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Jiang Long

Publications and source records attributed to Jiang Long.

At least 37 records · Page 2Linked to original sources
arXiv2024

On the definition of Carrollian amplitudes in general dimensions

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 Poincaré 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.

hep-th↗
arXiv2024

Quantum flux operators in higher spin theories

We construct Carrollian higher spin field theories by reducing the bosonic Fronsdal theories in flat spacetime to future null infinity. We extend the Poincaré 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 $s=0,1,2$.

hep-th↗
arXiv2024

Feynman rules and loop structure of Carrollian amplitudes

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 $Φ^4$ theory. As a consequence of Poincaré 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 $χ$ invariant under translation. The four-point Carrollian amplitude is a polynomial of the two-point Carrollian amplitude whose argument is replaced with $χ$. 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 $Φ^4$ theory by designing the Feynman rules for more general Carrollian amplitude.

hep-th↗
arXiv2024

Holographic dictionary from bulk reduction

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.

hep-th↗
arXiv2023

Quantum flux operators for Carrollian diffeomorphism in general dimensions

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.

hep-th↗
arXiv2023

Symmetry group at future null infinity III: Gravitational theory

We reduce the gravitational theory in an asymptotically flat spacetime to future null infinity. We compute the Poincaré 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.

hep-th↗
arXiv2023

Symmetry group at future null infinity II: Vector theory

In this paper, we reduce the electromagnetic theory to future null infinity and obtain a vector theory at the boundary. We compute the Poincaré 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.

hep-th↗
arXiv2023

Symmetry group at future null infinity I: Scalar theory

We reduce the massless scalar field theory in Minkowski spacetime to future null infinity. We compute the Poincaré 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.

hep-th↗
arXiv2022

Classification of radial Kerr geodesic motion

We classify radial timelike geodesic motion of the exterior non-extremal Kerr spacetime by performing a taxonomy of inequivalent root structures of the first order radial geodesic equation using a novel compact notation and by implementing the constraints from polar, time and azimuthal motion. Four generic root structures with only simple roots give rise to eight non-generic root structures when either one root becomes coincident with the horizon, one root vanishes or two roots becomes coincident. We derive the explicit phase space of all such root systems in the basis of energy, angular momentum and Carter's constant and classify whether each corresponding radial geodesic motion is allowed or disallowed from existence of polar, time and azimuthal motion. The classification of radial motion within the ergoregion for both positive and negative energies leads to 6 distinguished values of the Kerr angular momentum. The classification of null radial motion and near-horizon extremal Kerr radial motion are obtained as limiting cases and compared with the literature. We explicitly parametrize the separatrix describing root systems with double roots as the union of the following three regions that are described by the same quartic respectively obtained when (1) the pericenter of bound motion becomes a double root; (2) the eccentricity of bound motion becomes zero; (3) the turning point of unbound motion becomes a double root.

gr-qc↗
arXiv2020

Area law of connected correlation function in higher dimensional conformal field theory

We present a new area law which is associated with the correlator of OPE blocks in higher dimensional conformal field theories (CFTs). The area law shows similar behaviour as black hole entropy or geometric entanglement entropy. It includes a leading term which is proportional to the area of the entanglement surface, and a logarithmic subleading term with degree $q$. We extract the UV cutoff independent coefficients and discuss various properties of the coefficients.

hep-th↗
arXiv2020

Correlation function with the insertion of zero modes of modular Hamiltonians

Zero modes of modular Hamiltonian of one interval are found in momentum space for two dimensional massless free scalar theory. Finite correlators are extracted from separate region connected correlation functions with the insertion of zero modes. Correlators of $(n,1)$-type are claimed to be conformal block up to a set of theory dependent constants. We fix the correlators of $(2,1)$-type with the coefficients of three point function in 2d CFTs.

hep-th↗
arXiv2020

Logarithmic behaviour of connected correlation function in CFT

We study $(m)$-type connected correlation functions of OPE blocks with respect to one spatial region in two dimensional conformal field theory. We find logarithmic divergence for these correlation functions. We justify the logarithmic behaviour from three different approaches: massless free scalar theory, Selberg integral and conformal block. Cutoff independent coefficients are obtained from analytic continuation of conformal blocks. A UV/IR relation has been found in connected correlation functions. We could derive a formal ``first law of thermodynamics'' for a subsystem using deformed reduced density matrix. Area law of connected correlation function in higher dimensions is also discussed briefly.

hep-th↗
arXiv2019

Correlation function of modular Hamiltonians

We investigate varies correlation functions of modular Hamiltonians defined with respect to spatial regions in quantum field theories. These correlation functions are divergent in general. We extract finite correlators by removing divergent terms for two dimensional massless free scalar theory. We reproduce the same correlators in general two dimensional conformal field theories.

hep-th↗
arXiv2019

Gravitational waves from plunges into Gargantua

We analytically compute time domain gravitational waveforms produced in the final stages of extreme mass ratio inspirals of non-spinning compact objects into supermassive nearly extremal Kerr black holes. Conformal symmetry relates all corotating equatorial orbits in the geodesic approximation to circular orbits through complex conformal transformations. We use this to obtain the time domain Teukolsky perturbations for generic equatorial corotating plunges in closed form. The resulting gravitational waveforms consist of an intermediate polynomial ringdown phase in which the decay rate depends on the impact parameters, followed by an exponential quasi-normal mode decay. The waveform amplitude exhibits critical behavior when the orbital angular momentum tends to a minimal value determined by the innermost stable circular orbit. We show that either near-critical or large angular momentum leads to a significant extension of the LISA observable volume of gravitational wave sources of this kind.

gr-qc↗
arXiv2019

Spin and Quadrupole Couplings for High Spin Equatorial Intermediate Mass-ratio Coalescences

Intermediate mass-ratio coalescences are potential signals of ground-based and space-based gravitational observatories. Accurate modeling of their waveforms within general relativity can be achieved within black hole perturbation theory including self-force and finite size effects. In this paper, we present analytic results to the Teukolsky perturbation of equatorial orbits in the near-horizon region of an extremely high spin black hole including spin coupling and finite size effects at leading order in the high spin limit while neglecting the self-force. We detail the critical behavior occuring close to the smallest specific angular momentum, and we discuss features of spin and quadrupole couplings.

gr-qc↗
arXiv2019

Invariance of Unruh and Hawking radiation under matter-induced supertranslations

Matter fields are supertranslated upon crossing a shock wave, which leads to entanglement of the quantum vacuum between the two regions on either side of the shock wave. We probe this entanglement for a scalar field in a planar shock wave background by computing the Bogoliubov transformation between the inertial and uniformly accelerated observer. The resulting Bogoliubov coefficients are shown to reproduce the standard Unruh effect without dependence on the form factor of the shock wave. In contrast, excited states lead to observables that depend upon the form factor. In the context of nonspherical gravitational collapse, we comment that the angular dependence of the limiting advanced time leads to similar supertranslation effects that do not affect the Hawking spectrum but do affect scattering amplitudes.

hep-th↗
arXiv2019

Waveform Selective Surfaces

The role of frequency is very important in electromagnetics since it may significantly change how a material interacts with an incident wave if the frequency spectrum varies. Here, we demonstrate a new kind of microwave window that has the unique property of controlling transmission and reflection based not only on the frequency of an incoming wave but also on the waveform or pulse width. This surface can preferentially pass or reject different kinds of signals, such as short pulses or continuous waves, even if they occur at the same frequency. Such a structure can be used, for example, to allow long communication signals to pass through, while rejecting short radar pulses in the same frequency band. It is related to the classic frequency selective surface, but adds the new dimension of waveform selectivity, which is only possible by introducing nonlinear electronics into the surface. Thus, our study is expected to provide new solutions to both fundamental and applied electromagnetic issues ranging from traditional antenna design and wireless communications to emerging areas such as cloaking, perfect lenses, and wavefront shaping.

physics.app-ph↗