Papers

We show that the quantum entanglement between the conformal field theories (CFTs) living on the future and past boundaries in the de Sitter/conformal field theory (dS/CFT) correspondence can be described by Wick rotating to a geometry with two timelike directions. We propose a new realization of the dS/CFT correspondence in which quantum gravity on this two-time geometry is holographically dual to a CFT defined on a Lorentzian torus. We show that this duality reproduces key features of dS holography, including the dS entropy, correlation functions, and pseudoentropy. Finally, by extending the framework of path-integral optimization, we explain how dS spacetime emerges from the CFT on the Lorentzian torus.

It is common for separate factorization and renormalization scales to be discussed in connection with phenomenological applications of QCD factorization theorems. We observe that simultaneously preserving renormalization group invariance, Ward identities, and the basic sum rules in the definitions of parton densities forces these scales to be equal. The statement applies to generalized pole subtraction schemes that use dimensional regularization and to collinear factorization theorems for basic processes like deep inelastic scattering. We discuss implications for estimating the effects of scale sensitivity in phenomenological calculations, consistent extractions of Standard Model parameters alongside parton densities in global QCD analyses, and generally connecting phenomenologically extracted parton densities to first principles non-perturbative techniques like lattice QCD.

In this study, we discuss the clique percolation in the ensembles of random geometric graphs with different kernels that quantify the geometrical constraints. For the sharp cut-off we find the wide Griffiths phase of extended criticality with the power-law behavior. One boundary of the Griffiths phase is the generalization of a percolation critical point for the ER ensemble when the percolation within the large but finite cluster emerges. The second boundary corresponds to the point in the parameter space when the percolation in the entire clustered system becomes available. For the power-law kernel, richer behavior with a clique-size-dependent boundary between the effective ER and geometric regimes has been identified. The Griffiths phase in this case exists as well. Finally, the pattern with the exponential kernel has been analyzed. We briefly discuss the possible applications of our findings.

The Standard Model does not determine quark masses or the CKM matrix. In the exceptional-Jordan programme, square-root masses occupy short $\operatorname{Sym}^{3}(\mathbf{3})$ chains. Compressing the symmetric-cube lift onto occupied nodes gives a root-mass operator whose square yields the proposed mass ratios, packaging that spectrum and relative left frames in one finite Dirac operator without deriving the frames. Conditional on the transport, virtual-node-amplitude, real-$(2,3)$ and balanced-quadrature choices, the no-fit layer gives $|V_{us}|=0.2371$ ($5.3\%$ high) and $|V_{cb}|=0.0422$ ($0.8\%$ high) at $M_Z$. The relation $|V_{ub}|/|V_{cb}|=\sqrt{m_u/m_c}$ is a factor two low; one complex long edge is fitted. The two balanced orientations give branches $(\varepsilon,\omega)=(0.002079,288.2^\circ)$ and $(0.005358,202.2^\circ)$, so the former $\varepsilon$ ratio is not robust and raw $\omega$ is convention-dependent. For an adopted $F_1$–$F_2$ family embedding, we construct an exact Peirce-changing Albert lift in $\mathfrak f_4(\mathbb C)$, reproducing conjugate up/anti-down transport and $\varphi_{12}=-2\chi$. For an adopted cyclic Majorana placement and real-linear projection, its completion has real $(e_4,e_3,e_6)$ support while the $e_1$ quadrature vanishes; $J_\ell=0$ and $\delta^\ell_{CP}=0$ or $\pi$ are compatibility results in this class. The minimal radial-quartic cyclic truncation has equal-magnitude full-rank extrema or a flat direction; a mixed Albert cubic gives stable alignment only in a chosen three-edge subspace. Six diagonal mass links plus three directed Peirce links would form a connected one-cycle nine-link graph if the Yukawa block is linear in the projected bridge. This is a candidate Arkani-Hamed et al. texture skeleton, not a derivation: family-vacuum selection, chiral projection and right-frame locking remain open.

We investigate how nonmetricity affects particle creation and evaporation in rotating bumblebee black holes by comparing metric and metric-affine solutions. We normalize the stationary Killing vectors at spatial infinity before defining physical frequencies, angular velocities, and temperatures. This procedure changes the static comparison and gives the leading calibration $\ell=3X/4$. In the metric solution, $\ell$ shifts the horizons, stationary limit surfaces, and extremal boundary, increases the normalized horizon angular velocity, and suppresses the Hawking temperature. Nevertheless, the surface gravity remains uniform and the scalar wave equation separable. We derive the tunneling factors, quantum occupation numbers, radial potential, and an analytical lower bound for the axisymmetric greybody factor. In the metric-affine geometry, nonmetricity preserves the Kerr coordinate locations of the horizons and stationary limit surfaces, but changes the physical horizon area, normalized angular velocity, and meridional sector. The component $g_{r\theta}$ couples angular channels, whereas the local surface gravity depends on latitude when $aX\neq0$. Consequently, the generic rotating configuration admits neither a single global Hawking temperature nor an independent channel-by-channel emission spectrum. In the static limit, under the same Stefan-Boltzmann prescription, both Lorentz-violating geometries have lower luminosities and longer lifetimes, with the metric-affine black hole radiating less and evaporating more slowly. A local slow-rotation expansion preserves this tendency but does not establish a global rotating evaporation hierarchy. Existing weak-field constraints limit fractional corrections to static quantum-emission observables to below $1.3\times10^{-11}$.

We describe the image of a quantized BFN Coulomb branch $\mathcal{A}_{G,N}^{\hbar=1}$ under localization (abelianization) map for any $G,N$. In most cases, such as quiver gauge theories without loops, this description works for any flavors, sometimes we need to take generic or formal flavor parameters. The answer is given by a roots and residue condition similar to Ginzburg—Kapranov—Vasserot construction of DAHA arXiv:alg-geom/9512017. As a corollary, for any quantized conical Coulomb branch (and zero or small flavors) we provide a mathematical construction of the sphere trace introduced by Gaiotto and Okazaki arXiv:1911.11126.

We consider the quantization of the non-relativistic limit of electrodynamics called Galilean electrodynamics. To that end, we apply the Dirac bracket formalism to understand the constraints and dynamics of the theory and analyze its gauge structure. We show that the theory is fully constrained, which eliminates all the degrees of freedom from the path integral.

We investigate the minimal composite Higgs model based on the symmetry-breaking pattern $\mathrm{SU}(4)\rightarrow\mathrm{Sp}(4)$, where electroweak symmetry breaking is governed by the vacuum alignment angle $\theta$. Through the leading-order relations $\kappa_V=\cos\theta$ and $m_\eta=m_h/\sin\theta$, precision measurements of Higgs couplings are translated into direct constraints on the vacuum structure and the singlet pseudo-Nambu–Goldstone boson mass. Using the current ATLAS Run-2 measurement of $\kappa_V$, we construct a Bayesian posterior for $\theta$, including the Jacobian associated with the transformation from $\kappa_V$ to $\theta$, and validate the results through an independent frequentist $\Delta\chi^2$ analysis. The same framework is then applied to the projected sensitivities of the High-Luminosity LHC and FCC-ee. The current data imply a conservative lower bound of approximately $440~\mathrm{GeV}$ on the singlet mass at the $95\%$ credibility level, while the projected sensitivities improve this limit to about $600~\mathrm{GeV}$ at the HL-LHC and beyond $2~\mathrm{TeV}$ at FCC-ee. The close agreement between the Bayesian and frequentist determinations demonstrates the robustness of the extracted constraints. These results show that future Higgs precision measurements will probe the vacuum alignment of the minimal $\mathrm{SU}(4)/\mathrm{Sp}(4)$ composite Higgs model with unprecedented sensitivity, placing increasingly stringent constraints on the allowed parameter space and establishing the singlet scalar as a compelling target for upcoming collider programs.

We compute the exact finite-\(N\) superconformal index of four-dimensional \(\mathcal N=4\) \(U(N)\) Yang–Mills theory with antisymmetric elliptic Ruijsenaars–Schneider (eRS) surface-defect insertions. By matching the inserted eRS Hamiltonians to their independent realization in five-dimensional \(\mathcal N=1^*\) gauge theory, we interpret that the solvable locus \(t=q\) corresponds to vanishing adjoint mass. Motivated by this massless specialization, we impose the four-dimensional balancing condition \(p=uv\). At this point, the eRS operators are conjugate to free \(q\)-shifts, and the self-glued matrix integral reduces to a bilateral free-fermion determinant. This gives closed finite-\(N\) formulas for every antisymmetric rank. On \(v=0\), we determine the stable pure \(u^{kN}\) corrections at all wrapping orders; the bilateral formula also captures the reflected \(v^{kN}\) sectors and mixed \(u\)–\(v\) contributions. We further formulate the balanced perturbation away from \(t=q\) through second order in terms of connected correlators. Finally, a maximal-D3 determinant reproduces the ordinary one-giant coefficient and isolates the microscopic input required for the defect correction.

The tracking condition $\dot{\phi}^2=\gamma H^{-m}$ for single scalar field theory leads to analytic inflationary solutions, which are compatible with the current cosmic microwave background radiation experiments. To our knowledge this is the only analytic solution of inflation which is compatible with the data, to date. In this work we seek for some theoretical basis that can lead to the tracking condition $\dot{\phi}^2=\gamma H^{-m}$. As we show, if the Universe is seen pre-inflationary as a quantum statistical system, the scalar field may emerge as a collective condensate of the quantum degrees of freedom. In the quantum-to-classical transition of the Universe, the scalar field two point function yields the susceptibility of the theory with an inherent correlation length. Using information theoretic motivation and Wilsonian quantum field theoretic arguments, we demonstrate that the tracking conditions $\dot{\phi}^2=\gamma H^{-m}$ emerge from this framework.

We test whether bare codimension-two areas in the D7-brane open string metric (OSM) reproduce the leading probe-brane contribution to boundary entanglement entropy in the massless finite-density D3-D7 system at zero temperature. The established Chang-Karch-Uhlemann benchmark contains shape-dependent volume terms in a controlled probe regime. By contrast, the connected strip family terminates at a maximal width and the selected strip finite part saturates at the disconnected-reference value, while the lower-area spherical branch is area-like rather than volume-like at large radius. The OSM construction nevertheless detects the density-induced crossover scale, and its geometric landmarks occur at order-one multiples of a pole-defined longitudinal response length. A low-temperature regulator shows that no density-controlled horizon-volume term survives the zero-temperature limit. Bare OSM areas therefore diagnose open-sector crossover physics but do not, in general, compute flavour entanglement entropy.

We develop a constructive framework for the three-point higher spin conformal correlation function, originally introduced in our previous work, and apply it as the foundation for constructing the quantum effective action of the corresponding higher spin conformal gauge theory. Employing a symmetric refinement of the earlier construction, we analyze the principal singularity of the three-point function and the associated effective action. This leads to a general method for extracting the dominant singularity and investigating the anomalous local contributions to the effective action.

The present article deals with gravitational-wave propagation affected by higher-derivative terms that break spacetime symmetries. Two dimension-6 contributions of the gravitational Standard-Model Extension pose our starting point. A linearization of the action implies a wave equation that contains additional terms with spacetime-constant background fields. The modified dispersion relations in covariant form for gravitational waves are derived, where we distinguish between nonbirefringent and birefringent sectors. A classification of the coefficients in terms of sets with index structures resembling those of the electromagnetic fields has proven to be valuable. We constrain the nonbirefringent coefficients based on the measured arrival time difference between the gravitational wave and photons from the events GW170817 and GRB 170817A, respectively. Bounds on the birefringent coefficients result from the absence of a perceivable separation of the two modes in the event GW150914. These findings quantify the extent to which standard linearized gravity is valid based on the modifications considered.

We investigate the propagation and resonance behavior of an Abelian massive vector field in the presence of a gauge-invariant, CPT-even, dimension-four Lorentz-violating kinetic operator constructed from a single preferred four-vector. In the massless theory, the propagator contains an additional algebraic pole that decouples from conserved currents, leaving two physical degrees of freedom. After spontaneous breaking of the internal U(1) symmetry, all three vector polarizations become physical but separate into two orthogonal dispersion branches carrying two and one physical polarization states, respectively. We show that this decomposition is preserved under Dyson resummation for a transverse matter vacuum polarization and calculate the corresponding decay rates and fermion-annihilation amplitude. The split-pole structure and associated double resonance behavior cannot be understood through a finite number of perturbative Lorentz-violating insertions. The contribution of the second branch in physical processes is strongly dependent on the initial momentum geometry: it vanishes for massless head-on fermions in a timelike background, whereas boosted nearly parallel configurations can generate an energy-enhanced correction. Spacelike and lightlike backgrounds additionally lead to directional and potentially sidereal variations of the resonance signal.

In this paper, we investigate topologically charged Morris-Thorne-type traversable wormholes by solving the Einstein field equations with an anisotropic fluid as the energy-momentum tensor and analysing the resulting solutions. In continuation to the earlier work (Eur. Phys. J C 84 (2024) 1037), we consider the shape functions such as: (i) $A(r)=r_0\,e^{r_0-r}$; (ii) $A(r)=r_0\,a^r/a^{r_0}$,\quad $0 < a<1$; (iii) $A(r)=r_0\,\left(\frac{\cosh r_0}{\cosh r}\right)^{\delta}$,\quad $\delta \geq 1$; (iv) $A(r)=\frac{1}{r}+\ln\!\frac{r}{r_0}$; (v) $A(r)=B\,r^n+(1-B)$; (vi) $A(r)=r_0\,\frac{\mbox{ln} (1+r)}{\mbox{ln} (1+r_0)}$, (vii) $A(r)=r_0+a\,r_0\,\left[\left(\frac{r}{r_0}\right)^\beta-1\right]$, where $\beta<1$ and $0 < a\,\beta <1$. We examine the energy conditions-namely, null, weak, strong, and dominant energy conditions and explore how topological charge influences or controls these conditions. Additionally, we calculate the anisotropy parameter to determine whether the wormhole geometry exhibits attractive or repulsive behavior. Our analysis demonstrates that the energy density of the anisotropic fluid is always positive. However, while some of the energy conditions are partially satisfied, others are violated.

We investigate the production of Dark Matter (DM) within the warm Higgs–Starobinsky (HS) inflation. By adopting the ultraviolet (UV) freeze–in mechanism – where the DM number density is initially negligible but is populated over time through non-renormalizable interactions of defined mass dimensions – we find that the DM production within the HS potential has a characteristic timing. For both DM masses, $m_\chi=1$ MeV and $m_\chi=100$ GeV, the yield of DM occurs close to the termination of inflation and its transition to the radiation dominated (RD) era. The present–day DM relic abundance is generated for both DM masses with non-renormalizable operators of mass dimension $D=\{8,9\}$ within strong dissipation regimes. The obtained results suggest that the form of the HS potential and the associated scalaron dynamics favor UV freeze–in DM production as the scalaron approaches the minimum of the potential, where energy transfer to the thermal bath becomes particularly efficient. This distinctive transition behavior differentiates the HS model from other inflationary models and advances our understanding of DM production.

We determine the small-oscillation period of a simple pendulum in Schwarzschild spacetime. After transients decay, the displaced rope coincides with a geodesic of the induced spatial metric. This determines the radial lift of the bob to quadratic order in the angular amplitude and leads to the period measured by an observer at the bob's equilibrium position, $r=r_2$, with the fulcrum at $r_1$, \[ T_{(2)}=4\pi\frac{r_2^2}{c r_s}\sqrt{N_2(N_1-N_2)}, \] where $N_i=N(r_i)$ and $N(r)=\sqrt{1-r_s/r}$ is the Schwarzschild lapse. The result is therefore expressed in terms of the same function that determines clock rates and gravitational redshifts. In the Newtonian limit, we reproduce the classical result $T=2\pi\sqrt{L_0/g}$. We interpret the period close to the horizon in terms of an effective pendulum length. We compare our treatment with the coordinate-length constraint adopted in an earlier study and argue that the two problems are inequivalent away from the classical, weak-field limit.

This thesis investigates quantum field theoretic approaches to classical gravity beyond General Relativity. Using worldline effective field theory, worldline quantum field theory, and on shell scattering amplitudes, it investigates compact-object dynamics in dark-sector models, scalar tensor gravity, dynamical Chern Simons gravity, and Einstein Maxwell dilaton theory. The thesis derives a range of conservative and radiative observables, including impulses, waveforms, eikonal phases, two-body potentials, and scattering angles, while incorporating effects associated with spin, parity violation, infrared structure, and multi-loop integrals. It also constructs celestial eikonal amplitudes and analyzes their conformal data in gravitational theories beyond General Relativity. Collectively, these results broaden the application of modern quantum field theoretic techniques to gravitational dynamics and contribute to a more detailed understanding of gravity beyond the Einsteinian framework. (Detailed abstract in the thesis.)

The canonical and path integral quantization for non-linear electrodynamics in the presence of an external electromagnetic (EM) field are proposed in this work. The EM background field is introduced expanding a general lagrangian of a generic non-linear electrodynamics around the background for small fluctuations of the propagating fields, where we consider up to the quadratic terms in the propagating fields. As consequence, we obtain an electrodynamics linearized by the presence of the external EM field. Thereby, we study the canonical quantization calculating the energy for the ground state of the linearized EM field in terms of an external magnetic field. The microcausality of the model also is discussed through the Pauli-Jordan function. We also define a generating functional for the linearized EM field, in which, in the Coulomb gauge, the Green function of the model is obtained, and we can construct the perturbative formalism like in standard quantum field theory (QFT). As application of the perturbation theory, the effective potential at one loop is calculated for the linearized EM field coupled to a complex scalar field. We apply the results in the case of the Modified Maxwell ED.

Quantum computing provides a promising framework for the simulation of quantum field theories, where the computational cost depends both on the quantum algorithm employed and on the representation of the Hamiltonian. We investigate a formulation of the $\phi^4$ model based on the harmonic-oscillator basis in coordinate space. We derive the lattice $\phi^4$ Hamiltonian in this representation and analyze the structure of the resulting one-body matrix and interaction tensor. We show that both exhibit an effective band-diagonal structure, allowing controlled truncations of the Hamiltonian while preserving the low-energy spectrum. We validate this formulation by comparing low-energy observables obtained from numerical diagonalization with those computed in the standard harmonic-oscillator momentum-space representation. Finally, we estimate the resources required to encode the Hamiltonian on a quantum computer using both binary and unary boson-to-qubit mappings. By exploiting effective locality, the coordinate-space representation reduces the resources required for quantum simulation over a broad range of parameters.

We investigate the spectral functions of the $J/\psi$ meson in a rotating thermal background within the soft-wall holographic model. The global rotation is implemented through a rotating AdS-like metric, while a local inertial frame is introduced in which the vector field can be decomposed into different spin states. We solve the equations of motion of the vector field in the bulk with incoming wave condition near the horizon and compute the retarded Green function, from which we extract the invariant-mass spectral functions for $J/\psi$. When the momentum is parallel to the rotation axis, the peak energies shift by $-\Omega J_z$, as expected by a coupling between rotation and angular momentum, while the widths are nearly independent to $\Omega$. When the momentum is in perpendicular direction, the spectral functions for spin-$\pm1$ states deviate significantly from the single-peak behavior and the energy shifts depart from $-\Omega J_z$. The resulting triplet splittings of the spectral functions provides a holographic perspective on spin-dependent vector meson properties in rotating systems.

For a stable compact quarkonium state in the pNRQCD multipole regime, chromoelectric polarizability arises at leading order from two E1 transitions through virtual color-octet states. For an unstable state, we define the corresponding response through the quadratic displacement of its complex resonance pole in a weak chromoelectric background, so that its real and imaginary parts describe field-induced shifts of the pole mass and width. Starting from a renormalized background-field correlator, we show that the resonance polarizability is given by the complete two-field kernel normalized by the energy derivative of the full inverse propagator at the pole. In an effective theory with explicitly separated intermediate sectors, the kernel contains the standard E1-octet-E1 contribution, the complete source response of decay channels already coupled at zero field, and local contributions. This distinction becomes essential above open-flavor threshold and reduces to the standard pNRQCD polarizability in the stable, energy-independent limit. A simple $D\bar D$ realization for the $\psi(3770)$ gives the complex pole-residue factor $1/[1-\sigma'(z_\psi)]=0.800-0.336$, illustrating that threshold dressing can substantially modify both the magnitude and phase of the response. The resulting pole-based relation identifies the quantity required for a source-dependent coupled-channel determination of the chromoelectric polarizability of a heavy-quarkonium resonance.

We propose a novel UV-IR mechanism in quantum gravity in which black hole instabilities act as a bridge to the most ultraviolet sector of the theory. Specifically, we argue that when black holes reach a critical temperature associated with a light tower of states, they undergo a phase transition that sources particles near the species scale, a threshold beyond which any effective field theory of gravity fails. Using the existing numerical results, we show that production of such particles through Hawking radiation is always subdominant. We also extend our investigation to a large family of dyonic and dilatonic black holes and show how the conclusion depends on the origin of the gauge symmetry, its dilatonic coupling, and the charge under that gauge symmetry.

Spontaneous scalarization provides a dynamical mechanism to evade the no-hair paradigm, but it has been argued to generically eliminate the Cauchy horizon in charged black holes. We show that this obstruction is not universal, but instead follows from the sign-definite structure of the Einstein-Maxwell source term. Within the $P$-dual formulation of nonlinear electrodynamics, we derive a general condition under which the effective scalar source changes sign between the horizons, allowing the integral constraint to be satisfied without destroying the Cauchy horizon. This establishes that the fate of the Cauchy horizon depends on the electromagnetic coupling and identifies candidate theories where scalarized horizons may persist. The resulting framework opens the possibility of studying scalarization in the interhorizon region and its interplay with mass inflation.

The mass spectrum of tetraquark states is examined using the spinless Salpeter equation alongside the Cornell potential. Analytical wave functions are derived through a variational approach, resulting in a specific mass formula for the bound states. This study investigates the mass spectra of heavy tetraquark states within a constituent diquark-antidiquark model. We employ a spinless Salpeter equation framework, incorporating the Cornell potential to describe the interaction between the diquark and antidiquark constituents. To account for relativistic effects, we utilize first-order perturbation theory to include the leading-order kinetic energy corrections arising from the expansion of the relativistic kinetic energy operator. A variational approach is adopted to determine the ground state masses, where the optimal variational parameter ${\beta}$ is found by minimizing the system's energy and then for higher states. We systematically calculate the masses of several experimentally observed and predicted tetraquark candidates, across a range of strong coupling constant values. Our results demonstrate a sensitivity of the calculated tetraquark masses to, and the model provides theoretical mass predictions that are in reasonable agreement with experimental observations for these exotic hadronic states. This work contributes to a deeper understanding of the internal structure and dynamics of heavy tetraquarks.

The divergence of Feynman graph integrals is one of the central issues in the study of perturbative quantum field theories. A rigorous formulation of these integrals usually requires renormalization. In this paper, we prove that the Feynman graph integrals arising from holomorphic field theories on closed real-analytic Kähler manifolds are convergent with respect to heat-kernel renormalization, Cauchy principal value renormalization, and zeta-function renormalization. Moreover, these three renormalization procedures produce the same value. Our proof is based on the theory of wonderful compactifications in algebraic geometry, which provides a geometric understanding of these integrals. As a consequence, we establish a gauge anomaly formula for these graph integrals.

The Nelson-Barr mechanism solves the strong CP problem through spontaneous CP violation, but the resulting CP-conjugate vacua generically lead to stable domain walls. We propose that the Nelson-Barr scalar itself drives hilltop inflation. A CP-symmetric double-well potential for its imaginary component forms two CP-breaking valleys, with inflation proceeding along one of them. Since the lowest CP-invariant ridge is generically much higher than the energy available after inflation, transitions between the two branches are energetically inaccessible, and the domain walls cannot be regenerated after inflation. A small CP-preserving linear deformation raises the scalar spectral index of quartic hilltop inflation and yields CMB-compatible parameter regions. The Nelson-Barr sector necessarily provides a portal to visible-sector reheating. When coupled to right-handed neutrinos, it can also transmit the spontaneous CP phase to the lepton sector and, in an extension that allows a higher CP-breaking scale, even realize nonthermal leptogenesis. This establishes a unified cosmological realization of the Nelson–Barr mechanism in which the same CP-breaking dynamics solves the strong CP problem, can generate quark and lepton CP violation, drives inflation and reheating, and enables baryogenesis, while simultaneously eliminating the associated domain-wall problem.

While General Relativity remains our most rigorously tested framework for gravitation, the theoretical persistence of singularities within standard black hole solutions continues to motivate the exploration of mathematically regular alternatives. Gravitational vacuum stars (gravastars) offer a non-singular model, substituting the event horizon with a physical, ultra-stiff thin shell. Recent studies have demonstrated that extended theories, such as $f(R, L_m, T)$ gravity, can structurally support these objects by utilizing the non-minimal coupling between geometry and matter. Building upon these static foundations, this paper presents a phenomenological propositional model to explore the dynamic interactions between modified-gravity gravastars and equatorial accretion flows. By numerically solving the modified Tolman-Oppenheimer-Volkoff equations and applying a non-complexifying algorithm, we construct a mathematically regular rotating metric ansatz. We demonstrate that the modified gravity coupling parameter systematically alters the effective potential, shifting the location of the Innermost Stable Circular Orbit (ISCO). Furthermore, we explore the idealized thermodynamics of plasma colliding with the gravastar surface, suggesting a distinct thermal emission that could theoretically produce a “filled-in” central shadow in interferometric observations. While acknowledging the challenges of observational degeneracy and the deliberate omission of complex radiation pressure feedback, we offer these geometric and thermal signatures as a transparent conceptual baseline to motivate future general relativistic magnetohydrodynamic (GRMHD) campaigns.

We prove a conjecture of Dubrovin, Liu, Yang, and Zhang that states that the Poisson bracket of the Dubrovin-Zhang hierarchy of a rank-one cohomological field theory is constant if and only if it is given by the triple Hodge class with the parameters satisfying the Calabi-Yau condition.

We study a restricted fibre-dependent $\alpha'$-loop sector in Type IIB Large Volume Scenario fibre inflation beyond the conventional Berg-Haack-Pajer (BHP) parametrisation. Motivated by effective-field-theory corrections in K3-fibred Calabi–Yau orientifolds, we analyse BHP-complete, partially BHP-driven and BHP-free configurations. For BHP-driven cases, the additional corrections act as effective deformations of the standard fibre potential and are bounded at the percent level relative to the corresponding BHP structures, with logarithmic terms typically more restricted due to their effects on the slope and curvature. At the effective-field-theory level, we identify a BHP-free fibre-inflation regime, referred to as $\alpha'$-loop inflation, in which the conventional KK- and winding-type BHP channels vanish while the generalized loop sector stabilises the fibre modulus and supports slow-roll inflation. This regime exhibits a characteristic hierarchy between fibre-dependent loop structures controlled by the large-volume suppression and satisfies CMB, Kähler-cone, large-volume and heavy-modulus constraints. Our results show that fibre inflation is sensitive to the orientifold and brane configurations, and that corrections beyond the BHP ansatz can generate new controlled inflationary regimes.