Papers

We derive deterministic equations for the evolution of non-Gaussian fluctuations in relativistic stochastic hydrodynamics. This is achieved by defining the average local Landau frame and corresponding fluctuating hydrodynamic variables. Fully nonlinear stochastic hydrodynamics is expressed in a unified multi-component matrix form. A novel relativistic formalism, also manifestly covariant under SO(3) rotations of the local spatial basis in the average local Landau frame, is introduced. The equations describe correlators of all hydrodynamic variables, including fluctuating velocity (or momentum density) – a nontrivial problem in relativistic hydrodynamics.

The localization of chiral fermionic zero modes in scalar field backgrounds with domain wall structure is a central mechanism in brane-world scenarios. We investigate this mechanism in a system that provides an effective realization of the $(1+1)$-dimensional Jackiw–Rebbi model, using a two-kink scalar background generated by the deformation method applied to the $\varphi^4$ model. The two-kink profile introduces two physically distinct parameters: an asymmetry parameter $a_2$ controlling the left-right symmetry of the scalar background, and an inter-kink separation parameter $b$ controlling the distance between the constituent domain walls. We establish two independent scaling laws. First, the collective center-of-mass position of the chiral zero modes responds linearly to $a_2$, providing a mechanism for continuously tuning the effective brane position in the extra dimension. Second, the differential spatial separation between the two chiral modes diverges as the two-kink background collapses into a simple kink, following a power law in $(b-1)$ with exponent statistically consistent with $-1$. These two results are physically independent and each admits a precise interpretation in the language of brane-world scenarios. The mechanism is realized concretely in bilayer graphene under an asymmetric two-kink electrostatic potential, providing a tunable platform for probing extra-dimensional localization physics.

Matrix models are an important class of systems in string theory and theoretical physics, with applications to random matrix theory, quantum chaos, and black holes. Hamiltonian Monte Carlo simulations and gauge/gravity duality have been used to study these systems at thermal equilibrium, and the bootstrap program has been used to efficiently determine operator expectation values by imposing positivity constraints. However, simulating real-time, non-equilibrium dynamics remains a fundamental challenge. In this work, we present the first digital quantum simulation of a bosonic matrix model, executed on the Quantinuum System Model H2 trapped-ion quantum computer. We focus on an $\mathrm{SU}(2)$ gauge theory with a quartic potential as it is simple enough to validate against exact classical solutions and yet complex enough to reflect the non-local structure of larger theories. Using the Loschmidt echo as our primary dynamical observable, we systematically decompose simulation errors into three distinct sources: Hilbert space truncation, Trotterization, and hardware noise. We demonstrate a new post-selection scheme that detects and discards gauge-symmetry violations in the Fock basis and show that at small scales it, along with zero-noise extrapolation, can give modest improvements in fidelity. These approaches struggle to scale to larger system sizes in their current implementations, emphasizing the need to move beyond them and to focus on depth reduction through improved compilation and unitary synthesis, and run-time error handling such as additional error suppression, error detection, as well as error correction approaches. This work establishes a foundation for extending digital quantum simulation to more complex matrix models – revealing that fundamental challenges in qubit resources and circuit depth remain formidable obstacles for scaling to holographically interesting regimes.

We study physical (near-kernel of constraints) states of 4-d Euclidean loop quantum gravity in Smolin's weak coupling limit on the complete graph $K_5$ using variational Monte Carlo with neural network quantum states. We investigate the Hamilton constraint $\hat{H}$ in the ordering proposed by Thiemann, as well as $\hat{H}^\dagger$ and $\hat{H}+\hat{H}^\dagger$. We find that the variational optimisation selects distinct solution families for $\hat{H}$ and $\hat{H}^\dagger$ across several considered cutoffs on the kinematical degrees of freedom. The solution family of $\hat{H}$ is flat on all minimal loops and has non-vanishing volume expectation values. Its edge-charge marginals delocalise with increasing cutoff, which indicates they are approximations to solutions that are non-normalisable in the kinematical inner product. The solution family for $\hat{H}^\dagger$ is normalisable, shows non-trivial charge correlations, lies in the kernel of volume and is not flat. $\hat{H}+\hat{H}^\dagger$ turns out to be much harder to solve and yields quasi-solutions combining features of both previous families. We characterise all solutions using chromaticity 1- and 2-point functions, minimal loop holonomies, geometric area and volume observables and show that the two families can be interpreted as, on the one hand, a family of states close to the Ashtekar-Lewandowski vacuum and the Dittrich-Geiller vacuum with some numerical noise on the other hand. We also present some results that link solutions of the truncated theory to solutions of the continuum theory.

Within the wide variety of topological solitons supported by Yang–Mills theory, merons occupy a particularly distinguished role. Despite their simplicity, they represent genuinely non-Abelian configurations that can be regarded as the fundamental building blocks of instantons, and they provide a qualitatively accurate picture of confinement. In this work, we show that such configurations are, in fact, supported by a broad class of non-Abelian gauge theories beyond Yang–Mills, provided that suitable physical conditions are satisfied. Taking into account their gravitational backreaction, we further demonstrate that both black holes and Euclidean wormholes sourced by merons admit natural extensions within this generalized framework, which regularizes the singular behavior they exhibit in constant–curvature backgrounds. As a byproduct, we construct a regular black hole solution supported by genuinely non-Abelian gauge fields, based on a non-Abelian generalization of the Ayón–Beato–García nonlinear electrodynamics. As a consequence, physical effects intrinsic to merons are likewise expected to be inherited by these classes of theories beyond the Yang-Mills framework. A notable example is the spin from isospin effect, whereby bosonic excitations charged under the gauge group can effectively behave as fermionic degrees of freedom.

Kollár showed that small deformations of elliptically fibered smooth $K$-torsion varieties with $H^2(X,\mathcal{O}_X)=0$ remain elliptically fibered. We extend this result to any fibered smooth $K$-torsion variety $X$ with $H^2(X,\mathcal{O}_X)=0$, using Hodge theoretic techniques and the $T^1$-lifting criterion of Kawamata–Ran. More generally, our strategy implies that even without the cohomological assumption, small deformations of a semiample line bundle on a smooth $K$-torsion variety remain semiample up to homological equivalence.

We investigate the properties of charged black hole geometries in nonlinear electrodynamics. We focus on the recently reported analytic charged black hole solutions to illustrate the consequences of a non-monotonic lapse function that exists for a wide range of black hole solutions. The spacetime admits stable light-rings, static near-horizon observers, and trapped near horizon photon orbits. We also show that although these modifications near the horizon are screened from afar, they nonetheless lead to additional branches of quasinormal modes for the black hole that are longer lived than the canonical Einstein branches.

The mean value of the stress-energy tensor of a given quantum field theory at global thermodynamic equilibrium in a curved space-time can be expressed in terms of the derivatives of the Killing four-temperature field and the derivatives of the metric tensor. Its asymptotic expansion about zero includes an analytic part made of integer powers of these derivatives - corresponding to the so-called gradient expansion - as well as non-perturbative corrections. By using available exact solutions for the free real massless scalar field, we show that in the case of Minkowski, de Sitter, anti-de Sitter, and closed Einstein universe, the analytic part - obtained through the procedure of analytic distillation - has a finite number of terms and it is the same once expressed in a covariant form. On the other hand, non-universal terms are non-analytic in these derivatives and correspond to boundary conditions or to specific global properties of the space-time. We argue that the universality of the analytic part extends to any quantum field theory on a curved background.

We study bipartite entanglement harvesting from the quantum vacuum of a massless scalar field between two subsystems, each composed of a finite number of Unruh-DeWitt detectors. Using perturbation theory, we show that the leading-order negativity is fully determined by a submatrix of the reduced density matrix, with the submatrix dimension scaling only linearly with the number of detectors. Within this framework, we analyze how the detectors' spatial arrangement influences harvesting. For all three-detector configurations and several symmetric four-detector configurations, we derive analytic expressions for the negativity and identify the configurations that maximize it. For a linear chain, we find that the harvested entanglement scales linearly with the number of detectors. These results clarify how to arrange multiple detectors to optimize harvesting and show that increasing their number broadens the ranges of energy gaps and separations over which entanglement can be extracted from the field.

Transient noise artifacts, commonly referred to as glitches, pose a major challenge to parameter inference for space-based gravitational-wave (GW) observations. We develop a glitch-robust amortized inference framework for massive black hole binaries in the Taiji detector configuration by combining conditional normalizing flows, a time-frequency multimodal fusion encoder, and contrastive learning. To enable large-scale training on contaminated data, we further introduce a neural glitch generator that produces high-fidelity synthetic transients at substantially reduced computational cost. Systematic experiments show that, under glitch contamination, the proposed method yields more accurate and better-calibrated posteriors than a conventional Markov Chain Monte Carlo baseline. In ablation studies, the full time-frequency model with contrastive learning performs best overall and remains robust to variations in glitch duration and merger-relative timing. We further show that standard coverage diagnostics alone are insufficient to fully assess posterior fidelity. We therefore complement them with the continuous ranked probability score, which provides a stricter assessment of global distributional agreement in non-ideal GW data. Taken together, these results establish deep-learning-based amortized inference as a promising framework for fast and robust Bayesian parameter estimation in future space-based GW observations.

We investigate one-loop corrections from torsion-induced four-fermion interactions to inflaton three-body decay and their impact on the associated stochastic gravitational-wave signal. We find a pronounced asymmetry in the dependence on the renormalization scale $u$. While the enhancement of the gravitational-wave spectrum remains modest, not exceeding roughly a factor of order unity for representative inflaton masses well below the Planck scale within the perturbative regime, the suppression can be much stronger, reaching up to two orders of magnitude, corresponding to reductions at the percent level. These results imply that loop corrections, particularly fermionic self-interactions, can significantly reduce the predicted gravitational-wave signal in models based on tree-level analyses. This suppression may shift the signal outside the sensitivity range of future observations and should therefore be taken into account in realistic phenomenological studies.

We extend the hidden zeros and $2$-split of tree-level ${\rm Tr}(\phi^3)$ amplitudes to loop-level Feynman integrands, apart from some physically irrelevant scaleless integrals. Our method is based on a certain factorization mechanism that occurs in Feynman diagrams when summing over shuffle permutations. The loop-level hidden zeros and $2$-split identified in this work differ from those in the literature. In our result, the kinematic conditions for loop-level hidden zeros and $2$-split are remarkably simple. Their connection is as tight as at tree-level, with the same procedure for obtaining the $2$-split condition from the zero condition. The resulting $2$-split formula at loop-level represents a generalization of that at tree-level: the $L$-loop integrand is expressed as a sum over $L+1$ terms, each of which exhibits a $2$-split structure.

We examine the leading-power fragmentation of fully heavy pentaquarks in high-energy hadronic collisions. To this end, we complete the release of the hadron-structure-oriented PQ5Q1.0 fragmentation functions, by discussing the $P_{5c}$ set and delivering the $P_{5b}$ one. These functions incorporate an improved computation of the initial-scale input for the constituent heavy-quark fragmentation channel, making them particularly suitable for describing both the direct formation of a compact multicharm state and the hadronization from a diquark-antiquark-diquark configuration. For phenomenological applications, we employ the data-validated (sym)JETHAD framework to compute and analyze NLL/NLO$^+$ semi-inclusive production rates of pentaquark-plus-jet systems at the upcoming HL-LHC and the future FCC. This study marks a further step toward connecting hadronic structure, precision QCD, and the emerging physics of exotic matter.

The study of spin polarization of $\Lambda$ hyperons in ultrarelativistic heavy-ion collisions provides insights into the angular momentum and vortical structure of the possible existence of QGP. The present study examines the global spin polarization of $\Lambda$ hyperons using a second-order relativistic viscous hydrodynamic framework that incorporates medium vorticity, shear viscosity, and evolving magnetic fields. It explores thermal vorticity evolution in relativistic heavy-ion collisions and evaluates its value at the decoupling isothermal freeze-out surface. We quantify the contributions of thermal vorticity and magnetic field to the global spin polarization of $\Lambda$ hyperons. Comparing results with recent ALICE measurements in Pb+Pb collisions at $\sqrt{s_{NN}}$ = 2.76 and 5.02 TeV shows qualitative agreement, offering new insights into the vortical structure of QCD matter. It also explores the relationship between magnetic and rotational dynamics, with implications for spin polarization at RHIC and LHC energies.

The Heisenberg position-momentum uncertainty relation is a cornerstone of quantum mechanics. However, its standard formulation is not fully consistent with special relativity. While partial understanding has been achieved in the ultra-relativistic regime, a comprehensive description is still lacking, particularly in the intermediate velocity domain, where particle speeds remain well below the speed of light yet relativistic corrections are expected to become appreciable. This regime constitutes the most promising arena for experimentally probing relativistic modifications of quantum uncertainty. By adopting a variational approach, in this work we derive a relativistic extension of the Heisenberg algebra within the framework of $\kappa$-deformed Kaniadakis statistics. The latter emerges from the application of the Maximum Entropy Principle to Kaniadakis entropy, a one-parameter generalization of the Boltzmann-Gibbs-Shannon entropy naturally induced by Lorentz transformations. We investigate the physical implications of the resulting uncertainty relation, deriving constraints on the Kaniadakis parameter from precision measurements of the fine-structure constant and confronting our construction with other extensions discussed in the recent literature.

We show that the self-dual classical double copy can be straightforwardly extended to the higher-spin case when formulated in terms of light-cone gauge prepotentials. This allows us to construct a higher-spin extension for any self-dual spacetime that admits a Kerr-Schild form. We also discuss the counterpart of this procedure at the level of Weyl tensors. We find that, depending on the class of the original gravitational background, higher-spin Weyl tensors may follow various multicopy patterns.

Response theory describes the reaction of observales to perturbations in external fields. We review this formalism for quantum fiels in isolation that have unitary time evolution. An emphasis is put on consequences of causality and the resulting spectral representations for linear and nonlinear response functions, on functional techniques and generating functionals, including the description of the initial state, the evolution, and measurements. We review consequences of time reversal symmetry and relations for the statistics of work, and discuss a large class of quantum correlation functions, and their relation to response functions through fluctuation-dissipation relations. Consequences of conservation laws and gauge symmetries are mentioned briefly.

We extend Schwinger's proper-time formalism to provide a method for computing the one-loop effective action for both spinor and scalar quantum electrodynamics in $d=2n>4$ dimensions. We give the closed form expression for the higher-dimensional Euler-Heisenberg Lagrangian, and extract its weak-field approximation in 6, 8 and 10 dimensions. A subsequent analysis of pair production in $d$ dimensions is also given. In the $d=6$ case, we present a composite conformal primary field of dimension $+6$ which determines the contribution of the electromagnetic field to the Weyl anomaly in curved space.

Multiple potential wells for massive test particles, allowing distinct families of bound orbits to coexist, are a characteristic feature of certain exotic compact objects beyond general relativity. Taking the dyonic black hole as a representative example, we demonstrate that such multi-well geometries generically support multiple coexisting branches of bound orbits, in contrast to the single-branch behavior observed in the Schwarzschild spacetime. Crucially, the periodic orbits sharing identical rational rotation number, and hence identical topological indices can nevertheless produce radiatively distinct gravitational waves in a representative extreme-mass-ratio inspirals: their amplitude modulation and harmonic content differ because each branch spans different regions of spacetime curvature. These “topologically equivalent yet waveform-distinguishable” signatures provide a direct observational probe of strong field gravitational dynamics beyond general relativity, potentially accessible to future space-based gravitational wave detectors.

[Abridged] A variety of model-dependent as well as model-independent approaches suggest that certain localized features in the primordial scalar power spectrum can lead to a significantly better fit to the observed anisotropies in the cosmic microwave background (CMB). In this work, we focus on three types of such features and examine whether these features can be generated in inflationary scenarios driven by a single, canonical scalar field. We consider a slowly rolling baseline model that is described by a specific time-dependence of the first slow roll parameter and we generate the desired features in the power spectrum through suitable modifications to the functional form of the slow roll parameter. To systematically reconstruct the desired features in the scalar power spectrum (or, equivalently, the modifications in the behavior of the first slow roll parameter) that are consistent with the data, we implement a machine learning pipeline based on the genetic algorithm (GA). Assuming the standard values for the background $\Lambda$CDM model (arrived at for a nearly scale-invariant primordial scalar power spectrum), we apply our method to the Planck 2018 CMB data, and show that the reconstructed features improve the fit to the observed angular power spectra by $\Delta \chi^2 \lesssim -10$. Moreover, we find that GA points to other sets of background parameters and primordial features, which lead to a similar level of improvement in the fit to the data. Such alternative sets of background parameters and scalar power spectra offer possible pathways to alleviate existing cosmological tensions. Our approach provides effective single-field inflationary dynamics to generate features that are supported by the data.

We compute the quasinormal mode spectrum of scalar perturbations on Kaigorodov pp-wave spacetimes, the horizonless gravity duals of zero temperature null fluids. The pp-wave deformation promotes the Poincaré horizon at $r=0$ to an irregular singular point of rank $(d+2)/2$, which acts as a geometric absorber for ingoing waves: rank~$0$ corresponds to thermal dissipation, rank~$1$ to quantum-critical (extremal black hole), and rank~$\geq 2$ to gapped, horizonless dissipation. For $d=2$ (extremal BTZ) the radial equation reduces to the Whittaker equation with exact non-dissipative spectrum $\mathrm{Im}(\omega)=0$; for $d \geq 3$ all modes satisfy $\mathrm{Im}(\omega_n) < 0$, establishing zero temperature dissipation without horizon or entropy. At zeroth order the radial equation becomes Bessel's equation of order $\mu=d/(d+2)$, proving all scalar QNMs are gapped. Numerical spectra for $d=3,4,5$ yield a discrete dissipative tower and confirm linear stability.

We apply the Operator Product Expansion (OPE) algorithm to the renormalization of scalar-QED theory, with a specific focus on the fixed-charge operator $\phi^Q$. Within the OPE framework, the anomalous dimension of the $\phi^Q$ operator is perturbatively computed to four-loop order in the modified minimal subtraction scheme, extending beyond the previously available three-loop result. The beta functions, as well as the mass and field anomalous dimensions, are also computed at this order. An alternative loop-integrand construction method is proposed, based on graph decomposition and skeleton expansion techniques, for deriving the integrands of one-Particle-Irreducible correlation functions. This work represents the first non-trivial validation of the OPE algorithm for higher-loop renormalization beyond pure scalar theories. The present successful computations further confirm the efficiency and versatility of the OPE algorithm in renormalization analysis.

Collinear factorization and the leading-twist operator product expansion (OPE) in perturbative QCD express suitably inclusive observables in scale-separated kinematics as composites of perturbative short-distance coefficients with universal long-distance non-perturbative correlators such as parton distribution functions (PDFs), up to controlled power corrections. A persistent structural feature is presentation non-uniqueness: coefficients and correlators are not individually physical, but are defined only up to finite factorization-scheme redefinitions induced by collinear subtractions and renormalized-operator mixing. We formalize this redundancy categorically by introducing an interface algebra object encoding admissible finite collinear counterterms/mixing kernels and by organizing coefficient data and hadronic data as right/left modules over this algebra in a symmetric monoidal category encoding the chosen recomposition calculus. Our main result, the Core Representation Theorem, identifies the universal scheme-invariant carrier: the functor of balanced (scheme-invariant) pairings is represented by the relative tensor product $C\otimes_A f$, which is terminal among all quotients of the naive composite $C\otimes f$ that preserve scheme-invariant semantics. Finally, we show how standard physics inputs (symmetry constraints, locality/OPE, and a stated accuracy truncation) canonically induce the interface algebra and module structures, and we prove a minimal closure principle for completing a generating set of long-distance operators/correlators to an $A$-stable sector.

We extend Penrose's quasi-local mass definition to include higher-spin charges associated with the celestial $Lw_{1+\infty}$ symmetries and relate them to traditional definitions of multipoles. The resulting formulae provide explicit expressions that can be computed on finite 2-surfaces, given a choice of null hypersurface. They yield a geometric definition of celestial symmetries and multipoles in generic spacetimes in terms of higher-valence solutions to the twistor equations. This, in turn, gives rise to natural flux-balance laws along the null hypersurface. We also present a first-principles phase-space derivation of these charges, starting from a twistor space action for self-dual gravity that can be identified with the standard gravitational asymptotic phase space at null infinity, performing a large gauge transformation analysis and using the Penrose transform to connect with the corresponding spacetime expressions. Finally, we formulate the spacetime analysis in the Plebanski gauge and relate the celestial symmetries to the integrability of self-dual gravity in the case of a self-dual background.

If an operator $H$ anticommutes with a chirality operator $\Gamma_*$ such that $\Gamma_*^2=1$, the null space of $H$ can be decomposed in a direct sum of two spaces having positive and negative chiralities, respectively. When both spaces are finite dimensional, one can define an index, $\mathrm{Ind}(\Gamma_*,H)$, as the difference of dimensions of these two spaces. The key issue is whether $\mathrm{Ind}(\Gamma_*,H)$ is topologically protected, i.e., whether it remains constant under smooth variations of the parameters and background fields entering $H$. For Hermitian Dirac operators, topological protection of the index is guaranteed by the Atiyah–Singer theorem. In this paper, by using the heat kernel methods, we show that $\mathrm{Ind}(\Gamma_*,H)$ is topologically protected also for non-hermitian operators $H$ as long as they are diagonalizable and satisfy some ellipticity conditions. The index is given by a heat kernel coefficient which is an integral of a local expression depending on background fields.

We study replica symmetry breaking (RSB) for multi-entropy in the random-tensor-network (RTN) domain-wall spin model. Our main result is that, within this framework, multi-entropy has a structural obstruction to RSB for any Rényi index $n$ and any multipartite number $\mathtt{q}$. This obstruction arises because the boundary permutations relevant to multi-entropy are organized along mutually incompatible coordinate directions of the replica hypercube, and therefore do not admit a nontrivial common geodesic intermediate permutation $\tau$ in the Cayley graph of $S_N$. This is in sharp contrast to entanglement negativity, which does admit such a $\tau$-mediated saddle and exhibits RSB in the same framework. As a robustness check, we also consider a toy $\mathbb{Z}_2$ gauge extension of the spin model with a minimal bulk gauge constraint. Numerical evidence in this gauged model indicates that multi-entropy continues to show no sign of RSB at $n=2$ and $n=3$, while negativity continues to exhibit RSB. Our results show that, within the RTN spin-model description, multi-entropy is not "RSB-friendly”: its boundary data are structurally incompatible with a nontrivial common geodesic intermediate permutation, unlike negativity.

We evaluate the effective action for the Dynamical Casimir Effect (DCE) for a real scalar field in $d+1$ dimensions within the worldline formulation of quantum field theory. The scalar field is coupled to a spacetime-dependent mass term, which here plays the role of the moving medium and imposes imperfect boundary conditions on time-dependent surfaces. Expanding in powers of the departure of the geometry from a planar configuration, the worldline path integral factorizes into simpler, lower-dimensional ones. In the limit of a strong coupling to the surface, we recover the Dirichlet result and derive the systematic corrections in inverse powers of the coupling, calculating the imaginary part of the effective action up to arbitrary order of said powers. Finally, we also apply the method to a two-surface configuration.

In this paper, we study the gravitational lensing around the static and spherically symmetric DD black holes, which we recently derived as perturbations of the Schwarzschild geometry within the revised Deser-Woodard theory of nonlocal gravity. We first present general analytical expressions for the deflection angle in both weak- and strong-deflection limits, explicitly relating them to the nonlocal corrections to Schwarzschild spacetime. Subsequently, we analyze lensing observables, such as the post-Newtonian effects and the black hole shadow, to constrain the DD black hole parameter space using current observational bounds. Finally, we perform a joint statistical analysis based on the Fisher information matrix, combining these findings with our previously obtained constraints from quasinormal modes. Our results indicate consistency with general relativity at the $1.13\sigma$ level. This work provides a first assessment of the DD parameter space and offers new insights to probe deviations from Einstein's gravity in view of future larger datasets.

We introduce a cyclotomic representation for finite $q$-hypergeometric series and $q$-deformed amplitudes that separates algebraic structure from evaluation. By expressing each summand in a sparse exponent basis over irreducible cyclotomic polynomials, all products and ratios of quantum factorials reduce to integer vector arithmetic. This ensures that cancellations between numerator and denominator are resolved exactly prior to any evaluation. This formulation yields the deferred cyclotomic representation (DCR), a parameter-independent combinatorial object of the series, from which evaluation in any target field is realized as a ring homomorphism. For quantum recoupling coefficients, we demonstrate that this framework achieves linear memory scaling in the compilation phase, eliminates intermediate expression swell in exact arithmetic, and substantially extends the range of reliable double-precision computation by reducing cancellation-induced error amplification. Beyond its computational advantages, the DCR provides a unified perspective on $q$-deformed amplitudes. Structural properties like admissibility at roots of unity, and the classical limit all emerge as intrinsic properties of a single underlying combinatorial object.

We study noncommutativity in open strings using the covariant phase space formalism. For tensile open strings in a constant Kalb-Ramond background, we show that the (pre)-symplectic current splits into a bulk kinetic term plus an exact boundary term, recovering the Seiberg-Witten noncommutativity parameter. We then extend the analysis to intrinsically tensionless strings. In the absence of background fields, the reduced phase space is degenerate and carries no intrinsic Poisson structure. In the presence of a constant Kalb-Ramond field, the symplectic current localises entirely on the boundary, so that the physical phase space becomes purely boundary-supported and the endpoint coordinates acquire a noncommutative Poisson algebra. Including a boundary gauge-field coupling similarly leads to a boundary symplectic form governed by the effective Born-Infeld combination on the D-brane. Our results provide a unified description of noncommutativity in both tensile and tensionless open strings.