Papers

We compute the scaling dimensions of charge $q$ monopole operators in QED$_3$ with $N$ two-component complex fermions and Chern-Simons level $k$, to subleading order in the limit where $k,N$ are large and $k/N$ is fixed. We use this and previous results for scalar QED$_3$ (sQED$_3$) to check the duality between QED$_3$ with $N=1,k=-3/2$ and sQED$_3$ with $N=1,k=2$, whose $U(1)$ monopole symmetry is enhanced to $SO(3)$. We find that the lowest charge monopole value for QED$_3$ is close to 2 as expected for the emergent $SO(3)$ current, the second lowest charge monopole matches a prediction from a fuzzy sphere calculation, while higher $q$ monopoles match the corresponding sQED$_3$ values with relative error of just one percent. We also find similar evidence for dualities between QED$_3$ with $N=1,k=-(2m+1)/2$ and one scalar coupled to two $U(1)$ gauge fields, which has an effective description as sQED$_3$ with $N=1,k=\frac{m+1}{m}$ and $q_s=mq_f$ for $m>1$. Finally, by fitting many values of $q$ we show that the $q^0$ term at large $q$ for QED$_3$ takes the same nonzero value that appears in the universal EFT for parity preserving $U(1)$ theories, even though parity is broken for $k\neq0$. For sQED$_3$, a similar fit gives zero $q^0$ term for $k\neq0$, unlike the universal nonzero value previously observed for $k=0$.

In this paper, we investigate the first-order one-loop quantum corrections generated by all possible nonminimal dimension-6 additive CPT-odd Lorentz-violating (LV) terms to analyze the radiative induction of the Carroll-Field-Jackiw (CFJ)-like terms. We demonstrate that for dimension-6 operators, the resulting CFJ term can diverge for some choices of LV operators; however, in all these cases, this divergence is eliminated for certain relations between LV parameters.

The Festina-Lente bound is a swampland conjecture motivated by the behavior of charged BHs in dS spacetime, which imposes a constraint on the masses of charged particles. Although relatively weak in the present-day Universe, it can severely constrain inflation. We clarify its underlying assumptions and show that breaking all gauge symmetries during inflation, with gauge boson masses above the Hubble scale, provides a natural way to evade these constraints. We catalogue single flat directions in the Minimal Supersymmetric Standard Model that completely break its continuous gauge group, together with pairs that achieve complete breaking only when both directions are excited and simultaneously satisfy F- and D-flatness. With suitable lifting operators, such condensates can also generate the baryon asymmetry through the Affleck-Dine mechanism. Within this classification, all single-direction monomials that admit complete breaking carry nonzero $B-L$, providing candidates for Affleck-Dine baryogenesis. We further show that, in this setting, a large condensate compatible with the observed baryon asymmetry and isocurvature constraints readily satisfies the Festina-Lente bound, establishing a natural connection between the FL bound and Affleck-Dine baryogenesis.

We show that inflation with a large number of fields, as predicted by concrete ultraviolet embeddings, generically produces almost-local cosmological collider signals in the bispectrum squeezed limit. We construct the most general boost-breaking mixings between the curvature perturbation and $N_{\rm f}$ additional fields, and extract the late-time scaling dimensions that dictate the soft limits of cosmological correlators. For a handful of fields, an enhanced squeezed limit (with potential oscillations) is a fine-tuned signal. At large $N_{\rm f}\sim100$, however, mixings generically drive the scaling dimensions toward the unitarity boundary. We show that this is a direct consequence of extreme value statistics and random-matrix universality, turning an almost-local bispectrum shape into a generic prediction for almost any masses and mixings.

The scale evolution of parton distributions is governed by splitting functions. We compute the four-loop pure-singlet contribution to the quark-to-quark splitting function in perturbative QCD. Together with the known non-singlet contribution, our result completes the quark-to-quark splitting function at this order. We confirm previous partial results and obtain, for the first time, a fully analytic expression valid for all momentum fractions. We examine its behavior at small momentum fractions and provide precise numerical representations suitable for parton evolution.

We prove that scalar Feynman integrals are Stieltjes functions in each kinematic variable $-p_i\cdot p_j$, as well as in the particle masses, for arbitrary loop order, arbitrary numbers of external legs, and arbitrary internal masses, whenever a certain exponent condition is satisfied. The proof rests on a canonical decomposition of the second Symanzik polynomial with manifestly non-negative coefficients indexed by spanning two-forests. We present a dedicated analysis of the case in which the kinematic variables satisfy relations, as frequently happens in physical applications. We argue that integration-by-parts relations allow the selection of master-integral bases in which every element is a Stieltjes function. The Stieltjes property guarantees the convergence of Padé approximants and provides determinantal (Hankel) constraints on the Taylor coefficients of master integrals that go beyond previously known complete-monotonicity bounds. We develop a numerical strategy that combines these Stieltjes constraints with differential equations to determine the master integrals in the Euclidean region via semidefinite optimization. We demonstrate this approach on the pedagogical example of the six-dimensional massive box integral, and then apply it to the calculation of previously unknown three-loop two-mass integrals needed for three-loop electroweak corrections to the $Z$- and Higgs-boson self-energies.

We construct a five-dimensional generalization of the swirling universe and embed in it the Myers-Perry black hole and the rotating black ring. We prove that both solutions are free of conical singularities, analyze their geometrical properties, compute their mass and angular momentum, and discuss their uniqueness.

We note that the description of elementary particles in anti-de Sitter (AdS) quantum theory differs radically from standard approaches. Since the Cartan subalgebra of the AdS algebra has rank 2, it is necessary to consider only those elements that explicitly depend on the eigenvalues of operators in the irreducible representations (IRs) of the algebra. In the literature, AdS symmetry is widely invoked in various quantum applications, such as AdS/QCD. However, such frameworks typically do not take into account the unconventional properties of the AdS algebra IRs investigated in the present paper.

In a companion paper, we found that near the untwisted point of a four-boundary AdS$_3$ wormhole, whenever the complete bipartite Ryu-Takayanagi entropy vector is insensitive to a Fenchel-Nielsen twist, the holographic $\mathtt q=4$ multi-entropy is insensitive as well. Here we show that the situation changes at finite twist. The twist lengthens the crossing geodesics and thereby enlarges the region in which all bipartite RT entropies remain invariant. In part of this enlarged region, a twist-sensitive $\mathtt q=4$ network becomes globally minimal. We thus find an open region of wormhole moduli space in which the complete bipartite RT entropy vector is exactly unchanged while the $\mathtt q=4$ multi-entropy detects the twist. Our result provides an explicit example in which the $\mathtt q=4$ genuine multi-entropy probes bulk geometric information invisible to all bipartite entanglement entropies.

We ask whether multipartite entanglement can probe bulk moduli invisible to bipartite entanglement. We study this question in an explicit family of four-boundary AdS$_3$ wormholes related by a Fenchel-Nielsen twist $\tau$, asking whether the complete set of bipartite RT entropies can remain exactly $\tau$-independent while the holographic $\mathtt q=4$ multi-entropy is sensitive to the twist. Within the class of configurations analyzed here, for sufficiently small $|\tau|$, we find no such regime along the symmetric line $\ell=m$: the globally minimal $\mathtt q=4$ network is itself exactly $\tau$-independent throughout the parameter range analyzed. This conclusion is not a priori obvious: it emerges from a competition among several admissible configurations whose relative ordering changes multiple times as the geometry is varied, and persists up to the point where the bipartite RT entropies themselves become twist-sensitive.

The kink soliton provides a simple construction of a topological thick 3-brane sourced by a minimally coupled canonical scalar field in five-dimensional general relativity. Although the flat-space kink is a solution of $\varphi^4$ theory, the gravitating configuration requires $M_*$-suppressed $\varphi^6$ corrections to support a stable warped geometry. Unlike its flat-space counterpart, the scalar perturbation spectrum contains no normalizable bound state. We nevertheless identify a single quasi-bound, or resonant, mode. Using a time-independent relative-probability analysis, direct time evolution, and a four-turning-point WKB calculation, we establish a direct connection between this resonance and the massive bound shape mode of the flat-space $\varphi^4$ kink. We also show that, within an EFT-consistent parameter window, the resonance can transfer energy from bulk geometric fluctuations to localized matter, thereby allowing the possibility of high-scale reheating in the early universe.

We study the ferromagnetic Ising model on finite hyperbolic tessellations of Euclidean AdS$_2$ with open and wired boundary conditions. Because a finite fraction of spins remains at the boundary as the lattice grows, these conditions select distinct thermodynamic behaviours. In the $\{5,4\}$ tessellation, Monte-Carlo simulations using efficient worm algorithms on open boundaries (OBC) yield a transition near $\beta_c J=0.632(3)$, with susceptibility data collapsing under scaling by the total number of spins $N$. The fitted finite-size exponents, $1/\bar{\nu} \simeq 0.162$ and $\gamma/\bar{\nu} \simeq 0.743$, differ substantially from the mean-field volume scaling. Wired boundaries (WBC), which correlate boundary spins, instead show a transition around $\beta_c J=0.348(4)$ to an ordered phase consistent with the mean-field exponents. While the mean-field criticality with WBC is consistent with previous studies and with the suppression of independent boundary fluctuations, the OBC exponents hint at the presence of a new universality class. Results from other tessellations support the robustness of the observed scaling with OBC. We discuss a possible route to interpolate between the different boundary conditions. Our findings show that boundary dynamics must be specified when characterizing critical behaviour on hyperbolic lattices.

This dissertation investigates scalar field descriptions of the dark sector (of the Universe), with emphasis on scalar-tensor cosmology, inflationary effective field theory, quintessence, and ekpyrotic/cyclic alternatives to inflation. The thesis first reviews scalar-tensor theories of gravity, starting from Brans-Dicke theory and extending to general non-minimally coupled scalar fields. Particular attention is paid to the interpretation of the scalar field, the relation between the Jordan and Einstein conformal frames, and the role of conformal transformations in cosmology. This provides the theoretical basis for treating scalar fields either as modified matter or as additional gravitational degrees of freedom. The second part discusses cosmological inflation from the viewpoint of effective field theory. The spontaneous breaking of time translations, the Goldstone description of adiabatic perturbations, higher-dimensional operators, radiative corrections and Planck-suppressed terms are analyzed in the context of ultraviolet sensitivity and the eta problem. The third part is devoted to quintessence as the simplest dynamical dark energy model. 'Tracking', 'scaling', 'thawing' and 'freezing' behaviors are discussed, together with observational diagnostics such as the statefinder parameters, the $(\omega_{\phi},\omega'_{\phi})$ plane and the $Om(z)$ diagnostic. The DESI DR2 results are used as motivation for considering time-dependent effective dark energy beyond a strict cosmological constant. The final part studies ekpyrotic and cyclic cosmologies. The ekpyrotic phase is analyzed as a smoothing mechanism based on an ultra-stiff scalar field equation of state. Perturbations, non-Gaussianity, tensor modes, bounce conditions, entropy production, geodesic incompleteness and phase-resolved field-space distance bounds are discussed.

The two-fluid model provides a powerful phenomenological framework for superfluids, where components interact through vortex-induced mutual friction. Quantum turbulence in such coupled two-fluid systems has become a central theme in low-temperature physics. However, the fundamental incompatibility between discrete vortex-line and continuum descriptions has historically forced reliance on phenomenological parameters. Here, we present an ab initio holographic simulation of this active two-fluid dynamics. Using a fully backreacted gravitational model, we intrinsically incorporate reciprocal momentum exchange and finite-temperature dissipation without empirical inputs. Contrasting continuously driven and freely decaying turbulence, we uncover pronounced non-Gaussian tails and spatial anisotropy in the normal-fluid velocity statistics, arising directly from the dynamical quantized vortex backreaction. Raising the temperature suppresses normal-fluid velocity fluctuations despite increasing the vortex density. This suppression is unambiguously traced to the thermal depletion of the superfluid condensate. Our results establish holographic duality as a rigorous first-principles framework for quantum turbulence, revealing the active role of the normal fluid far from equilibrium and yielding predictions for ongoing cold-atom and superfluid experiments.

Partially entangled thermal states (PETS) provide semiclassical families of black-hole microstates prepared through heavy shell insertions. We extend this shell-state framework and propose three-boundary partially entangled thermal states (PETS$_3$) by replacing the two-index insertion data with a trivalent junction tensor. The corresponding bulk three-boundary booklet geometry is constrained semiclassically by the Israel junction condition, allowing us to identify candidate symmetric and mixed-orientation branches. We verify the self-consistency of this construction by counting states in the symmetric all-black-hole sector. Using a heavy-operator probe, we further estimate the detection-to-universal ratio to be $Z_D/Z_U \simeq 3$, twice the two-boundary value of $3/2$. These results suggest that a fine-tuned probe localized on one boundary can test the proposed three-boundary shell state and potentially distinguish it from its two-boundary counterpart.

Coleman–De Luccia tunneling can exhibit an infinite tower of rapidly oscillating negative modes, complicating the semiclassical evaluation of the path integral. We show that this tower does not represent infinitely many bounce-specific instabilities, but instead is tied to a single underlying gravitational conformal sector. This sector is exposed in two different ways: by a large scalar gradient near the bubble wall and by the turning point of a compact Euclidean geometry. The corresponding conformal sector is already present in fluctuations about the false vacuum. Treating the bounce and the false vacuum in the same well-defined gauge and with a common regulator, we find that their high-frequency negative spectra approach one another. The ultraviolet tower therefore cancels from the relative negative-mode count, leaving a single bounce-specific negative mode. This finite-backreaction spectral cancellation provides a corresponding picture of the result obtained in the small-backreaction limit.

Neural network conformal theories were first introduced in \cite{Halverson:2024axc} and exact two-, three- and four-point correlators were computed from an ensemble of infinite-width neural networks. In particular, the four-point correlator of any scalar operator satisfied crossing-symmetry and conformal block decomposition across different channels were in agreement without any constraint on moments. An infinite tower of degenerate operators with the same scaling dimension were found. In this note, we take a closer look at the structure of correlators and relation between operators. We also layout a recipe to construct the algebra of the theory.

We derive the AdS deformation of the flat-space soft-graviton algebra with Dirichlet boundary conditions. Starting from the AdS$_4$ spinor-helicity representation, we Mellin-transform linearized graviton solutions and construct the AdS wedge, including its Laurent completion. The Dirichlet boundary condition pairs opposite helicities, while AdS covariance fixes their relative normalization. Assuming linear closure and normalizing the global modes to reproduce the geometric AdS isometries, covariance and the Jacobi identities uniquely determine the soft-mode bracket. The result is the wedge of $\mathcal L_\Lambda w_{1+\infty}$, where $\Lambda=-\ell^{-2}$. This provides a bulk derivation of the cosmological-constant deformation that incorporates the AdS boundary condition, without relying on collinear splitting functions or a self-dual truncation.

Only a handful of elementary color building blocks are known to participate in the double copy, most notably the structure constants of gauge theory. This work extends the double copy to include the infinite family of totally antisymmetric “structure constants” with arbitrarily many indices. We propose and motivate the Jacobi identities relating these $n$-index structure constants. For each $n$, we provide a derivatively-coupled scalar theory that is color-dual off-shell. The lowest level in this tower is two-dimensional Zakharov-Mikhailov theory, with one theory for each higher spacetime dimension. Each member of the tower exhibits a conserved current associated with color-kinematics duality, a soft theorem, an on-shell recursion relation, and classical conformal invariance. We also provide a tower of modified non-abelian Chern-Simons theories whose fields couple non-linearly through the $n$-index structure constants. The modified Chern-Simons theories are trivially topological and classically conformal but generally exhibit unusual features like kinetic mixing. A potentially unphysical gauge condition is identified that would ensure that the tower is color-dual off-shell.

We formulate a precise sense in which a BRST anomaly may possess a classical phase space shadow. It is the non-equivariance class of a Hamiltonian symmetry action on covariant phase space. To organize this statement, we introduce the Weil covariant phase space bicomplex, whose basic subcomplex controls equivariant Hamiltonian lifts. We then compare this purely classical class with local BRST descent. For a Hamiltonian admissible mixed transgression, the ghost-number-two descendant $a^{2}_{d-1}$ defines a deghostification map to the charge algebra, which is generated by the failure of the Cartan representative to be equivariant. The induced cohomology class is independent of Bardeen type changes of descent representative. Thus the classical anomaly is a shadow of the BRST anomaly in the precise sense that both are realizations of the same Weil transgression class, while remaining objects of different theories. As an explicit example, we analyze a five dimensional inflow transgression and show that the classical charge cocycle and the BRST descendant arise as two realizations of the same Weil transgression class.

It is widely believed that there are no exact global symmetries in quantum gravity. We review recent works showing that global symmetries can nevertheless emerge after ensemble averages of theories, as encountered in holography. As a precision case study, we discuss the ensemble average of two-dimensional Narain-type conformal field theories associated with an even quadratic form of general signature, which is computed by the Siegel-Weil formula and interpreted as a sum over geometries in a three-dimensional Abelian Chern-Simons theory. Global symmetries of the bulk anyons can emerge after the average, as T-dualities relating different theories in the ensemble are "folded" into symmetries of a single theory (duality origami). We discuss the relation to the Swampland program, including the emergence of global symmetries at infinite distance. Finally, we recast strong-to-weak spontaneous symmetry breaking (SWSSB) of mixed states as an emergence of symmetries in ensemble averages; in holography, wormholes connecting the two sides of a thermofield-double construction provide its bulk realization. This motivates a new Swampland conjecture.

Time-reversal symmetry and its violation (T-violation) are fundamental across diverse physics domains, from particle physics to fluctuation theorems and reciprocity. While time-reversal symmetry for isolated systems is simply determined by the Hamiltonian, quantifying the magnitude of T-violation, especially in noisy quantum processes, has been a subject of ongoing debate. Here, we propose an operationally meaningful framework to quantify the intrinsic T-violation of quantum channels. We integrate operationally defined time-reversal transformations into dynamical resource theory to formulate T-violation as a resource. T-violation decomposes into two distinct components: kinematic T-violation originating from antiunitary motion-reversal, and nonunitality driven purely by thermodynamics. This decomposition resolves the longstanding confusion between broken time-reversal symmetry and non-invertibility. Finally, we analyze the resulting resource theory of kinematic T-violation, showing that it is neither quality-like nor quantity-like, and proving the existence of a universal golden unit even within classical channels.

We quantize the exterior region of an odd-dimensional Kerr-AdS black hole, in which all rotational parameters are equal, using our model of quantum gravity. The resulting hyperbolic equation is solved by products of temporal eigenfunctions $w_i$, whose corresponding eigenvalues all have multiplicity one, and spatial eigendistributions $v_{ij}$ corresponding to the same eigenvalues but having multiplicities $m_i\ge 1$. In principle, the $m_i$ may be arbitrarily large. When only the exterior region is considered, there is no criterion for determining the values of the $m_i$. However, when the quantization of the interior region is also considered, the same ambiguity does not arise, because the multiplicities can be chosen to be maximal. It is therefore natural to use the same values in the exterior region. Because the temporal Hamiltonian is the same in both regions, the interior and exterior eigenvalues coincide, and this choice defines a unitary equivalence between the respective Hilbert spaces and Hamiltonians. The unitary equivalence between the Hilbert spaces and their respective Hamiltonians preserves the complete quantum-statistical information carried by all normal states in the interior and exterior regions of the black hole. Hence, there is no information paradox at the quantum level.

We construct a sheaf of $\frac{1}{2}\mathbb{Z}$-graded meromorphic open-string vertex algebras from a transitive Courant algebroid $E$ equipped with a generalized metric and a chosen generalized Levi-Civita connection on a smooth manifold. Using a holonomy principle for transitive anchored bundles, we realize these algebras as parallel sections of a tensor algebra bundle built from bosonic-fermionic affinizations of $E$. For even-rank $E$ with suitable Clifford module bundle data, we construct a sheaf of canonically twisted modules containing the canonical weighted spinor bundle in weight zero. The associative algebra of parallel tensors acts on spinor sections through iterates of an $E$-connection combining covariant differentiation and Clifford multiplication, with mixed terms incorporating the action of the bosonic connection on fermionic tensors. Distinguished states built from the inverse Courant pairing and inverse generalized metric give vertex-operator components, acting on embedded spinor sections as the canonical Dirac generating operator, its formal adjoint, and their anticommutator, the generalized Hodge Laplacian. In the exact Courant case with three-form $H$ and the exterior algebra Clifford module, the operators specialize to $d-H\wedge$, its adjoint, and the twisted Hodge Laplacian, reducing to the ordinary de Rham and Hodge operators when $H=0$. This extends the vertex-operator realization of geometric differential operators from functions to weighted spinors and differential forms, within the program of studying two-dimensional supersymmetric nonlinear sigma models.

We extend the interpolation of the Poincaré algebra between instant form dynamics (IFD) and light-front dynamics (LFD) to the conformal algebra in $(3+1)$ dimensions. Building upon our recent formulation of the interpolating conformal algebra in $(1+1)$ dimensions, we propose an interpolation method for the conformal group $SO(4,2)$. A central feature of this work is classifying the $15$ conformal generators into kinematic and dynamic categories as a function of the interpolation angle ($0 \leq \delta \leq \frac{\pi}{4}$). We show that among the five additional generators beyond the Poincaré group, the dilatation generator remains strictly kinematic across the entire interpolation region. We also find that in the exact light-front limit ($\delta = \frac{\pi}{4}$), one additional generator from the Special Conformal Transformations (SCT) becomes kinematic in $(1+1)$ but dynamical in $(3+1)$. This behavior shows the advantage of LFD in maximizing kinematic generators and minimizing dynamical complexity. To support this algebraic framework, we construct a $6 \times 6$ interpolating projective spacetime matrix representation. We detail the explicit transformations of the interpolating time under all $15$ generators, providing a systematic view of conformal symmetry across the relativistic dynamics.

Disk-level scattering amplitudes involving one Ramond–Ramond and two NSNS states on a D-brane obey nontrivial identities among scalar world-sheet integrals imposed by gauge and T-duality Ward identities. We investigate the cohomological organization of these relations using twisted de Rham cohomology and show that the Ward identities admit twisted-exact representatives. In the $I/J$ sector, the unique generic linear dependence among the Ward identities is realized one degree lower in the same twisted de Rham complex, revealing a common cohomological origin for the identities and their syzygy. We also identify independent pointwise algebraic relations among the integrands. An independent cohomological rank computation then establishes that the physically selected $I/J$ family spans a five-dimensional subspace of the top twisted cohomology at generic complexified kinematics. Extending the construction to the $K$-family, including the exceptional double-pole representative $K_3$, introduces no additional cohomology direction. Hence the complete $I/J/K$ family considered here spans the same five-dimensional subspace.

We obtain a general decay rate between Kaluza-Klein (KK) gravitons, resolving an ambiguity in the literature concerning these decays. The amplitude is determined not only by the mass $m_n$ of the decaying particle, but also by the momentum $q$ of the decay products in the parent's rest frame, and is suppressed relative to the expression commonly used in the literature by $(q/m_n)^2$. Phase space gives a general $q^5$-dependent decay rate obtained earlier in Randall-Sundrum models. We identify the cancellation that gives this result as a consequence of the massless 5D graviton, and argue for its universality even with scalar-induced KK violation by absorbing non-minimally coupled scalar fields into the warp-factor. This has significant implications for the potential for cascading dark matter models, and can be used to rule out existing Dark Dimension models, because the rapid cascade that was needed to evade constraints is severely suppressed. The amplitude is established by an explicit calculation that accounts for the backreaction of fields and branes and applies broadly to non-minimal diffeomorphism invariant two-derivative couplings between scalar fields and gravity.

In a restricted untwisted sector, Diaconescu, Moore & Witten (2000, 2003) gave a quantum M-theoretic consistency check, at the level of partition functions, of what one may call "Hypothesis K", namely that magnetic and electric type IIA brane charges are jointly quantized in K-theory. We show that the more recently discussed "Hypothesis H" — that magnetic and electric charges in 11D are jointly quantized in coHomotopy — together with a topological smallness condition on the M-theory circle, systematically implies that IIA charges are quantized in a nonabelian deformation of twisted K-theory by the previously neglected non-linear NS1-brane charge. This is essentially a derivation of twisted K-theory from IR-completed 11D SuGra, and conversely a further consistency check on Hypothesis H from Hypothesis K. We motivate and precisely state this result, discuss its structural implications, and outline the elaborate algebro-topological proof.

We investigate aspects of the relationship between global sections of divisors and birational geometry. We show that for varieties $X$ of klt Calabi-Yau type, global sections are governed by the same birational data that control the $D$-minimal model program ($D$-MMP). As a consequence, global sections of arbitrary big divisors can be systematically reduced to Euler characteristics $\chi(Y,\mathcal O_Y(D))$ on suitable birational models $Y$ using vanishing theorems, extending classical positivity-based methods beyond the movable cone. The reduction proceeds by removing fixed divisorial components, which do not contribute to the space of global sections, either directly by subtraction or birationally by contraction to a suitable $D$-minimal model. We obtain piecewise quasipolynomial formulae for global sections on the big cone, whose domains are the Mori chambers of the $D$-MMP. Restricting to the subclass of Fano type varieties extends such formulae to the entire effective cone. These formulae can be constructed from just the small birational class of $X$, yet encode properties of all birational contractions of $X$. Alongside the computation of global sections from birational geometry, we study the inverse process, wherein finite computations of $h^0(X,\mathcal O_X(D))$ determine aspects of the chamber decomposition and the associated birational models.

The degenerate geometry of a null boundary admits an enlarged local conformal freedom: in two dimensions, a Carrollian coframe allows two independent Weyl rescalings, one modulating and the other preserving the boundary volume form. We investigate whether both transformations can be realized as charged asymptotic symmetries in three-dimensional flat holography. We show that Einstein gravity canonically realizes the volume-modulating Carroll-Weyl transformation, together with local Carroll boosts, but does not admit the volume-preserving rescaling as an additional independent asymptotic symmetry. We trace this obstruction both back to the conformal completion of null infinity and to the absence of two independent commuting semisimple generators in the Poincaré algebra. Conformal gravity overcomes this obstruction through bulk dilatations, which supply the missing algebraic direction. We construct an asymptotically flat phase space of conformal gravity in which both types of Carroll-Weyl transformations and local Carroll boosts admit finite, integrable, and generically nonvanishing canonical charges, and derive their centrally extended algebra. Finally, we show that these central extensions arise from boundary anomalies through symplectic descent, yielding a gravitational prediction for Carroll-Weyl anomalies in flat holography.