Papers

This short communication investigates impurity coupling in generalized field theories where scalar coupling is introduced directly at the level of the kinetic and gradient contributions of the energy. We show that the fundamental aspects of the original theory, which has been previously investigated in the impurity-free setting, can be extended to the inhomogeneous scenario. In particular, an interpretation in terms of geometrically-constrained effective one-field theories with impurities is possible in the separable case. We show that BPS multi-kink configurations are possible in the model, as well as in the usual half-BPS scalar theories.

Given the canonical seesaw mechanism as a most natural extension of the standard model in its neutrino sector, we find out a special but brand new solution to the exact seesaw equation: $m^{}_i/M^{}_i = - R^2_{\alpha i}/U^2_{\alpha i}$ for the masses and flavor mixing matrix elements of light and heavy Majorana neutrinos of the $i$-th family (for $i = 1, 2, 3$ and $\alpha = e, \mu, \tau$). This family-separated seesaw scenario allows us to establish simple relations between the original seesaw parameters and the active degrees of freedom, and thus offers a number of testable predictions in neutrino phenomenology.

Quark-gluon dynamics within protons and high-energy radiation phenomena in the universe are typically regarded as two entirely distinct fields. This paper aims to demonstrate that gluon condensation (GC) may serve as a direct bridge between these two fields. We review three key aspects of GC research: first, the Zhu-Shen-Ruan (ZSR) equation, as a nonlinear evolution equation based on structural symmetry, exhibits self-consistent connections with the DGLAP, BFKL and GLR-MQ-ZRS equations, providing a theoretical foundation for the generation of GC; second, the chaotic solutions and the shadowing-antishadowing synergy inherent in this equation can drive gluons to aggregate near the critical momentum, thereby forming a novel type of high-density, strongly interacting matter; third, these changes in microstructure manifest themselves as a broken-power-law feature in high-energy cosmic gamma-ray spectra, thereby offering new insights into the hadronic scenarios underlying certain astrophysical sources. Consequently, GC not only concerns the novel behaviour of quantum chromodynamics under extreme conditions but may also serve as a vital window for probing the deep structure of protons using cosmic-ray signals. With the advancement of higher-precision gamma-ray observations, hadron collision experiments and related theoretical research, the physical picture of GC and its observational criteria are expected to undergo more rigorous testing. Should this picture be confirmed, certain features in the high-energy gamma-ray spectrum will need to be re-examined within the deeper context of hadronic dynamics; simultaneously, GC may also provide a new entry point for research into pion condensation in nuclear physics and even condensed matter physics. Consequently, the significance of the search for GC extends beyond the model itself, reaching into multiple fields of natural science.

In the spirit of the geometric approach to two-dimensional conformal field theory, we explicitly associate to every holomorphic vertex operator algebra a section of a power of Hodge line bundle on the moduli space of curves of arbitrary genus - or equivalently a Teichmüller modular form in any genus. As a first application, we connect the geometry of the moduli space of curves to the classification program for holomorphic vertex algebras. We then discuss how to use the theory of holomorphic vertex algebras to reach new results about the moduli space of curves. In the last part of the paper we study how the above mentioned forms can be used to reconstruct the vertex algebra.

Imaginary-time evolution by a local Hamiltonian cannot induce a phase transition in one dimension, but longer-range interactions may subvert such constraints. Starting from the ground state of the Kitaev Majorana chain, we modify the wave function by an imaginary-time evolution generated by a quadratic Hamiltonian with power-law couplings that enhance pairing correlations, typically of the form $1/r^{\alpha}$, where $r$ is the distance between two sites. As the state remains Gaussian, entanglement and correlation functions can be computed analytically. We find that the decay exponent $\alpha$ controls three distinct infrared regimes: for $\alpha>1$, the deformation produces only smooth crossovers at finite deformation strength, while the topological regime is reached only asymptotically as the deformation strength tends to infinity. At $\alpha=1$, the deformation induces an immediate flow to the topological phase: an infinitesimal deformation strength drives the system to a topological regime, and in a particular case, an emergent Kramers-Wannier symmetry enforces Ising-like scaling at long distances. For $\alpha<1$, the deformed state shows the same critical-like behavior for all non-zero deformation strength. We observe that even with arbitrarily long-range interactions, these models do not display a sharp phase transition at non-zero deformation strength.

Constrained symplectic quantization is a functional formulation of quantum field theory in which quantum fluctuations are sampled through a deterministic Hamiltonian flow in an auxiliary intrinsic time $\tau$. In this paper we extend the quantum-mechanical framework introduced in [1] to a relativistic scalar quantum field theory in Minkowski space-time. The construction is based on the analytic continuation of fields and action from $\mathbb{R}$ to $\mathbb{C}$ together with constraints that select stable intrinsic-time trajectories and, at the same time, define convergent integration cycles for the corresponding microcanonical functional. We show that, in the continuum limit, the microcanonical generating functional reproduces the Feynman generating functional. For the free scalar field in $1+1$ dimensions we derive the constrained equations of motion, implement the resulting dynamics numerically, and verify real-time two-point correlators, equal-time commutator relations, and Dyson–Schwinger equations including the expected contact terms.

We introduce a nonabelian surface holonomy that is constructed from a one-form gauge potential that takes values in a loop algebra of the $U(N)$ gauge group. The surface holonomy parallel transports a nonabelian string. Although it is not manifest in our formulation, we will see that our nonabelian surface holonomy is invariant under reparametrizations of the surface.

Reported violations of the Maldacena-Shenker-Stanford (MSS) chaos bound in black hole spacetimes raise the question of whether they reflect a genuine breakdown, a feature of particular geometries, or a limitation of the probe used to test the bound. We show that the violations are apparent and arise predominantly in the near-extremal regime, where the black hole develops an $AdS_2\times S^2$ throat, the surface gravity becomes parametrically small, while the Lyapunov exponent of an orbit separated from the throat remains nonzero. We establish a geometric criterion governing this behavior and demonstrate its resolution in two complementary ways: a charged-particle construction that localizes an otherwise excluded orbit within the throat and restores exact saturation, and an out-of-time-order correlator (OTOC) calculation in the Jackiw-Teitelboim (JT) throat, which identifies the near-horizon Lyapunov scale and shows why the photon-sphere exponent does not reproduce it when the orbit remains outside the throat. We illustrate the criterion for static and rotating black holes in Einstein, scalar-tensor, and higher-curvature gravity, representative of a broader class of geometries to which it applies. In the absence of external effects that displace the relevant trajectories from the throat, the MSS bound remains respected; the apparent violations instead reflect a geometric decoupling between the probe and the near-horizon region.

We observed that the null strings, tensionless strings with Carrollian worldsheets, exhibit an extra gauge symmetry, Carroll-Weyl gauge symmetry, which cannot be obtained from ultra-relativistic Carrollian limit of tensile strings. Due to the existence of this symmetry, the BMS$_3$ algebra of constraints, which is obtained as the Carrollian limit of two Virasoro algebras of the standard tensile strings, should be replaced with an BMS$_3$ algebra extended by a weight one operator. To establish further the existence and necessity of the Carroll-Weyl gauge symmetry, we carefully work through Hamiltonian analyses of constrained/gauged systems. We also discuss the extended BMS$_3$ algebra of constraints.

The recent cosmological picture contains a significant tension indicating that our standard $\Lambda$CDM picture may be incomplete. Early Dark Energy models can alleviate the Hubble tension, by assuming an early acceleration that could explain the divergence between the early and late-time cosmological data. We investigate the implications of Early Dark Energy models on the Big Bang Nucleosynthesis processes by considering several cosmological models, including a model assuming a simple cosmological constant, alongside with varying equations of state dark energy models. We construct a simulator through a nested sampling algorithm, with the help of which we estimate the upper bounds for model parameters, and determine the maximum allowable dark energy density contribution during the radiation-dominated era. Our results are obtained through the \href{https://github.com/croi900/eden}{eden} program. We show that for a linear or polytropic equation of state, the dark energy density is constrained to less than $10^{-13}$ MeV$^4$ and $10^{-5}$ MeV$^4$, respectively, at the 95% confidence level. Furthermore, we identify a temperature-dependent equation of state of dark energy as the most physically compelling framework, which remains consistent with primordial abundances for coupling parameters $\lesssim 10^{-2}$. This model successfully allows for high-temperature deviations from the standard $\Lambda$CDM expansion history, while rapidly diluting to obtain standard general relativistic results in the weak freeze-out era.

We study the finite-temperature Casimir effect for a massless scalar field confined between two parallel plates in a Schwarzschild-like wormhole spacetime. Imposing Dirichlet boundary conditions, we compute the renormalized Casimir free energy in the comoving frame. We find that the thermal correction to the renormalized Casimir free energy decreases gradually with the temperature and becomes independent of the background geometry in this frame. Thermodynamic quantities derived from the Casimir free energy, namely, the renormalized Casimir entropy, internal energy, and heat capacity at constant volume, exhibit distinct temperature dependence. At low temperatures, all thermodynamic quantities recover the expected behavior, consistent with the fundamental laws of thermodynamics. These results provide a compact framework for analyzing quantum vacuum forces in gravitational backgrounds.

The nonlinear Breit-Wheeler process is a fundamental phenomenon of strong-field quantum electrodynamics and is usually studied for classically prescribed laser backgrounds. Here we examine how the statistical properties of a squeezed coherent driving field modify nonlinear Breit-Wheeler pair production. Using a polarization-resolved Monte Carlo framework with stochastic averaging over the field-amplitude distribution derived from the Husimi Q-function, we simulate collisions of gamma photons with squeezed light and identify clear source-state-dependent modifications of the pair production signal. These effects include the smoothing of harmonic structure, the enhancement of higher-order multiphoton channels, and the suppression of the single-laser-photon absorption channel when stronger-field realizations raise the dressed-mass threshold. Within the selected spectral window, the degree of positron polarization increases monotonically with the squeezing parameter, while the angular distributions broaden as the statistical weight of larger field amplitudes increases. Our results show that, even at fixed mean electric-field amplitude, the statistical fluctuations inherent to the squeezed coherent state can substantially reshape spectral, angular, and spin-resolved observables in strong-field pair production. These findings illustrate a direct link between source-state-dependent field statistics and strong-field pair production observables, and provide a theoretical framework for studying how squeezed-state preparation of the driving field can influence high-energy QED processes.

We ask whether two classical time-machine geometries, the Ori (2005) compact-vacuum-core metric and the Ahmed (2018) four-dimensional generalisation of Misner space, remain admissible exact solutions when the gravitational sector is enlarged to the recently proposed $f(R,\mathcal{L}_{m},\Phi,X)$ class, an extension of $f(R,\mathcal{L}_{m})$ that couples curvature, the matter Lagrangian density, a scalar field $\Phi$, and its kinetic invariant $X = g^{\mu\nu}\nabla_{\mu}\Phi\nabla_{\nu}\Phi$. Working with the explicit model $f = R + \mathcal{L}_{m} + (\lambda/2)\,X$ and a vanishing scalar potential, we compute the curvature invariants, the modified field equations, and the effective stress-energy components produced by the harmonic scalar profile $\Phi(x,y) = a(x^{2}-y^{2})/2$ in both backgrounds. The Ricci scalar vanishes for the Ori metric and obeys $R = e^{f}(f_{,xx}+f_{,yy})$ for the Ahmed metric; the kinetic invariant takes the explicit forms $X = a^{2}(x^{2}+y^{2})$ and $X = a^{2}e^{f}(x^{2}+y^{2})$, respectively. Both metrics solve the field equations of the modified theory with anisotropic matter sources, and the chronology-violating regions $g_{zz}<0$ (Ori) and $g_{\psi\psi}<0$ (Ahmed) survive the modification. Energy-density profiles measured by a closed-timelike-curve observer match those measured by a static observer outside the chronology horizon, so the additional scalar degree of freedom in $f(R,\mathcal{L}_{m},\Phi,X)$ gravity does not enforce a chronology-protection mechanism in either background. The conclusion mirrors the parallel result for the Li time-machine and supplies a consistency test for scalar-extended modified gravity in non-globally-hyperbolic settings.

A novel inequality involving the residual entropy and genuine multi-entropy was proposed in \cite{Balasubramanian:2025hxg} for tripartite holographic pure states, using which it was argued, that purely GHZ-like tripartite entanglement is not allowed in holography. In this work, we generalize this holographic signal inequality to mixed states. In a minimal extension, we compute the reflected genuine multi-entropy following \cite{Yuan:2024yfg} and find a class of holographic geometries that violate this minimally extended inequality due to vanishing Markov gap. We can symmetrize this prescription, where instead of computing the residual entropy on the given mixed state $\rho_{ABC}$, we compute it on its canonical purification. The inequality is restored on the canonically purified state, as expected. Finally, we conjecture a new inequality for tripartite holographic states and give supporting evidence.

We study entanglement harvested by Unruh DeWitt detectors following Rindler trajectories in compactified and superposed Minkowski spacetime. We consider different directions of acceleration (both parallel and antiparallel), separation between detectors and direction of spatial compactification mutually perpendicular to each other. Using the standard entanglement harvesting protocol, we analyze how these features influence the extracted correlations. When detector separation is perpendicular to the direction of acceleration, the harvested entanglement is uniformly suppressed due to increased spacelike separation. Compactification enhances field correlations leading to an increased concurrence and an extended harvesting range at higher accelerations. Additionally, we show that spacetime superposition introduces interference effects that further enlarge the entanglement harvesting region in parameter space, particularly in the high acceleration regime. We also find that the effect of antiparallel acceleration yielding significantly higher entanglement than parallel acceleration prevails in compactified and superposed spacetime.

We give a recognition and reconstruction theorem for finite strictly convex tetrahedra in ${\rm dS}^3$ and ${\rm AdS}^3$ with spacelike, timelike, or null faces. The input consists of four nontrivial based ${\rm SO}^+(1,2)$ holonomies satisfying the closure relation. We construct their Gram data and give a global condition ensuring that the reconstructed tetrahedron lies within the required geometric domain. This condition is strict copositivity of the signed inverse Gram form on the outward branch. Together with nondegeneracy of the Gram data, it guarantees a unique finite tetrahedron up to ambient isometry, with exactly the prescribed Levi–Civita face holonomies. We express this criterion as finitely many polynomial inequalities in trace coordinates, leading to an identification of the finite tetrahedra and a subset of the relative ${\rm SL}(2,\mathbb R)$ character varieties of the four-holed sphere. We also discuss the degenerate Gram strata, vector closure in the curvature-zero limit, and the projective dual tetrahedra, which include ideal and hyperideal tetrahedral sectors. The results provide classical geometric input for quantizing Lorentzian curved tetrahedra and for quantum gravity models with a nonzero cosmological constant.

In the direct horizon convention, the fixed-pressure Gibbs curve of the four-dimensional Bardeen-AdS black hole passes through an intermediate sequence between the Reissner-Nordstrom-AdS swallow-tail class and the single-branch regime as the regularization scale is increased. The on-shell curve is classified by its turning points and self-intersections, followed by local heat-capacity filtering and construction of the lower Gibbs envelope over stable branches. The deformation is resolved into three boundaries: g_*(P), where the RN-AdS-like topology is lost; g_c(P), where the c-shaped sector begins; and g_s(P), where the positive-temperature multibranch structure terminates. A reduced-variable analysis shows that these boundaries are controlled by the dimensionless combination 8 pi P g^2, accounting for their inverse-square-root pressure dependence and giving an analytic value for the final single-branch boundary. The equilibrium construction further shows that stable small/large coexistence can survive the first topology change, whereas the representative c-shaped regime has no stable crossing. Within the direct convention, these results define a Gibbs bifurcation structure for Bardeen-AdS thermodynamics.

We formulate a one-parameter extension of Weyl transformations in first-order gravity and show that it defines a conformally coupled scalar sector with dynamical torsion. The construction reduces to the standard torsionless conformal coupling in the limit $\lambda\to 1$. In the corresponding Einstein-Cartan-Maxwell theory, we derive exact static solutions in asymptotically flat and asymptotically locally AdS spacetimes. These solutions describe scalar-dressed black holes, regular black holes, and traversable wormholes, depending on the values of the integration constants and of the deformation parameter. We show that torsion can regularize the scalar field and, for suitable branches, also improve the geometric singularity structure. In the AdS sector, the existence of topological black holes requires a nonvanishing electric charge. These results provide new exact examples of regular and torsional configurations in four-dimensional gravity.

We study Krylov construction in periodically driven conformal field theories and their lattice realisations via critical fermions. Two types of driving are considered: a square-wave drive and a continuous sinusoidal drive. Using the Arnoldi construction, we examine Arnoldi coefficients and return amplitudes in periodically driven conformal field theories in the heating and non-heating phases. In the heating phase, the Arnoldi coefficients approach unity exponentially; in contrast, in the non-heating phase, they exhibit oscillatory behaviour. For the lattice realisations, we further analyse the Krylov complexity of the correlation matrix, quasi energy level statistics, and the graph structure induced by the Floquet operator. Although the two drives exhibit similar Krylov growth on the CFT side, their lattice realisations exhibit markedly different spectral and graph signatures, indicating distinct mechanisms governing the transition between the heating and non-heating phases.

We study Abelian $S$-duality of Maxwell theory on $A$-type asymptotically locally Euclidean (ALE) spaces. Unlike on closed four-manifolds, the Maxwell path integral on an ALE space is not naturally a scalar partition function. Rather, it decomposes into theta-function blocks labeled by flat $U(1)$ holonomy sectors on the asymptotic lens-space boundary. We interpret these blocks as components of the Hilbert-space boundary state prepared by the ALE path integral. With this interpretation, the apparent failure of ordinary modularity is replaced by vector-valued modular covariance under the action of the modular group. We test this picture explicitly for Eguchi-Hanson space by gluing it to its orientation reversal. The resulting closed four-manifold is diffeomorphic to $S^2\times S^2$, and the natural pairing of the two ALE boundary states reproduces the standard Maxwell partition function on $S^2\times S^2$. We then refine the construction by turning on electric and magnetic $1$-form symmetry backgrounds. In their presence, the ALE theta blocks are not ordinary functions, but sections of a line bundle over the Cartan torus associated with the $A_{N-1}$ root lattice, reflecting the mixed electric-magnetic $1$-form anomaly. We also discuss gauging discrete $\mathbb Z_k$ subgroups of the $1$-form symmetries and show that the vector-valued boundary-state structure remains the natural covariant framework after gauging. In this sense, ALE spaces behave as chiral building blocks for four-dimensional Maxwell theory: individual ALE blocks carry sector-resolved boundary data, while gluing pairs these sectors to produce an ordinary closed-manifold partition function, much like the pairing of left- and right-moving conformal blocks in two-dimensional CFT.

Black holes respond to infalling quantum matter fields by changing their entropy. Since such matter is quantum in nature, the entropy response should be sensitive to its quantum fluctuations. We show, within stochastic semiclassical gravity, that a horizon cannot record relevant quantum information with arbitrarily small entropy fluctuations. For the infalling photons encoding which-path information in the Danielson-Satishchandran-Wald decoherence experiment, we derive a trade-off relation between the stochastic variance of the black hole entropy change and the photon number.

The Swampland Distance Conjecture (SDC) states that, for any infinite-distance limit in the moduli space of a quantum gravity effective field theory (EFT), there should exist an infinite tower of states that become exponentially light. According to the Emergent String Conjecture, such a tower should consist either of tensionless strings or of Kaluza-Klein modes, each with a mass-decay rate that depends in a precise way on the dimension of the effective field theory. In this paper, we use the results obtained in arXiv:2508.18401 on the SDC for symmetric moduli spaces and how these rates are encoded in the weight polytope of the corresponding particle-state representations to determine the symmetric space EFTs and representations that have these decay rates. Remarkably, assuming that the particle states transform in an irreducible representation, the list of possible polytopes and moduli spaces is finite. Different EFTs are related by embedding one moduli space in another or by taking a decompactification limit. Requiring compatibility of the particle representations under such branching, we find that, while most of the theories can be obtained from an EFT based on $E_{8(8)}$, there remain three in our list that appear to be impossible to get from M- or string-theory compactifications. Using the same embedding procedure, we also identify the string and brane representations that should be present in the spectrum.

Twist fields are a powerful formal tool to compute Rényi entropies in quantum many-body systems, but their conventional formulation in tensor network states involves operations acting on virtual degrees of freedom, which are not directly accessible in experiments. In this work, we construct explicit local operators acting on the physical Hilbert space whose expectation values reproduce the action of twist fields in matrix product states. Our construction is exact in the injectivity limit and when the tensor is chosen at the center of orthogonality, and provides a direct operational method to evaluate Rényi entropies without accessing auxiliary tensor indices. We test our formulation numerically in the transverse-field Ising model, demonstrating rapid convergence to the exact entanglement entropy as the injectivity scale is reached. Furthermore, we show that twist operators determined from relatively small reference systems can be reliably transferred to larger systems, once the reference size exceeds a characteristic scale set by the correlation length. Since the resulting operators admit a decomposition in terms of a finite number of local observables, our results provide a scalable and experimentally accessible framework to probe entanglement in quantum simulators.

Family puzzle asks why the Standard Model (SM) features exactly 3 families of quarks and leptons. Motivated by topological constraints, we study 4d fermionic anomalies with discrete $Z_n$ symmetry, classified by the 5d spin bordism group. We show that only the group-cohomology subclass H$^5(Z_n,U(1))\cong Z_n$ can be canceled by an anomalous $Z_n$-symmetric 4d $Z_n$-gauge topological quantum field theory (TQFT), while beyond-group-cohomology $A_{Z_n}p_1$ involving the Pontryagin class $p_1$ cannot (except $n=2,3$). More generally, we prove that any cocycle $\alpha_d\in$H$^d(Z_n,U(1))$ in odd spacetime dimension $d\ge3$ is trivialised by the symmetry extension $1\to Z_n\to Z_{n^2}\to Z_n\to 1,$ and we construct the corresponding symmetric anomalous boundary TQFT. For $d=5$ and $n=3$, this yields a Spin$\times Z_3$-symmetric 4d $Z_3$-gauge TQFT that cancels the mixed discrete $(\bf B+L)$-gauge-gravitational anomaly of the SM in the absence of 3 "sterile" right-handed neutrinos $\nu_R$. We analyze a generalized SM with $N_c$ colors and $N_f$ families and argue that missing $N_f$ copies of the $\nu_R$ can be naturally replaced by a 4d anomalous $Spin\times_{Z_2^F}Z_{2 N_f,{\bf B + L}}$ symmetric $Z_N$-gauge TQFT under the anomaly cancellation, via a $Z_N$ symmetry extension construction $1\to Z_N\to Spin\times Z_{NN_f}\to Spin\times_{Z_2^F}Z_{2N_f}\to1$ of anomalous topological order. For minimal nonzero $(N,N_f)$, the allowed minimal extensions are $N=1,3,4,12$, depending on divisibility of $N_f$ by 2 and 3. Combining Witten anomaly and other constraints, we prove that $N=N_c=N_f=3$, with 3 families and 3 colors, is the unique minimal solution to match with the color-center baryon-to-quark symmetry extension $1\to Z_{N_c}\to Spin\times_{Z_2^F}Z_{2N_cN_f,{\bf Q}+N_c{\bf L}}\to Spin\times_{Z_2^F}Z_{2 N_f,{\bf B+L}}^F\to1$. We also prove that $A_{Z_3}p_1=0\mod3$ for the mod 3 cohomology class.

In a recent article, arXiv:2605.12414, it is stated that a certain scale transformation has been "systematically overlooked" in discussions of the tensionless string. Here we point out that this kind of symmetry is treated in numerous places, in the classical as well as the quantum theory.

We study intersecting surface operators in 6d holomorphic field theories with the aim of unraveling associated quantum integrable structures. We first study the intersections of surface operators in 6d holomorphic Chern-Simons theory on $\mathbb{C}^3$. Computing their correlation function, we find a local operator at the intersection of the surface operators with a form reminiscent of the leading nontrivial term in the quasi-classical expansion of a rational $R$-matrix, as predicted by Costello. We provide evidence that this $R$-matrix-like operator satisfies a Yang-Baxter-type relation. We then derive the associated coproduct of the chiral algebra supported by surface operators from their OPE. We also study intersecting surface operators in 6d holomorphic BF theory and derive the local leading form of the corresponding $R$-matrix-like operator. When this theory is placed on twistor space, where it describes the self-dual sector of 4d Yang-Mills theory, this operator is expected to provide a local building block for quantum integrable structures anticipated in that setting.

A central lesson of gravity is that local observables are ill-defined. Coordinates themselves are a redundancy of description, so any particular point in spacetime is only meaningful once defined relationally by clocks, rulers, or asymptotic data. Despite extensive formal work on this subject, explicit calculations of the resulting gravitationally-dressed observables are more scarce. In this paper we perturbatively compute dressed matrix elements of local operators in electrodynamics and general relativity, including both potential and radiative photons and gravitons. Our expressions indicate that dressing is not ornamental: it universally induces kinematic singularities that can substantively reshape observables. We further show how dressing is mathematically equivalent to gauge fixing, as demonstrated by a dynamical temporal gauge in which the gauge-fixing vector is itself a geodesic fluid.

We study Krylov complexity in BMN Plane Wave Matrix Model at large mass deformation. We consider various consistent reductions of the matrix model that allow us to perform a Hamiltonian analysis which leads to different notions of the Krylov complexity. In the first part of the paper, we study the Krylov state complexity considering systematic reduction of $N=3$ and $N=4$ representations of the matrix model, which reveals a universal characteristic scaling for the Lanczos coefficients and fix them completely in terms of the mass deformation parameter. In the second part of the paper, we study the Krylov operator growth in the matrix model and compute the corresponding Lanczos coefficients. In both cases, we observe a linear scaling of Lanczos coefficients with the mass parameter. The early time growth in Krylov complexity receives quadratic correction due to the presence of the massive deformation in the matrix model. Our analysis reveals that such massive corrections appear at same order in time for both the notion of the Krylov complexity.

We inspect $\mathfrak{su}(n)$ forms, providing greater detail for $n=2,3$, as a toy model for a field theory in finite dimensions and with gauge symmetries. Relying on homological perturbation theory, we show that there are no scattering amplitudes with trivalent tree-level diagrams, except for the interaction vertex, thus extending a known argument of Cattaneo–Mnëv to arbitrary $n$. In contrast to this, we show how to obtain non-trivial higher products when transferring to a larger space of fields.

Using the $\mathcal{N}=1$ superfield formalism, we prove that the superconformal symmetry of $\mathcal{N}=4$ super-Yang-Mills theory is preserved in the quantum theory. We demonstrate that the $\mathcal{N}=1$ calculation is sufficient to guarantee the full $\mathcal{N}=4$ supersymmetry, and show that the results are exact without receiving any higher-order corrections.