Papers

Pair creation from the vacuum in the presence of a U(1) gauge field in de Sitter $(\mathrm{dS})$ spacetime provides an important setting for exploring quantum field theory in curved backgrounds. In this work, we investigate massless fermion production and the associated induced current generated by a constant electric field in (1+2)-dimensional $\mathrm{dS}$ spacetime. Assuming the Bunch–Davies vacuum and employing adiabatic regularization, we derive, for the first time, a finite expression for the induced current of massless fermions in $\mathrm{dS}_{3}$. The produced fermions generate a net current opposite to the external electric field. In the strong-field regime, the induced current exhibits the expected semiclassical scaling and reproduces the standard Schwinger behavior in the flat-spacetime limit. In the weak-field regime, the current is linear in the electric-field strength. This behavior is characteristic of the fermionic nature of the particles, since the corresponding bosonic case exhibits infrared hyperconductivity, which is absent in our study. We further show that the induced current remains monotonic throughout the parameter space and, unlike in $\mathrm{dS}_4$, does not exhibit any sign change. Our results thus highlight the role of dimensionality and clarify the interplay between spin and infrared physics in $\mathrm{dS}$. This work provides a consistent basis for future investigations including backreaction effects, topologically massive fermions, and time-dependent electromagnetic backgrounds.

We study the large-charge bootstrap in three-dimensional CFTs with a global U(1) symmetry using scalar, current, and stress-tensor probes, restricting to parity-even exchanged operators. Under minimal assumptions, the bootstrap requires at least one Regge trajectory with the dispersion relation of the standard Goldstone mode of the conformal superfluid. With additional assumptions, this trajectory is unique, while all non-Goldstone trajectories contribute only to the scalar-scalar channel at this order.

Solving quantum field theory, which is at the basis of the standard model of particle interactions, is one of the main tasks of contemporary theoretical physics. Minimal asymptotically free pseudoreal theories, containing one or two species of massless Weyl fermions in pseudoreal representations of the gauge group, flow towards a poorly understood infrared dynamics. We provide a comprehensive study of all pseudoreal theories, identifying the ones that likely flow towards a conformal dynamics, while we show that the remaining ones confine with a non-trivial condensate dynamics. Among the latter, all but one one-species theories feature a massless spin-1 state. Instead, the only confining two-species theory likely features two massless spin-1 states and one Nambu-Goldstone boson. These predictions could be further tested, for instance by use of Lattice simulations, the functional renormalization group, and supersymmetric analogs.

Cones of future and past are rigorously constructed under the horizon of black hole by completions of geodesics continued from causally connected space-time regions outside the black hole interior. Treating the Schwarzschild black hole as a zero charge limit of Reissner–Nordsrøm black hole reforms the Penrose–Carter diagram into the infinite band that excludes the closed proper-time cycles under the geodesic motion. The marginal trajectories between the cones of future and past compose paths common with a compact non-Hausdorff spherical extension of black hole interior forming the thermal bath for particles fallen to the black hole.

The AdS/CFT correspondence relates gravity in anti-de Sitter space to a boundary conformal field theory, and in its AdS$_3$/CFT$_2$ instance the Virasoro symmetry of the boundary theory organizes correlation functions into conformal blocks. In the semiclassical limit these blocks are computed by lengths of geodesic networks in the bulk, most sharply in the heavy-light regime, where heavy operators source a background probed by light ones. We relate the classical monodromy method to this bulk geometry in holographic coordinates, showing that the eigenvectors of the monodromy matrix encode the endpoints of bulk geodesics. This yields the light action and the equations determining the internal geodesic network; crucially, the internal network equations are independent of the heavy background. For two heavy operators we rederive the same equations from elementary Euclidean geometry, which provides an independent geometric check. As an application we compute the full non-vacuum 5-point HHLLL block, so far known only in the superlight approximation. More broadly, our construction gives a general framework for computing heavy-light blocks from the bulk, while at the same time fixing its threshold of computability.

In this work we introduce and study a family of holomorphic–topological field theories, which we call generalized Poisson sigma models. These theories are higher-dimensional analogues of the two-dimensional Poisson sigma model, with target data encoded by shifted chiral Poisson structures. We investigate their relationship with deformation quantizations of holomorphic–topological factorization algebras. Along the way, we give a systematic construction of extended objects, including interfaces, enriched boundaries and defects based on relevant notions in derived algebraic geometry. We employ Koszul-duality methods to study boundary algebras, yielding various versions of quantum groups. We illustrate the general framework through a range of examples, including twists of supersymmetric gauge theories as well as examples beyond the supersymmetric origin.

We study non-Abelian strings supported in $r$-vacua of 4D $\mathcal{N}=2$ supersymmetric QCD (SQCD) with gauge group $U(N)$ and $N_f$ quark hypermultiplets ($N_f\ge N$), where $r<N$ (scalar) quarks develop vacuum expectation values. At the quantum level, $N-r-1$ monopoles in the orthogonal sector of the gauge group also form a condensate. This leads to the formation of flux tubes (strings) that carry both color-electric and color-magnetic fluxes and confine quarks and monopoles, respectively. We present a unified description of the 2D effective theory living on the world sheet of this non-Abelian string. In particular, we derive the exact twisted superpotential of the world sheet theory, which is deformed by the presence of non-perturbative gaugino condensate in 4D hybrid vacua, using the Gaiotto-Gukov-Seiberg method of resolvents. Next, we extrapolate the 2D-4D correspondence of BPS spectra of the world sheet theory and 4D SQCD (known for quark vacua) to hybrid vacua. Namely, our key result is the precise matching between the masses of the two-dimensional kinks and the four-dimensional confined monopoles or quarks. In addition, we provide a physical picture of the quark/monopole confinement in hybrid vacua.

The 7th ALEGRO workshop, hosted by INFN Frascati National Laboratories from 3rd to 5th March 2026, brought together the international Advanced Novel Accelerators (ANA) community to discuss the role of advanced wakefield accelerators (AWA) in particle and high-energy physics. Organized under the ICFA-ANA panel, the workshop highlighted recent progress in plasma- and structure-based wakefield acceleration and strengthened international collaboration toward future energy-frontier colliders. A major focus was the ongoing 10 TeV linear collider design study, launched in 2025 following the US P5 recommendations. A dedicated session covered accelerator concepts, enabling technologies, and the associated physics case, while recognizing that future priorities will depend on the outcome of the European Strategy for Particle Physics Update. The workshop also reviewed nearer-term applications of advanced accelerators, including fixed-target experiments, injectors for future colliders and light sources, plasma-based Higgs factory concepts, and proton-driven plasma wakefield acceleration. Beyond high-energy physics, sessions covered free-electron lasers, synchrotron light sources, and strong-field QED. Recent demonstrations of FEL lasing with plasma-accelerated electron beams highlighted significant progress in beam quality and accelerator performance. Operational challenges for reliable user facilities, including high-availability laser and electron-beam systems, were discussed alongside the growing role of artificial intelligence and machine learning for accelerator optimization and control. This report summarizes the workshop discussions and conclusions from the chairs, together with short contributions from the presenters, providing an overview of the current status and future prospects of advanced wakefield accelerators.

We investigate the dynamics of domain walls in scalar field theories with degenerate vacua (i.e., vacua of equal energy density) in which the scalar field mass depends on the vacuum state. Using analytical arguments and numerical simulations, we show that this vacuum dependence of the scalar field mass renders the emission of scalar radiation from domain walls anisotropic, preferentially toward regions with smaller scalar field mass. We further show that the resulting recoil (rocket) effect biases the evolution of cosmological domain wall networks in favor of the lower-mass vacuum, thereby promoting network decay. We also demonstrate that the biased evolution of domain walls in theories with degenerate vacua, previously attributed to asymmetries of the potential barrier near the local maximum, is instead primarily controlled by the vacuum dependence of the scalar field mass. More generally, in theories with non-degenerate vacua, this recoil mechanism constitutes an additional source of dynamical bias that can either hasten or delay network decay relative to the standard expectation based solely on differences in vacuum energy density.

The low-energy dynamics of many-body systems is governed by gapless modes whose properties are dictated by symmetry. Their existence follows from Goldstone's theorem, while their effective description at zero temperature is determined by the pattern of symmetry breaking. At finite temperature, an analogous role is played by hydrodynamics, which describes the universal behavior of many-body systems over long times and large distances. These principles are well understood for uniform symmetries, which act homogeneously in spacetime and lead to a correspondence between massless Goldstone modes and broken generators, as well as gapless hydrodynamic modes and conserved charges. However, this simple picture changes in the presence of nonuniform symmetries, whose generators do not commute with spacetime translations. The low-energy implications of these symmetries remain less understood, as they do not introduce additional gapless modes but instead constrain the dynamics of the existing degrees of freedom. In this thesis, we develop a unified framework for many-body systems with nonuniform symmetries and show that their effects can be understood in terms of additional fields that are not independent at low energies and can be eliminated, leading to kinematic constraints that reshape the infrared dynamics. In systems with spontaneous symmetry breaking, this mechanism modifies the effective theory and often softens the dispersion relations of the remaining modes. At finite temperature, it manifests in hydrodynamics as constraints on macroscopic currents. As a result, nonuniform symmetries give rise to qualitatively new physical phenomena, including modified spectra of collective excitations, exemplified by transverse Tkachenko oscillations in quantum vortex crystals, and unconventional transport phenomena, such as anomalously slow diffusion and softened sound modes in dipole-conserving systems.

In this work, we investigate quantum complexity diagnostics of primordial curvature perturbations within the inflationary paradigm. We compare canonical scalar-field inflation with the modified gravity model $f(\phi,R)$, focusing on the evolution of the two-mode squeezed state generated by the coupling between the $\vec{k}$ and $-\vec{k}$ momentum sectors. Starting from the quadratic action for curvature perturbations, we derive the evolution equations for the squeezed strength $r_k$ and squeezed angle $\phi_k$, utilizing them to evaluate both circuit complexity and Krylov-space diagnostics. Specifically, we compute the Krylov complexity, Krylov entropy, Lanczos coefficients $b_n$, and an effective dissipative contribution $c_n$ within an open-system extension. Our numerical results demonstrate that the $f(\phi,R)$ coupling enhances the squeezed strength relative to the canonical scalar field inflation. Since the Krylov complexity of the two-mode squeezed state is directly controlled by the mean pair number ($K=\sinh^2 r_k$), this enhancement leads to a smaller growth in Krylov complexity and related Krylov-space quantities. Furthermore, circuit complexity displays a more pronounced evolution in the $f(\phi,R)$ framework, particularly after the horizon exit regime. Ultimately, our work sheds new light on the quantum complexity of modified gravity $f(\phi,R)$.

We develop a rigid $\mathcal{N}=(1,1)$ superspace formulation for multifield scalar models coupled to localized impurities through spurion superfields in two-dimensional spacetime. The spurionic completion gives a manifestly supersymmetric action and provides a systematic framework for describing interacting scalar fields in the presence of impurity backgrounds. In this setting, supersymmetry acts as an organizing principle for a controlled bosonic half-BPS sector, with the preserved projector selecting the impurity-compatible first-order equations. We derive the corresponding coupled BPS equations, energy density, boundary conditions, and Bogomol'nyi bound, showing that localized impurities deform the BPS profiles and redistribute the local energy density while leaving the total BPS energy fixed by the topological boundary term. We illustrate the formalism through representative one-, two-, and three-field models, analyzing the resulting BPS configurations and their local energy density profiles.

This work is motivated by the proposed relationship among finite cut-off holography and generalized $T\bar T$ deformations, and examines holographic complexity within the framework of the "complexity = anything" proposal. Employing a Fefferman-Graham expansion near the finite cut-off surface, the deformation-induced correction to generalized complexity is derived and shown to allow a systematic expansion in terms of generalized Willmore-type functionals. The resulting formulation broadens earlier findings for the complexity-volume proposal to encompass arbitrary geometric complexity measures. Furthermore, the structure of the correction allows a natural interpretation as multiple-flavor Lorentzian threads, where distinct thread sectors correspond to different curvature invariants in the complexity functional. These results show a geometric connection among finite cut-off holography, generalized complexity, and the emergence of non-local computational structures in holographic quantum field theories.

We study the effects of the running of the QCD coupling on the anti-collinear resummation in JIMWLK evolution in the linear (BFKL) regime. We determine the appropriate scale choice for the coupling entering the JIMWLK kernel, and derive the anti-collinearly resummed BFKL kernel, which includes running-coupling effects both in the resummation equation (i.e. DGLAP) and in the JIMWLK kernel proper. We find that the running of the coupling generally further slows down BFKL evolution, as expected. Surprisingly however the value of the generalized characteristic function at $\gamma=1$ is unaffected by the running coupling owing to subtle cancellations. We develop an approximation that allows us to use the generalized characteristic function to study the BFKL Green's function. Within this approximation we find that the Pomeron intercept in the anti-collinear regime is significantly reduced by both, the resummation and the running of the coupling.

We present a new picture of primordial black holes mass evolution through neutrino absorption. Using semi-classical approach and a closer look at the kinetic of the early plasma we revisit the thermal absorption of radiation by a population of primordial black holes ranging from $10^{-3}-10^9 M_\odot$ embedded in a thermal bath. We find significant mass growth of intermediate mass and supermassive PBHs, the effect shift the predicted $e^+e^-$ peak from thermal history. Depending on the value of the collapse fraction an additional peak around the intermediate mass range, might become significant. Moreover, because PBH grow from the thermal bath the fraction of DM in PBH $f_{\rm PBH}$ also change. These results revise the previous view on mass evolution of PBH and have implications for dark matter PBH observations.

We present a novel real-time framework for the decay of metastable states in quantum field theories using Wigner functions. The framework introduces a nonperturbative nucleation rate formula that captures both quantum tunneling and over-the-barrier nucleation, alongside steps to evaluate it perturbatively. We apply it to a simple thermal example with direct relevance to current analog experiments. Our derived one-loop nucleation rate fundamentally differs from the widely cited high-temperature result by Linde: The prefactor contains quantum effects and also asymptotes to a differing form at high temperatures, where the quantum effects become negligible. Rather, the result is a generalization of Affleck's rate formula to quantum field theories, asymptoting to the effective field theory approach, and Langer's rate, at high temperatures. The example also reveals that the high-temperature side of the “quantum-to-classical” transition of thermal vacuum decay is still inherently quantum mechanical, even though the bounce background possesses the classical, $\mathrm{O}(d)\times S^1$, symmetry.

Symmetric Macdonald polynomials of $N$ variables provide eigenfunctions of the $N$-body trigonometric Ruijsenaars-Schneider integrable system at particular eigenvalues. In order to construct eigenfunctions with arbitrary eigenvalues, M. Noumi and J. Shiraishi used a recursion in $N$ (branching rule) for the symmetric Macdonald polynomials and analytically continued them. This generated a power series, which is a part of triad (universal solution). In the present paper, we demonstrate that a similar procedure is available for another integrable system, $N$-body Cherednik integrable system inspired by the DAHA of type $A$, which has non-symmetric Macdonald polynomials as its polynomial eigenfunctions. However, in this system, the generic eigenfunction is more complicated: it is not just a simple power series as in the Noumi-Shiraishi case, but has an involved structure with $N!$ branches, each of them being a sum over the Weyl chambers of power series of the Noumi-Shiraishi type. As an illustration, we also provide explicit formulas for particular cases.

In this paper, we review the Zamolodchikov-like recursion relations for torus one-point conformal blocks in both Liouville and $A_2$ Toda theories. Starting from these relations, we derive the corresponding recursion relations in the light asymptotic limit. In Liouville theory, the light-limit recursion reproduces the known expression for the one-point light conformal block in terms of the Gauss hypergeometric function. For $A_2$ Toda theory, our recursion relation provides a new, efficient method for explicit calculations, and we have verified that it is in full agreement with previously known results in the literature. Last but not least, we present closed-form expressions for the coefficients of the insertion-point expansion for both the generic and light $A_2$ Toda one-point blocks.

Recent Atacama Cosmology Telescope (ACT) observations, combined with Planck, favor a scalar spectral index in tension with Starobinsky inflation. Two main strategies have been proposed to reconcile Starobinsky inflation with these data: (i) including higher-curvature operators in the gravitational action, and (ii) modifying the post-inflationary reheating dynamics. We critically re-examine both approaches. When higher-curvature corrections are included, dimensional-analysis arguments allow introducing a second mass scale suppressing higher-dimensional operators, resulting in a one-coupling, two-scale effective theory. We show that fitting the ACT data drives this class of effective theories toward a regime of stronger sensitivity to UV physics, potentially implying fine-tuning of the inflationary observables. We illustrate our general point with two concrete models, namely no-scale supergravity and metric-affine gravity, showing that they provide different realizations of the same underlying $f(R)$ theory. On the reheating side, requiring the CMB modes to re-enter the horizon before recombination leads to stringent constraints on the reheating equation of state, and fitting the ACT data favors an exotic reheating phase with $\omega_{\rm reh} > 1/3$, incompatible with inflaton oscillations about the minimum of the standard Starobinsky potential. Finally, we explore the possibility that a phase of cosmological stasis, driven by a tower of decaying massive states, could play the role of the post-inflationary epoch. We find that accommodating ACT-preferred $n_s$ in this setup requires a tower of states with negative energy density. Taken together, our results suggest that reconciling Starobinsky inflation with the ACT data demands ingredients that are challenging to motivate from the perspective of UV-complete theories, undermining the minimality of the original Starobinsky model.

We develop a field-theoretic framework for quantum error correction centred on fusion-space codes in unitary fusion categories. Admissible clusters determine total-charge sectors and orthogonal footprint projectors recording locally visible data left by error histories. The central distinction is between diagnostic footprint algebras and syndrome-admissible commuting algebras: the latter can be measured without revealing logical information and resolve chosen error representatives into measured sectors. For such algebras, exact correctability is equivalent to fibrewise Knill–Laflamme conditions, yielding a measure-then-recover factorization. Under a contractible-vacuum locality hypothesis, closed neutral composites give a categorical sufficient criterion for scalar action on the code. In the Ising theory, four $\sigma$ punctures show that pair-charge footprints can be complementary logical diagnostics and realize an exact one-qubit Clifford shadow. A proper six-$\sigma$ code instead admits a syndrome-admissible pair-charge measurement and exact recovery from an explicit Majorana bilinear error. A second bilinear has the same measured footprint but differs by a logical bit flip, producing a concrete nontrivial footprint fibre and genuine decoding ambiguity. We also formulate conformal-block likelihood data and compute geometry-dependent Ising four-point weights. For growing code families, we prove a conditional Peierls-type threshold theorem: bounded connected-region growth, local stochastic noise, local neutralizability of small residual components, and componentwise decoder balance imply $\Pr_L(\mathrm{fail})\le C|\Omega_L|e^{-cL}$ below a nonzero constant error rate. We conclude with representation-theoretic and algebro-geometric directions involving tube and Hopf algebras, Yangian-type structures, Higgs bundles, spectral curves, Jacobians, and abelian varieties.

We study the coupling of anomaly mediated supersymmetry breaking (AMSB) to $\mathcal{N}=2$ supersymmetric theories with $SU(2)$ gauge group. Perturbatively, $\mathcal{N}=1$ supersymmetry (SUSY) is preserved in the UV description with the AMSB terms being equivalent to a supersymmetric mass term for the adjoint chiral multiplet, as considered in the original Seiberg-Witten papers. We show, however, that nonperturbative instanton contributions break supersymmetry completely. In the IR description, the theory with AMSB is qualitatively similar to its $\mathcal{N}=1$ analog, exhibiting monopole condensation and confinement. However, the effective Lagrangian breaks supersymmetry completely, and the values of the condensates are different from their $\mathcal{N}=1$ analogs. Under physically reasonable assumptions, it can be shown that the vacua must change to those of the perturbatively identical $\mathcal{N}=1$-preserving deformation as the SUSY-breaking scale crosses the strong coupling scale. This change must be caused by effects that cannot in principle be described within the effective weakly coupled IR theory. It is not a phase transition, and the vacua appear to lie in the same universality class at any finite SUSY-breaking scale. Nonetheless, this work highlights the subtle manner in which AMSB coupling to nonperturbative effects can change the vacuum field configuration and the global symmetries of a theory.

A consistent all-order treatment of $\gamma_5$ in dimensional regularisation (DReg), as provided by the Breitenlohner-Maison/'t Hooft-Veltman (BMHV) scheme, is essential for high-precision electroweak calculations, but comes at the cost of a regularisation-induced violation of gauge and BRST invariance that must be reinstated via symmetry-restoring counterterms. We report on the current status of our research on the BMHV scheme, from its $D$-dimensional realisation and its multi-loop behaviour up to the 4-loop order, to its most recent application: the complete 1-loop renormalisation of the Standard Model (SM), including both divergent and finite symmetry-restoring counterterms. For the latter, we discuss the main intricacies of the BMHV treatment and present a representative excerpt of the resulting counterterms.

We introduce the Seesaw Reheating scenario, in which the inflaton transfers its energy to a long-lived intermediate scalar associated with the spontaneous breaking of lepton number before the Universe is reheated through its decay into right-handed neutrinos. As a result, the reheating temperature is no longer determined by the inflaton decay width but by the dynamics of the seesaw sector. We derive analytical solutions describing the complete reheating history, revealing two characteristic features of this scenario: the relativistic time dilation of the intermediate scalar, which suppresses its decay and delays the transfer of energy to the thermal bath, and its subsequent transition from a relativistic to a non-relativistic regime, introducing a new characteristic timescale in the thermal history. Together, these effects lead to simple analytical expressions for the reheating temperature. When the intermediate scalar is identified with the field responsible for the spontaneous breaking of lepton number, the same framework naturally connects the reheating temperature to the origin of neutrino masses and provides a well-motivated setting for sterile-neutrino dark matter.

Analyzing the dynamics of physical observables in open quantum many-body systems is a fundamental but highly challenging task that has yielded very few exact results. In this work, we identify intrinsic conformal structures that restore exact solvability in $(1+1)$D conformal field theories. For $N$ Majorana fermions with linear mode jumps, the adjoint Lindbladian is triangular on reduced even Majorana monomials, yielding recursive exact Heisenberg evolution. In Wess-Zumino-Witten models admitting conformal Majorana embeddings, this hierarchy gives exact dynamics of affine-current products realized as Majorana bilinears, including regimes where the Kac-Moody current algebra alone does not close. In diagonal rational conformal field theories, Verlinde topological defect lines furnish jump operators whose primary-sector dynamics is exactly diagonal: topological-charge probabilities are conserved, while intersector coherences dephase at rates fixed by the modular $S$ matrix and nonnegative measurement strengths. These examples show that intrinsic conformal structures, such as conformal embeddings and modular data, can organize exactly solvable open conformal dynamics.

We propose a small-throat prescription for the wave function of a closed universe in the Lorentzian path integral formalism, motivated by the idea that universe creation may be obtained as the decoupling, or pinch-off, limit of a tunneling geometry connected to another universe through a small throat. Instead of retaining the parent-universe side explicitly, we describe the remaining half-geometry by a minisuperspace path integral with boundary conditions imposed at the throat. To model the finite throat, we introduce a small radiation component parametrized by $\epsilon$ in a closed minisuperspace model with a positive cosmological constant. The radiation term produces two turning points, an inner one $q_-\sim O(\epsilon)$ and an outer one $q_+\sim H^{-2}$, where $q$ is the square of the scale factor. Our prescription imposes the Neumann condition $\dot q(0)=0$ at the initial endpoint and restricts the initial size $q_i=q(0)$ to a small-throat domain $0<|q_i|<\sqrt{\epsilon}/H$ that contains $q_-$. This restriction selects the Riemann sheet containing the small-throat tunneling saddle and its Picard–Lefschetz cycle, while excluding the unsuppressed saddle associated with the outer turning point $q_+$. Taking the limit $\epsilon\to0$ after this finite-throat saddle problem has been defined, the small-throat domain collapses to $q_i \to 0$, and the saddle action reduces to that of the standard tunneling saddle. Other choices of lapse contour can instead select Hartle–Hawking-type growing branches. In this sense, the tunneling wave function can be obtained as the limiting form of tunneling from an arbitrarily small universe in a Lorentzian path integral, rather than by imposing a boundary condition directly at a vanishing geometry.

The canonical QCD axion is minimal but not high quality. We identify a minimal high-quality QCD axion, in which the Peccei-Quinn symmetry emerges as a gauge-origin boundary remnant of five-dimensional $U(1)$ gauge invariance on a flat interval, and the axion is the surviving Wilson-line phase. QCD and the Standard Model remain four-dimensional, retaining much of the simplicity of KSVZ/DFSZ anomaly sectors. The construction requires no bulk QCD, warping, or color Chern-Simons term, yet retains exponential quality protection. Thus axion quality is compatible with minimality.

Vertex operator algebras (VOAs) are well studied in both mathematics and physics. The best understood class is that of strongly rational VOAs, whose representation category is maximally well behaved: indeed, it is a modular tensor category. At the next level of complexity are strongly finite but non-rational VOAs. Their representation category is not semisimple (it is “logarithmic”), but maintains nice structural properties. Only a few families of examples in this class are known, a fact that may have hindered the development of a comprehensive mathematical theory. The SCFT/VOA correspondence provides a natural way to generate more examples: strongly finite but non-rational VOAs are expected to arise from four-dimensional ${\cal N}=2$ Lagrangian superconformal field theories (SCFTs) that do not admit a Higgs branch moduli space of vacua. We tackle the combinatorial task of classifying all such “Higgsless” Lagrangian SCFTs. To our surprise, this set turns out to be rather sparse. Free vector multiplets and their discrete gaugings are immediate examples. The interacting Higgsless theories comprise one infinite sequence of SO/USp quivers and three sporadic examples. We construct and study the novel VOAs associated to two of the sporadic examples, and confirm that they are indeed strongly finite and logarithmic.

A central challenge in testing inflationary scenarios with cosmic microwave background (CMB) data is to derive predictions for cosmological observables that remain accurate beyond the slow-roll regime, where the standard consistency relations are no longer applicable. We address this issue in the context of Einstein–Gauss–Bonnet (EGB) gravity by introducing a phase-$\theta$ parametrization of the inflationary dynamics. Within this framework, the background evolution and the coefficients governing scalar and tensor perturbations are expressed entirely in terms of a single monotonic phase variable and the Hubble parameter. This construction provides a closed, analytical mapping between the background parameters of a given model and the associated inflationary observables. A notable advantage of the proposed parametrization is that it remains regular throughout the inflationary epoch, including the end-of-inflation regime, in which the conventional slow-roll consistency relations no longer hold. As an illustrative application, we consider a Starobinsky-type potential supplemented by a linear coupling between the inflaton and the Gauss–Bonnet invariant. Using the proposed formalism, we demonstrate that the resulting predictions of the Starobinsky model are consistent with the most recent constraints from ACT DR6 and BICEP/Keck, explicitly incorporating the impact of the non-minimal Gauss–Bonnet coupling on the expected values of the cosmological perturbation parameters. Finally, we compute the corresponding relic stochastic gravitational-wave background and evaluate its detectability with current and forthcoming gravitational-wave observatories.

The complex sine-Gordon (CSG) model contains an internal phase degree of freedom that strongly modifies the dynamics of its solitary-wave solutions. We present a numerical study of complex kink–kink collisions and determine how the final state depends jointly on the initial velocity and relative phase. In contrast with the elastic collisions of the real sine-Gordon model, the CSG system exhibits scattering, capture, long-lived bion formation, breather-like states, and emission of radiative profiles. The simulations reveal two distinct phase-dependent branches of critical velocity. In one branch, increasing the initial velocity promotes capture, whereas in the other it restores scattering. This dual structure highlights the rich velocity–phase dependence of the collision dynamics. We also compute the energy carried by radiative profiles and examine extreme values of the energy density, kinetic and gradient contributions, and field modulus at the collision center. These quantities show sharp transitions at critical points and provide sensitive diagnostics of phase-controlled dynamics. These results suggest that the relative phase behaves as an effective internal degree of freedom that plays an important role in the collision dynamics of complex solitons.

We investigate the angular eigenvalue problem of the extreme charged C-metric. Starting from a constrained five-point Fuchsian description of the non-extremal angular equation, we obtain its extreme limit by decoupling a hypermultiplet in the dual four-dimensional $\mathcal{N}=2$, $\mathrm{SU(2)}\times \mathrm{SU(2)}$ linear quiver gauge theory. We derive the parameter dictionary and renormalized Matone relations, and connect the physical limit $Q\to M$ to the quiver decoupling by an explicit coordinate transformation. Regular endpoint conditions give an algebraic quantization condition. Eigenvalues obtained from the truncated instanton prepotential are tested against independent angular spectra near extremality and at larger acceleration. The axisymmetric sector recovers the known exact spectrum.