane forms a common five-dimensional horizon whose intersection with our brane is observed as a black-hole seed. Donor-side matter accretes onto the common five-dimensional horizon, increases the horizon radius, and consequently enlarges its intersection with our brane. As a result, the gravitational mass inferred by an observer living on our brane grows. We slice the five-dimensional geometry onto each brane and show that the induced exterior on our brane has the usual Schwarzschild/Vaidya monopole form at leading order, with subleading Weyl/Kaluza-Klein corrections in the localized-feeding branch. We construct a perturbative gradient-expansion solution satisfying the regular bulk equations and brane junction conditions. The matter sector satisfies the null energy condition for positive mass growth. The linear perturbation stability is investigated, and for supermassive seeds with horizon radius far larger than the interbrane scale, the dangerous long-wavelength mode is absent. The primary observational consequences are overmassive high-redshift black holes in underdeveloped hosts, hidden mass growth relative to the luminous accretion budget, LISA-band heavy-seed mergers, and the absence of primordial fossils required by primordial-black-hole explanations.

We study a string-motivated class of $\tfrac12$-BPS boundary conditions for 4d $\mathcal N=2$ $A_{K-1}$ circular quiver gauge theories with gauge group $SU(N)^K$, engineered by D4-branes suspended between NS5-branes on a circle. For D4-branes ending on a boundary D6-brane sent to infinity, a single-pole ansatz reduces the BPS equations to a constrained algebraic problem. We characterize the structure of its solutions, which exhibit a winding phenomenon with no analogue for linear quivers, and solve several cases explicitly in closed form. A brane-duality argument suggests looking for the S-dual of the pure Neumann boundary condition within this class. We show that the residual gauge symmetry can be discrete only under a condition fixed by tracelessness, in which case it is the centre $\mathbb Z_N$, and that solutions with this property exist for every $N$ and $K$.

We recently constructed a two-field Degenerate Higher-Order Scalar-Tensor (DHOST) bouncing model which is fully viable at the linear level [1]. This model is completely free of Belinski-Khalatnikov-Lifshitz (BKL) instability, ghost instability, gradient instability and superluminality. It also predicts the scalar spectral index and tensor-toscalar ratio consistent with observations. The aim of this paper is to extend the viability of the model to the non-linear level. To this end, we first refine the original model such that its prediction on the (local) non-Gaussianity parameter fNL agrees with observations, leaving the viability of the model at the linear level intact. We furthermore demonstrate that the strong-coupling scale is well above the characteristic background energy scale all the time. Our model indeed exemplifies the fully viable two-field DHOST bouncing model, in the sense that it is weakly-coupled, stable and non-superluminal as well as consistent with observations.

We investigate the dynamics of charged particles around a Schwarzschild-like black hole sourced by a Kalb-Ramond field and immersed in a uniform external magnetic field. The Kalb-Ramond field introduces a Lorentz violation parameter $l$ that modifies the spacetime geometry, while the magnetic field profoundly influences the trajectories through the Lorentz force, leading to a rich variety of orbital behaviours including curled (epicyclic) motion and dramatic transitions between distinct energy boundary configurations. We derive the full equations of motion, the effective potential, and the fundamental frequencies of quasi-periodic oscillations, and perform a comprehensive Monte Carlo Markov Chain (MCMC) analysis using observational data from the microquasars GRO 1655-40, XTE 1550-564, and GRS 1915+105. The pure Schwarzschild model is statistically ruled out for all three sources. For GRO 1655-40 and XTE 1550-564, only the combined effect of the magnetic field and Lorentz violation yields statistically robust models, with best-fit values $\mathcal{B}\sim 0.03$-$0.04$ and $l\sim 0.08$–$0.10$. Remarkably, for GRS 1915+105, the most massive object in our sample, the Lorentz violation parameter alone is sufficient to model the QPO frequencies, yielding an optimal fit with $\Delta AIC = \Delta BIC = 0$. Across all three objects, a clear trend emerges: the required value of $l$ decreases as the mass of the astrophysical object increases, suggesting a mass-dependent scaling of the Kalb-Ramond parameter. These findings establish the combined KR and magnetic field framework as a viable and statistically robust scenario for modeling QPOs in microquasars, and indicate that Lorentz-violating modifications to gravity may leave observable imprints in the strong-field regime, offering new avenues for testing quantum-gravity phenomenology with current and next-generation X-ray missions.

We study defects in superconformal field theories using holography, focusing on the precise derivation of the defect observables from supergravity. We consider $\mathrm{AdS}_p \times S^q$ spacetimes fibered over an interval and coupled to higher-form gauge fields as well as scalar fields. We determine the coordinate system in which the defect geometry admits an asymptotically flat boundary and, in this setup, we systematically apply holographic renormalization to compute the fundamental observables of the defect theory. In particular, we derive the one-point correlators of the bulk fields, the holographic stress tensor, and its Ward identities. We implement explicitly this procedure for line and surface defects in five- and six-dimensional Romans supergravity. The relevant geometries are $\mathrm{AdS}_2\times S^2$, $\mathrm{AdS}_2\times S^3$ and $\mathrm{AdS}_3\times S^2$ backgrounds warped over an interval, preserving four supercharges and asymptotically $\mathrm{AdS}_5$ and $\mathrm{AdS}_6$. In each case, we discuss the implications of our results and compare them with the standard literature on defects in conformal field theory.

Quantum field theories in the presence of a static and uniform external magnetic field possess two characteristic spatial symmetries: magnetic translations and magnetic rotation. We investigate general consequences of these symmetries on correlation functions from a model-independent perspective, without relying on specific models or perturbative expansions. The projective structure of magnetic translation symmetry constrains correlation functions of charged operators to acquire the Schwinger phase and leads to a factorized form into a gauge-covariant phase factor and a reduced correlator depending only on relative coordinates. We further derive the spectral representation of two-point functions in terms of representations of the magnetic translation algebra, in which the Landau- and symmetric-gauge descriptions arise as different choices of basis. Our results provide a unified symmetry-based framework for quantum field theories in external magnetic fields.

We investigate holographic complexity within the Schwarzschild-de Sitter (SdS) black hole spacetime. Two distinct de Sitter holography prescriptions are examined: the static patch scheme restricted to the stretched horizon and the de Sitter/Conformal Field Theory (dS/CFT) correspondence scheme defined at asymptotic future and past infinities. We evaluate the Complexity equals Volume (CV) conjecture and extend the analysis to codimension-zero proposals, specifically Complexity equals Spacetime Volume (CV2.0) and Complexity equals Action (CA), through the Wheeler-DeWitt (WDW) patch we construct. The behaviors of the complexity in the static patch holography at late time and in the dS/CFT at infinite spacelike boundary coordinate are studied, respectively. We find that under both the CV and CV2.0 conjectures, the static patch holographic complexity and the dS/CFT holographic complexity consistently exhibit linear growth. Conversely, regarding the CA conjecture, the holographic complexity growth rates for both the static patch and the dS/CFT correspondence vanish. This behavior is attributed to the finiteness of the (regularized) action within the restricted WDW region. Furthermore, we find that, in the limit in which the boundary coordinate is taken to infinity, the complexity growth rate in the static patch prescription coincides with its counterpart in the dS/CFT prescription. This agreement suggests a deeper connection between the two descriptions and may point toward a unified understanding of bulk dynamics in de Sitter holography.

We develop a branch-sensitive thermodynamic framework for higher-curvature black holes using the off-shell Gibbs free energy $G_{\rm off}$ and the Wald entropy$S_W$ as the basic data. On fixed-parameter slices, equilibrium black holes are stationary points of $G_{\rm off}$, and their local stability is governed by the Hessian $H=S'_W(r_h)T'(r_h)$, rather than by the temperature slope alone. For the five-dimensional charged regular AdS black hole in quasi-topological gravity, $S_W$ remains monotonic on the physical branch, so the usual temperature-slope rule is recovered only as a special consequence. The same off-shell structure also gives the local $A_3$ cusp normal form near criticality, yielding the mean-field $1/2$ branch separation exponent and explaining why smooth nondegenerate observables, such as the Lyapunov exponent, inherit the same scaling. In Lovelock black holes, $S'_W$ can change sign on non-planar branches, reversing the temperature slope stability assignment. However, on ghost-free and branch-regular Lovelock exteriors $S'_W$ remains positive. Thus the off-shell Hessian criterion also diagnoses why the ordinary slope rule is protected on physically admissible black holes branches.

In the context of grand unified theories, any cosmic strings present in the post-inflationary universe are likely to be metastable, with a decay rate set by the spontaneous creation of monopole pairs on the string. Determining this decay rate is crucial in understanding the phenomenology of the cosmic string network, including a potentially observable gravitational wave background. The bounce action governing this rate has so far only been determined using the thin string approximation or specific ansätze for the field profiles in the monopole formation process. Here we solve this problem using classical lattice simulations, relying only on the inherent symmetries of the problem. Our results indicate a suppression of the bounce action and hence a faster string decay compared to previous estimates.