Papers

Twistor theory forms the basis for many surprising advances in areas ranging from dynamical systems to quantum field theory. Yet for almost fifty years, one of the main drawbacks of twistor theory has been its inability to give non-perturbative descriptions of non-chiral (or non-self-dual) field configurations. This difficulty is known as `the googly problem.' In this paper, we provide a resolution of the googly problem for a particular solution of the vacuum Einstein equations: the Schwarzschild metric. We start with the twistor space of the self-dual Taub-NUT Euclidean gravitational instanton, expressed in Kerr-Schild form. Within this twistor space, we then consider a quadric which corresponds to the anti-self-dual Taub-NUT metric. While the full quadric is not holomorphic with respect to the complex structure of the self-dual Taub-NUT twistor space, its holomorphic locus still has complex dimension two. This `coincidence locus' – points in twistor space on the holomorphic portion of the quadric – inherits a complex structure from the twistor space and a symplectic form from the quadric itself. Remarkably, these structures are compatible, giving rise to a non-self-dual, four-dimensional Kähler metric which is conformal to Schwarzschild (in Lorentzian or Euclidean signature). This is the first instance of a non-self-dual Einstein metric constructed entirely from holomorphic data in a twistor space.

We estimate the impact of Polyakov loop (PL) contributions on electroweak phase transitions (PTs). We show that the PL, which is unavoidable in thermal gauge field theory, tends to tame thermal contributions, thereby softening electroweak PTs and affecting bubble dynamics, nucleation, and the related gravitational-wave spectrum. Including this non-perturbative contribution in perturbative approaches results in a thermal effective potential that disfavours first-order PTs over either second-order PTs or smooth cross-overs. This feature is universal for both fermionic and bosonic contributions to the effective potential.

We investigate the stochastic Ricci flow of spherically symmetric perturbations of the Schwarzschild–Anti de Sitter black-hole metric. Elaborating on the Ricci-flow analysis of Headrick and Wiseman, we include a negative cosmological constant through a Ricci-target term and study how the flow is correlated with the thermodynamic heat capacity of the black hole. Numerical simulations show that, in the positive heat-capacity regime, perturbations of the angular sector of the metric relax toward the Schwarzschild–Anti de Sitter fixed point, while in the negative heat-capacity regime they grow under the deterministic Ricci flow. We then introduce a multiplicative stochastic noise and find that sufficiently strong stochasticity can suppress the growth of these perturbations, effectively stabilizing configurations that would otherwise be thermodynamically unstable. Finally, we reformulate the dynamics in terms of an entropy variable evolving on a thermodynamic free-energy landscape, and support the metric-flow results through Monte Carlo simulations and the associated Fokker–Planck equation. These results suggest that stochastic fluctuations can modify the relation between geometric stability under Ricci flow and thermodynamic stability in asymptotically Anti de Sitter black-hole spacetimes.

We investigate quasinormal modes of the graviscalar sector in a five-dimensional thick brane model in Rastall gravity. By considering a specific flat brane solution supported by a canonical scalar field, we derive a master equation and reduce it to a Schrödinger-like eigenvalue problem for the Kaluza-Klein modes. Using the Bernstein spectral method and direct integration in the frequency domain, complemented by numerical time-domain evolutions, we compute the complex quasinormal frequencies for the scalar perturbations. Our results reveal a strong dependence of the QNM spectrum on $\lambda$: the imaginary parts of the frequencies, governing the decay rate, decrease monotonically with increasing $\lambda$, indicating longer-lived modes. The real parts exhibit a more complex, non-monotonic behavior. Furthermore, we analyze the late-time behavior of the perturbations, showing that the asymptotic tail follows a power law whose exponent is determined by the Rastall parameter, in agreement with theoretical predictions for the asymptotic form of the potential. These findings provide a comprehensive dynamical characterization of the scalar sector of Rastall thick branes, offering potential observational signatures for probing modified gravity in extra-dimensional scenarios.

This dissertation develops a quantitative framework that provides a physical picture for non-perturbative QCD based on the topological structure of the QCD vacuum. By integrating out the ultraviolet degrees of freedom, the infrared gluon configurations are modeled as a liquid ensemble of instantons and anti-instantons, which induce effective interactions among quarks. This framework captures the origin of trace and axial anomalies through the infrared distributions of QCD and dynamically breaks chiral symmetry. More specifically, this framework can be formulated in two ways: in one, we construct a statistical ensemble with weights defined by the instanton action and Dirac determinant, while in the other we formulate an effective field theory (EFT) by rewriting the determinant as effective quark interactions. By reformulating the EFT on the light front, we explicitly construct the light-front wave functions and calculate various parton observables in linear factorization. We further embed the framework into transverse momentum dependent factorization and establish a vacuum origin for rapidity evolution by computing the soft functions. We also extend this approach to various form factors in light hadrons, including scalar, pseudoscalar, and energy-momentum tensor (EMT), as well as higher-twist color force and multigluon correlations, with applications to hadron mass and spin decomposition, near-threshold quarkonium production, and strong CP problem, highlighting the importance of the vacuum origin in hadron structures. Overall, this work demonstrates that the QCD vacuum provides a quantitatively crucial description of hadronic structure from low to moderate resolution, bridging nonperturbative vacuum physics with partonic phenomenology.

We study genuine multi-entropy as a diagnostic of multipartite entanglement in the toric code, which provides a controlled setting for probing multipartite structures in topologically ordered states. Our main question is whether genuine multi-entropy captures information that is not reducible to conventional lower-party entropic data, such as topological entanglement entropy. We first analyze toric-code ground states that admit a stabilizer-state description, where the relevant quantities can be evaluated exactly. In this sector, genuine multi-entropy reflects the topological structure and symmetries of the toric code, while exhibiting highly constrained relations to lower-party multi-entropies. We conjecture that, for stabilizer states and ${q}\ge4$, the ${q}$-partite genuine multi-entropy at replica index $n<{q}$ collapses to a linear combination of multi-entropies involving at most ${q}-2$ parties. We establish this pattern explicitly for ${q}=4$ in the toric code stabilizer sector: for $n=2,3$, the genuine multi-entropy is proportional to the tripartite information $I_3$ and, for the Kitaev–Preskill partition, contains no independent genuine four-partite information beyond that captured by the topological entanglement entropy. At $n=4$, however, this reduction breaks down: the genuine multi-entropy is no longer proportional to $I_3$, but remains a topological invariant of the toric-code stabilizer ground states. For generic non-stabilizer superpositions within the ground-state manifold and for coherent superpositions of local excitations, the low-$n$ reduction also fails. These results show that genuine multi-entropy probes multipartite entanglement structure beyond the tripartite information, and hence beyond the topological entanglement entropy in the Kitaev–Preskill partition, whereas for stabilizer states at low replica index it reduces to lower-partite entropic data.

We present a background-independent renormalization framework for one-loop primordial spectra. We apply it to two observables: the scalar-induced tensor spectrum sourced by a minimally coupled spectator field, and the scalar spectrum generated by potential self-interactions. In both cases, the UV part of the loops is isolated and, using the universal WKB behavior of the internal modes, the UV poles are extracted analytically and absorbed into local counterterms without having to specify either the background evolution or the full dynamics of the field running in the loop. This yields finite model-independent expressions for the renormalized spectra amenable to numerical analysis.

We investigate the structure of strange quark stars (SQSs) in the color–flavor–locked (CFL) phase in the presence of scalar bosonic dark matter within a two–fluid formalism employing perturbative QCD. By considering different dark matter masses and varying the pairing gap $\Delta$ and {the central dark matter pressure fraction} $f_r$, we analyze the impact of dark matter on the structural properties of SQSs, including the maximum gravitational mass $M_{\mathrm{TOV}}$, the ratio of dark matter to strange-quark-matter radii $R_{\mathrm{DM}}/R_{\mathrm{SQM}}$, and the dimensionless tidal deformability $\Lambda$. We further examine the compatibility of the resulting mass–radius relations with the recent NICER measurements of compact stars. Within the parameter space considered in this study, we find that $M_{\mathrm{TOV}}$ exhibits a non-monotonic dependence on the dark matter mass, with a critical value beyond which $M_{\mathrm{TOV}}$ decreases. We also show that some pure CFL strange quark star configurations, particularly those associated with very stiff EOSs and larger maximum masses, may not simultaneously remain compatible with the $\Lambda$ range inferred from GW170817 while occupying the lower mass–gap region. In contrast, the inclusion of dark matter allows two-fluid CFL strange quark star configurations to reproduce the observed properties of massive compact objects in the lower mass–gap region, such as the secondary component of GW190814, while remaining qualitatively compatible with the $\Lambda$ range inferred from GW170817. We note, however, that the GW170817 constraints were originally inferred within single-fluid compact-star frameworks and therefore provide only {qualitative guidance} for the present two-fluid halo configurations. Our results suggest that exotic compact-star configurations may populate part of the conventionally defined lower mass–gap region.

We develop an analytical framework to constrain Yukawa-type fifth-force interactions using the Lamb shift in hydrogen and deuterium. The sixfold coordinate-space integral for the energy shift is transformed into a one-dimensional momentum-space convolution of the atomic form factor and the Yukawa potential, eliminating the need for approximations. This formulation directly incorporates empirical nuclear charge distributions through their form factors, making the implementation of experimental results straightforward. Applying this method to the latest hydrogen and deuterium spectroscopy data, we derive constraints on the coupling constant $\alpha$ in the interaction range $\lambda \in [10^{-4}, 10^{6}]$~fm. A resonance-like cancellation between the $2s$ and $2p$ orbital shifts is identified at a critical range $\lambda \sim 10^{5}$~fm, where the energy shift vanishes and the constraint on $\alpha$ diverges, marking a transition between attractive and repulsive regimes. The constraints are shown to be independent of the nuclear charge distribution model. Our results indicate that the transition frequency shifts induced by such new forces lie well below current spectroscopic resolution, establishing spectroscopic precision as the primary bottleneck for probing these interactions.

These notes give a cross-dimensional crash course in supersymmetric field theory. The goal is to provide enough common language to recognize the basic setups used in talks and papers, while also working through representative computations that make the terminology concrete. We begin with supersymmetry algebras, multiplets, protected quantities, moduli spaces, deformations, and anomalies, then follow these ideas through examples in two to ten spacetime dimensions. The emphasis is on recurring structures, such as holomorphy, supersymmetric vacua, dualities, extremization principles, indices, BPS data, and anomaly constraints, rather than on a classification of theories in any one dimension.

We construct a $\frac{\mathbb{Z}}{2}$-graded meromorphic open-string vertex algebra from a finite-dimensional vector space with a nondegenerate symmetric bilinear form, together with its canonically twisted module. This algebra is generated by suitable noncommutative generalizations of bosonic and fermionic fields and is a noncommutative generalization of the free boson-fermion vertex operator superalgebra. Similarly to the purely bosonic and purely fermionic cases in the early works by the second author in [H1], by Fiordalisi and the third author in [FQ], and by the third author in [Q3], the usual super-commutatitive relations between creation and annihilation operators still hold while no relations exist among creation operators. In particular, normal-ordering remains well-defined. As in [H1], [FQ], and [Q3], we prove a generalized Wick's theorem in this case, which gives a formula for a product of two normal ordered products of bosonic and fermionic generating fields. Using this generalized Wick's theorem, we construct the $\frac{\mathbb{Z}}{2}$-graded meromorphic open-string vertex algebra and its canonically twisted module in this case. The construction in this paper is the algebraic part of our construction of suitable Dirac-like operators from spin manifolds.

In this work, we investigate the emergence of dipole ghost structures in gauge theories at both the classical and quantum levels. Traditionally, dipole ghosts are introduced through an auxiliary field $\chi$ satisfying $\Box^2\chi=0$, whose presence is reflected in the appearance of double poles in the propagator. We show that such dipole ghost sectors can instead be understood as a consequence of the multiplicity of solutions of the classical equations of motion. To establish this connection, we develop a constructive method and first apply it to covariant Maxwell theory in $(2+1)$ dimensions, where the essential ingredients can be identified in a transparent manner. We then extend the analysis to the constrained higher-order Chern-Simons theory, demonstrating that the same mechanism gives rise to dipole ghost sectors and associated double poles in the propagator. Our results provide a unified perspective on the origin of dipole ghosts, relating them directly to the degeneracy structure of the underlying classical dynamics. As a physical application, we investigate spontaneous symmetry breaking and compute the one-loop effective potential. We show that symmetry breaking removes the degeneracy underlying the dipole ghost sector, leading to a spectrum of ordinary massive gauge excitations that determine the quantum vacuum structure of the theory.

Despite riddles, mysteries, and enigmas the theory of elementary particles has not changed for 50 years. We argue that the current paradigm – Wilsonian quantum field theory – is inadequate for resolving the puzzles, and should be replaced by a new paradigm based on the Holographic Principle. We show how a simplified but still very rich standard model emerges from de Sitter holography in the flat-space limit and explain why the puzzle of huge quantum corrections to the cosmological constant simply does not occur in the holographic paradigm.

The integration kernels for polylogarithm functions on a compact Riemann surface of arbitrary genus $h$ are shown to close as the surface undergoes a non-separating degeneration to one of genus $h{-}1$. Explicit formulas are obtained for the non-separating degeneration of the multivariable Enriquez connection for genus $h$ with an arbitrary number of variables to the Enriquez connection for genus $h{-}1$ with two additional punctures whose Lie algebra generators are related to the original ones by the characteristic Bernoulli generating functions known from the degeneration at $h=1$. Analogous degeneration formulas are obtained for the single-valued DHS kernels at the leading order in the real degeneration parameter that is adapted to relating modular tensors at genus $h$ and $h{-}1$.

We track the chain of dualities relating five-brane webs in Type IIB to M-theory on noncompact Calabi-Yau threefolds, and follow the effect of adding $(p,q)$ seven-branes. T-dualizing along the seven-brane, a junction of D5-branes ending on a D7-brane becomes a single smooth D6-brane wrapping a smooth holomorphic curve, which uplifts directly to an M-theory geometry. Treating the branes as coherent sheaves (tachyon condensation), we obtain a spectral-curve dictionary that maps non-Abelian (T-brane) partition data to explicit complex-structure deformations of the threefold. As applications we (i) give a physical derivation of these deformations, (ii) exhibit a simple geometric prototype of an s-rule violation, and (iii) link T-brane data to geometry.

Large-$N$ three dimensional QCD with a level $k$ Chern-Simons term and $N_f$ massless flavours admits $N_f+1$ degenerate vacua. We discuss various aspects of the domain walls that interpolate between those vacua. Using a bosonic dual for the case $k \ge N_f/2$ we write down the profile of the composite wall. By fluctuating the profile, we find the 2d field theory that lives on the wall, a level-$N$ gauged WZW model, and compare it with a theory that was previously obtained by using anomaly inflow considerations. We also discuss the case $k < N_f/2$. Finally, we remark on the realisation of the wall as a D-brane in a holographic dual.

Massive quantum fields ordinarily produce strongly screened Casimir interactions at large separation. We show that a normalisable localised zero mode can change this asymptotic behaviour: it opens an additional interaction channel whose decay is parametrically slower than that due to the exchange of massive quantum fluctuations, even though the continuum itself remains gapped. We demonstrate this mechanism analytically and show that the massive quantum fluctuations provide the local dressing of each object's coupling to the zero-mode fluctuations. The sine-Gordon kink provides an exactly solvable realisation in which the Casimir interaction exhibits the predicted zero-mode-dominated large-distance behaviour, with the enhancement localised around the kink.

We construct equivariantly closed polyforms for the fluxes and the action of (massive) type IIA and type IIB supergravity directly in ten dimensions. We illustrate applications of our formalism to two distinct classes of solutions in massive type IIA. Our analysis straightforwardly reproduces and vastly generalizes all known results for on-shell actions in these classes, with no need for a consistent truncation. Where known, we match the corresponding field theory partition functions at leading order, and our results extend easily to other solutions of type II supergravity.

We investigate cosmological solutions in $f(Q,C)$ gravity formulated within symmetric teleparallel geometry, where gravitation is described by the nonmetricity scalar $Q$ and the boundary term $C$, related to the Ricci scalar of General Relativity through $\mathring{R}=Q+C$ in the absence of curvature and torsion. The symmetry requirements of FLRW spacetime admit three distinct realizations of the affine connection, leading in principle to three different cosmological sectors within the same theory. We show that the connection field equations play a crucial role in determining the cosmological dynamics. In their simplest realization, these equations impose a constraint that renders the theory dynamically equivalent to $f(\mathring{R})$ gravity, causing the cosmological background equations associated with the three connection realizations to coincide. This defines a degenerate cosmological sector of $f(Q,C)$ gravity, in which three a priori distinct geometric constructions converge to the same cosmological dynamics. We then consider the complementary class of genuinely nonequivalent $f(Q,C)$ models, for which the choice of connection becomes physically relevant. In this regime, the connection sector introduces additional dynamical degrees of freedom and gives rise to novel cosmological phenomenology absent in $f(\mathring{R})$ gravity.

We extend the spacetime duality programme of Burgess et.al. to massive theories in 1+1 dimensions. For the massive scalar, a heat-kernel computation tracking three contributions to the conformal-mode effective action reveals that the naive leading correction $\sim m^2(e^{\phi} -1)$ to the Liouville action cancels exactly, with the genuine leading deformation being $-\frac{m^2}{16\pi}(e^{\phi}-1)^{2}$. This breaks self-duality and renders the dual theory for the Lagrange multiplier field $\Lambda$ non-local. For the massive Dirac fermion, two independent derivations establish that the fermion mass dresses under conformal scaling as $m \to m\, e^{\phi/2}$, reflecting the Weyl weight $\frac{1}{2}$ of the two-dimensional spinor. Via the Coleman-Mandelstam bosonisation, this transfers to the mass bilinear as $\mu\cos(\beta\vartheta) \to \mu e^{\phi/2}\cos(\beta\vartheta)$, producing a coupled Liouville-sine-Gordon system as the natural starting point for the fermionic construction. Both results are interpreted in terms of the determinant line bundle over Met($\Sigma$)/Diff($\Sigma$).

Big Bang nucleosynthesis (BBN) predicts the primordial deuterium abundance to a precision now limited by the nuclear reactions that burn deuterium. For the simplest of them, proton-deuteron radiative capture, d + p -> \gamma + 3He [d(p,\gamma)3He], the precise LUNA data sit below the ab initio benchmark, and BBN reaction networks split on which to adopt. We develop an effective field theory (EFT) expanding in the finite size of the nuclei, building the amplitude with modern on-shell methods that enumerate every tree-level structure consistent with symmetries without the need for an explicit Lagrangian. A global Bayesian fit to the capture data and nuclear-theory priors returns S(0) = 0.209 +/- 0.008 eV b and traces the offset from the ab initio benchmark to a single natural-sized next-to-leading contact term (t_E1 ~ -0.15, the fractional shift of the electric-dipole amplitude) – equivalently a ~15% lower effective 3He asymptotic normalization. We estimate the leading EFT truncation errors and identify an elastic d-p observable that would separate them. Our results suggest that amplitude methods enable systematic and complete tree-level construction and matching of EFTs for low-energy nuclear reactions.

We study the multidimensional erratic structure of correlation functions produced by local operator quenches in finite-volume free massive scalar field theory in dimensions 2 and 3. The basic observable is the subtracted equal-time two-point function in the locally excited state and its spatiotemporal patterns of extrema. We analyze these extrema by the multidimensional diagnostics recently introduced for chaotic scattering amplitudes and related problems: all-pair distance distributions, nearest-neighbor spacings, greedy-path spacing ratios, and the extrema form factor. For the $1+1$-dimensional local quench we find that, in the regime of small Euclidean smearing, the fitted extremum statistics move close to the $\beta=1$ random-matrix benchmark, while increasing the smearing scale softens the effective repulsion and moves the distributions away from the GOE-like value. For the $2+1$-dimensional local quench we find that the nearest-neighbor statistics of the refined extrema are close to, or above, the $\beta=1$ benchmark, and the greedy-path ratio statistics are described by even larger effective $\beta$ values. Finally we studied the all-pair extrema spatial form factor and found that, in the one-, two-, and three-dimensional cases, its main structure is controlled by the corresponding uniform interval, rectangle, or cuboid geometry of the extrema cloud and found the dip-ram-plateau structure in the last two cases. Thus the form factor provides a complementary global diagnostic of how the extrema fill their effective metric support, while the genuinely nontrivial local and mesoscopic organization is carried by the nearest-neighbor and greedy-path statistics.

Self-interacting dark matter (SIDM) influences halo structure through collisional heat transport and may solve several small-scale puzzles in structure formation. SIDM creates thermalized cores in low-mass haloes, which may account for the observed cored dwarf galaxies. During late-time gravothermal core collapse, SIDM can produce dense low-mass DM haloes and substructures detected through perturbations to cold stellar streams and strong gravitational lenses. In this work, we present a new Monte-Carlo SIDM implementation in the moving-mesh code AREPO-2, designed for efficiency, scalability, and extensibility. The central feature of the implementation is a dedicated DM-only neighbour-search tree that decouples the scattering solver from gravity. This preserves compatibility with the hierarchical time integration used by AREPO-2 while leaving the optimized gravity solver unconstrained. A pairwise communication scheme between MPI tasks allows tracking multiple scattering events in a single timestep while conserving momentum and energy and maintaining parallel consistency by construction. This is complemented by a per-pair timestep criterion that significantly reduces unnecessary timestep restrictions. The implementation natively supports velocity-dependent cross-sections and inelastic interactions, while a compact interface is designed for additional SIDM physics to be implemented without knowledge of the parallelization layer. We validate the implementation for isotropic, elastic scattering using a suite of idealized and cosmological tests. We assess performance and scalability in isolated core-collapse simulations and in cosmological boxes, both DM-only and with baryons. Except during the late stages of gravothermal collapse, SIDM simulations incur only modest overhead relative to the corresponding CDM runs and are substantially faster than the previous SIDM implementation in AREPO-1.

We use the stringy dispersion relation (SDR) to ask the following question about gravitational effective field theories: once the universal large-impact-parameter eikonal carrier is supplied, where does the remaining positive spectrum go? Working in six dimensions for concreteness, we include the complete high-spin continuum tail of the carrier and first work at weak coupling, where $M_{\rm Pl}>M_{\rm EFT}$. The extremal spectra contain a saturated low-impact band whose outer edge stays at roughly five to six times the inverse EFT scale even as the gravitational radius shrinks. The same edge is reproduced by a strict $G_N=0$ capped-SDR problem on the present grids. Thus the weak-coupling band approaches an intrinsic non-gravitational baseline of the capped extremal problem. On a common high-energy grid, a coupling ladder crossing $M_{\rm Pl}=M_{\rm EFT}$ resolves the cap-saturated support as a wedge: its outer envelope has the rotating black-hole homogeneity $G_N^{1/3}E^ {4/3}$, while its approximately linear lower envelope flattens as $G_N$ grows. We then use the deliberately reversed hierarchy $M_{\rm Pl}<M_ {\rm EFT}$ as a microscope for strong-gravity structure. In this regime a cap-saturated low-impact band follows an order-one Giddings-Porto rotating black-hole scale, a separate Regge-like ridge appears at high spin and low energies, the broad available region between these structures and the eikonal layer remains mostly empty, while at the far-tail of energy, series of Regge trajectories emerge.

We propose a systematic framework for constructing six-dimensional supergravity theories with eight supercharges that respect all known consistency constraints, including anomaly cancellation and the non-perturbative ${\it H}$-string constraints recently discovered by Kim, Vafa, and Xu. The basic objects in this framework are ${\it supergravity\,blocks}$, which are minimal collections of tensor multiplets consisting of a single little string theory sharing the ${\it H}$-string charge together with additional tensors whose string charges intersect it positively. A characteristic feature of each supergravity block is that its Gram matrix has exactly one positive eigenvalue, and therefore it necessarily contains gravitational BPS strings that cannot become tensionless anywhere in tensor moduli space. Any consistent 6d $(1,0)$ supergravity theory can then be obtained by gluing compatible blocks and subsequently enhancing the gauge algebras and matter content. As a first step toward establishing this framework concretely, we provide a complete classification of the ${\it non\text{-}Higgsable\,supergravity\,blocks}$, (or ${\it non\text{-}Higgsable\,gravity\,blocks}$ for short) namely those built from tensor multiplets that support only non-Higgsable gauge algebras.

We develop a perturbative Green's function approach to gravitational lensing by weak gravitational potentials that need not be localized on a thin lens plane and that applies in both the wave optics and geometric optics regimes. We recast position-space integrals as Fourier, or momentum-space, integrals that appear in scattering amplitude calculations. The method gives the Born approximation directly in three dimensions and can be systematically extended to post-Born orders. For a Schwarzschild lens, we compute the leading Born term and new post-Born contributions arising from the order $\mathcal{O}(G^2)$ correction to the potential, keeping finite-distance corrections beyond the usual paraxial expansion. We show that these general-relativistic corrections are controlled by the parameter $GM\omega\,b/\chi_{\rm eff}$ in the small-angle regime, and are therefore negligible for standard weak-lensing configurations but become relevant in more extreme geometries (such as hierarchical triples with very small source–lens separations). We also discuss higher-order Newtonian corrections, their infrared sensitivity for a long-range potential, and the regulated form of the Newtonian potential given by the Yukawa potential. Finally, we formulate the corresponding calculation in an FLRW background, identifying the leading flat-space limit and estimating the size of curvature-induced corrections including tails. This method clarifies the regime of validity of the Born, large-distance, and paraxial approximations in gravitational-wave lensing and provides a framework for treating generic lensing potentials.

We provide a new formal extension of the BFSS matrix model by an additional 5-bracket. Maximal supersymmetry leads us to promote the BFSS 2-bracket structure constants to a dynamical field $H_{abc}$ governed by a Chern-Simons-like kinetic term. We first show that the full generic pseudo-action is invariant under maximal supersymmetry and that the associated supersymmetry algebra closes upon invoking a number of BPS-like quadratic constraints. We then present a special case based on the 5-Lie algebra $A_6$ that evades these additional constraints and allows for a Lagrangian description. These results hinge on a conspiracy of properties of the $SO(9)$ gamma matrices and the 2- and 5-brackets. Compellingly, the resulting model seems to realize some features expected of a theory containing M5-branes and opens up the possibility of further including higher brackets for the M6- and M9-branes.

The AInstein architecture introduced an unsupervised neural method for solving the Riemannian Einstein equations on arbitrary manifolds. This Physics Informed Neural Network approach (PINN) is extended here to Lorentzian signature, validated by recovering the maximally extended Schwarzschild geometry, and tested as novel search method for arbitrary black hole solutions. The topology is built into the architecture by treating $S^{2}$ globally through its standard embedding, such that the network learns an ambient metric on the manifold $\mathbb{R}^{2} \times \mathbb{R}^{3}$, where Penrose coordinates are chosen for $\mathbb{R}^2$ and the metric on $S^{2}$ is obtained by pullback. The architecture is first trained with the objective of recovering the Schwarzschild metric via losses encoding the vacuum Einstein equation, a quadratic Weyl scalar constraint, and the $SO(3)$ symmetry of the resultant metric; directly motivated by the Birkhoff–Jebsen theorem. Following this, the objective is generalised to use the Petrov speciality index, a horizon curvature anchor, and a trapped-surface constraint, to allow search for algebraically general Petrov type I solutions, finding potentially novel general-type Lorentzian Einstein metrics with a genuinely trapped interior.

Large charged black holes can create macroscopic, locally weakly curved regions in which moduli take values different from their asymptotic values. We study how robust this mechanism is once the scalar has a nontrivial potential. In four-dimensional Einstein-Maxwell-dilaton theory, the massless GHS solution provides a finite exterior throat in which the scalar and the gauge coupling vary logarithmically. We develop fixed-throat diagnostics for the competition between the black hole gauge source and a scalar potential, and compare them with back-reacted exterior evolutions when needed. The relevant criterion is not the mere presence of a potential, but how its force behaves along the scalar trajectory traced by the black hole throat. Quadratic stabilizing potentials erase the throat when the Compton wavelength becomes comparable to the horizon scale. Runaway, periodic, and barrier-type potentials instead exhibit distinct failure modes controlled by their slope, sign, oscillations, or barrier distance along the GHS trajectory. A quintessence-like scalar remains effectively massless on astrophysical black hole scales, leaving the throat essentially unobstructed. If the charge belongs to a hidden sector, and if the scalar also controls visible couplings or bulk propagation, such surviving altered-modulus regions could leave phenomenological imprints in near-horizon accretion or emission.

Due to the exponential growth in the number of terms, computing $\alpha'$-corrections to string theory's low-energy effective actions is a challenging matter. In order to fix all the couplings, one has usually to deal with a large number of string scattering amplitudes. This difficulty can be overcome by exploiting T-duality, which severely constrains the allowed structure of the effective action. It is then convenient to work in a formulation where T-duality is a manifest symmetry. Building on a series of previous works by some of the authors, we present a refined version of an elegant and effective procedure that allows to obtain all the higher-derivative corrections of the NS-NS sector of sting theories at order $\alpha'$ and $\alpha'^2$, up to an overall coefficient. We dub this approach $\alpha'$-bootstrap, since it is based only on consistency conditions and avoids the direct computation of scattering amplitudes. The procedure relies on an infinite dimensional algebraic structure that we present in full detail, and it is conjectured to work at all orders. Although, at the moment, it still misses the $\zeta$-like corrections starting at order $\alpha'^3$, the ease with which it can be generalized is promising for future developments in this direction.