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Carrollian amplitude is the natural object that defines the correlator of the boundary Carrollian field theory. In this work, we will elaborate on its proper definition in general dimensions. We use the vielbein field on the unit sphere to define the fundamental field with non-vanishing helicity in the local Cartesian frame which is the building block of the Carrollian amplitude. In general dimensions, the Carrollian amplitude is related to the momentum space scattering matrix by a modified Fourier transform. The Poincar\'e transformation law of the Carrollian amplitude in this definition has been discussed. We also find an isomorphism between the local rotation of the vielbein field and the superduality transformation., Comment: 58 pages, published version

The helicity flux operator is a fascinating quantity that characterizes the angular distribution of the helicity of radiative photons or gravitons and it has many interesting physical consequences. In this paper, we construct the electromagnetic helicity flux operators which form a non-Abelian group in general dimensions, among which the minimal helicity flux operators form the massless representation of the little group, a finite spin unitary irreducible representation of the Poincar\'e group. As in four dimensions, they generate an extended angle-dependent transformation on the Carrollian manifold. Interestingly, there is no known corresponding bulk duality transformation in general dimensions. However, we can construct a topological Chern-Simons term that evaluates the minimal helicity flux operators at $\mathcal{I}^+$., Comment: 54 pages

In this paper, we derive the Carrollian amplitude in the framework of bulk reduction. The Carrollian amplitude is shown to relate to the scattering amplitude by a Fourier transform in this method. We propose Feynman rules to calculate the Carrollian amplitude where the Fourier transforms emerge as the integral representation of the external lines in the Carrollian space. Then we study the four-point Carrollian amplitude at loop level in massless $\Phi^4$ theory. As a consequence of Poincar\'e invariance, the four-point Carrollian amplitude can be transformed to the amplitude that only depends on the cross ratio $z$ of the celestial sphere and a variable $\chi$ invariant under translation. The four-point Carrollian amplitude is a polynomial of the two-point Carrollian amplitude whose argument is replaced with $\chi$. The coefficients of the polynomial have branch cuts in the complex $z$ plane. We also show that the renormalized Carrollian amplitude obeys the Callan-Symanzik equation. Moreover, we initiate a generalized $\Phi^4$ theory by designing the Feynman rules for more general Carrollian amplitude.

We propose a holographic dictionary which comes from reducing the bulk theories in an asymptotically flat spacetime to its null infinity. A general boundary theory is characterized by a fundamental field, an infinite tower of descendant fields, constraints among the fundamental field and its descendants as well as a symplectic form. For the Carrollian diffeomorphisms, we can construct the corresponding Hamiltonians which are also the fluxes from the bulk, and whose quantum operators realize this algebra with a divergent central charge. This central charge reflects the propagating degrees of freedom and can be regularized. For the spinning theory, we need a helicity flux operator to close the algebra which relates to the duality transformation., Comment: 8 pages

We construct Carrollian higher spin field theories by reducing the bosonic Fronsdal theories in flat spacetime to future null infinity. We extend the Poincar\'e fluxes to quantum flux operators which generate Carrollian diffeomorphism, namely supertranslation and superrotation. These flux operators form a closed symmetry algebra once including a helicity flux operator which follows from higher spin super-duality transformation. The super-duality transformation is an angle-dependent transformation at future null infinity which generalizes the usual electro-magnetic duality transformation. The results agree with the lower spin cases when restricting to $s=0,1,2$., Comment: 48 pages, 2 figures

We construct Carrollian scalar field theories in general dimensions, mainly focusing on the boundaries of Minkowski and Rindler spacetime, whose quantum flux operators form a faithful representation of Carrollian diffeomorphism up to a central charge, respectively. At future/past null infinity, the fluxes are physically observable and encode rich information of the radiation. The central charge may be regularized to be finite by the spectral zeta function or heat kernel method on the unit sphere. For the theory at the Rindler horizon, the effective central charge is proportional to the area of the bifurcation surface after regularization. Moreover, the zero mode of supertranslation is identified as the modular Hamiltonian, linking Carrollian diffeomorphism to quantum information theory. Our results may hold for general null hypersurfaces and provide new insight in the study of the Carrollian field theory, asymptotic symmetry group and entanglement entropy., Comment: 65 pages, 3 figures, typos are fixed

We reduce the gravitational theory in an asymptotically flat spacetime to future null infinity. We compute the Poincar\'e flux operators at future null infinity and construct the supertranslation and superrotation generators. The generators are shown to form a closed symmetry algebra by including a generalized gravitational duality operator. We could regard all the generators as the Hamiltonians with respect to the symmetry transformation in the boundary field theory. Our construction of the generators may relate to the BMS fluxes defined in the literature by adding counterterms to the Bondi mass and angular momentum aspects., Comment: 67 pages, revised version

In this paper, we reduce the electromagnetic theory to future null infinity and obtain a vector theory at the boundary. We compute the Poincar\'e flux operators which could be generalized. We quantize the vector theory, and impose normal order on the extended flux operators. It is shown that these flux operators generate the supertranslation and superrotation. When working out the commutators of these operators, we find that a generalized electromagnetic duality operator should be included as the generators to form a closed symmetry algebra., Comment: 45 pages, revised version

We reduce the massless scalar field theory in Minkowski spacetime to future null infinity. We compute the Poincar\'e flux operators, which can be generalized and identified as the supertranslation and superrotation generators. These generators are shown to form a closed symmetry algebra with a divergent central charge. In the classical limit, we argue that the algebra may be interpreted as the geometric symmetry of a Carrollian manifold, i.e., the hypersurface of future null infinity. Our method may be used to find more physically interesting Carrollian field theories., Comment: 51 pages, revised version

In this study, we investigate high-accuracy three-dimensional surface detection in smoothed particle hydrodynamics for free-surface flows. A new geometrical method is first developed to enhance the accuracy of free-surface particle detection in complex flows. This method detects free-surface particles via continuous global scanning inside the sphere of a particle through a cone region whose vertex corresponds to the particle position. The particle is identified as a free-surface particle if there exists a cone region with no neighboring particles. Next, an efficient semi-geometrical method is proposed based on the geometrical method to reduce the computational cost. It consists of finding particles near the free surface via position divergence and then detecting these particles using the geometrical method to identify free-surface particles. The accuracy and robustness of the proposed method are demonstrated by performing tests on several model problems.