arXiv subjects

Yu-fan Zheng

Publications and source records attributed to Yu-fan Zheng.

9 recordsLinked to original sources

arXiv2026

Carrollian Dictionary for Massive Particles at Null Infinity

Massive particles reach timelike rather than null infinity, leaving their Carrollian boundary description unresolved. We construct a Carrollian dictionary for massive one-particle states on $\mathscr I^\pm$ without requiring their worldlines to reach null infinity. The dictionary encodes the bulk momentum through its projections onto the null frame associated with each celestial point. The Poincaré intertwining equations require the complete Carrollian representation to describe massive states. We apply the dictionary to the Källén--Lehmann representation and to soft photon and graviton theorems. The Källén--Lehmann application fixes the coefficient function of the non-contact two-point function in terms of the bulk spectral density. Soft theorems show that global modes reproduce the ordinary $U(1)$ and Poincaré actions, whereas local actions remain integrals over celestial directions.

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arXiv2026

Missing Descendants in the Carrollian Conformal Family

In the Carrollian conformal algebra, the relation $[P^0,K^0]=0$ implies that $K^0$ annihilates all operators generated from a primary by temporal translation $P^0$. The standard conformal family defined by translation descendants does not contain the independent descendant chain that $K^0$ lowers successively to the primary. We construct the complete Carrollian conformal representation by including this chain together with all of its translation descendants. We derived the corresponding local operators, orbit structures, and checked their Casimirs in 2D and 3D. For each orbit configuration, the global two-point Ward identities fix the kinematic factors and selection rules for both magnetic non-contact branches and electric contact branches. Unlike ordinary conformal symmetry, Carrollian conformal symmetry generally determines the correlators only up to arbitrary functions of Carrollian invariants rather than constants. The complete representation contains sectors with $\mathcal{C}_2=m^2=κρ-β^2>0$ for 2D and $\mathcal{C}_2=m^2=κρ-\vecβ^{\,2}>0$ for 3D, which may describe massive states in flat holography.

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arXiv2026

Carrollian holography with agentic AI: Real mass is imaginary

We introduce LACIA, a verification-driven agentic AI workflow for theoretical physics, and apply it with independent human checks to construct Carrollian conformal bases. We develop the Poincare-Carrollian intertwiner as the central method. It reproduces the celestial and Carrollian conformal bases for massless particles and constructs the missing Carrollian bases for massive and tachyonic particles. The massive basis requires a complex momentum shift in scattering amplitudes.

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arXiv2025

Supersymmetric BMS$_4$ Algebras Revisited: Electric/Magnetic Superalgebras and Free Field Realization

In this work, we present a systematic classification of supersymmetric extensions of the BMS$_4$ algebra and their realizations in free field theories. By requiring that supercharges admit finite-dimensional subsectors, we identify ten distinct electric super BMS$_4$ algebras and six magnetic ones. The electric case is characterized by supercharge anticommutators closing on supertranslations, while the magnetic case necessarily involves superrotations. To realize these algebras in free field theories, we follow a constructive procedure: first identify the modes bilinears of which generate the symmetry algebra, then determine the fields with appropriate transformation properties under the BMS$_4$ algebra, and finally construct consistent theories whose equations of motion admit the desired supersymmetry. Notably, $R$-symmetry with nonvanishing spin is essential for the Type II-II, Type I-II, and Type II-I magnetic super BMS$_4$ algebras, shedding new light on spacetime structure of string theory for flat holography. Moreover, in the Type I-I theory, $R$-symmetry relates electric and magnetic scalars, indicating their equal significance. In addition, $R$-symmetry maps the electric scalar to a spin-$1$ field and vice versa, offering a novel perspective on supersymmetric extensions of soft theorems.

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arXiv2025

Structure of Carrollian (conformal) superalgebra

In this work, we investigate possible supersymmetric extensions of the Carrollian algebra and the Carrollian conformal algebra in both $d=4$ and $d=3$. For the super-Carrollian algebra in $d=4$, we identify multiple admissible structures, depending on the representations of the supercharges with respect to the Carrollian rotation. Some of these structures can be derived by taking the speed of light $c\to 0$ limit from super-Poincaré algebra, but others are completely novel. In the conformal case, we demonstrate that the nontrivial Carrollian superconformal algebras for $d=4$ and $d=3$ are isomorphic to super-Poincaré algebra of $d=5$ and $d=4$ respectively. Remarkably, neither of these constructions requires R-symmetry to ensure the algebraic closure. Furthermore, we discover two distinct classes of super-BMS$_4$ algebras, i.e. one singlet super-BMS$_4$ algebra and two multiplet chiral super-BMS$_4$ algebras. The singlet case arises from extending the $3$D Carrollian superconformal algebra, whereas the multiplet cases do not admit this pathology due to their finite-dimensional subalgebra containing supercharges with conformal dimension $Δ=\pm\frac{3}{2}$.

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arXiv2024

Quantization of Carrollian conformal scalar theories

In this work, we study the quantization of Carrollian conformal scalar theories, including two-dimensional(2D) magnetic scalar and three-dimensional(3D) electric and magnetic scalars. We discuss two different quantization schemes, depending on the choice of the vacuum. We show that the standard canonical quantization corresponding to the induced vacuum yields a unitary Hilbert space and the 2-point correlation functions in this scheme match exactly with the ones computed from the path integral. In the canonical quantization, the BMS symmetry can be realized without anomaly. On the other hand, for the quantization based on the highest-weight vacuum, it does not have a unitary Hilbert space. In 2D, the correlators in the highest-weight vacuum agree with the ones obtained by taking the $c\to 0$ limit of the 2D CFT, and there is an anomalous term in the commutation relations between the Virasoso generators, whose form is similar to the one in 2D CFT. In 3D, there is no good definition of the highest-weight vacuum without breaking the rotational symmetry. In our study, we find that the usual state-operator correspondence in CFT does not hold in the Carrollian case.

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arXiv2023

Constructing Carrollian Field Theories from Null Reduction

In this paper, we propose a novel way to construct off-shell actions of $d$-dimensional Carrollian field theories by considering the null-reduction of the Bargmann invariant actions in $d+1$ dimensions. This is based on the fact that $d$-dimensional Carrollian symmetry is the restriction of the $(d+1)$-dimensional Bargmann symmetry to a null hyper-surface. We focus on free scalar field theory and electromagnetic field theory, and show that the electric and magnetic sectors of these theories originate from different Bargmann invariant actions in one higher dimension. In the cases of the massless free scalar field and $d=4$ electromagnetic field, we verify Carrollian conformal invariance of the resulting theories, and find that there appear naturally chain representations and staggered modules of Carrollian conformal algebra.

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arXiv2023

Path-integral quantization of tensionless (super) string

In this work, we study the tensionless (super)string in the formalism of path-integral quantization. We introduce BMS $bc$ and $βγ$ ghosts intrinsically by accounting for the Faddeev-Popov determinants appeared in fixing the gauges. We then do canonical quantization and obtain the critical dimensions for different tensionless strings. We find that among four kinds of tensionless superstrings, the $\mathcal{N}=2$ homogeneous and inhomogeneous doublet tensionless superstrings have the same critical dimension as the usual superstrings. Taking the BMS $bc$ and $βγ$ ghosts as new types of BMS free field theories, we find that their enhanced underlying symmetries are generated by BMS-Kac-Moody algebras, with the Kac-Moody subalgebras being built from a three-dimensional non-abelian and non-semi-simple Lie algebra.

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arXiv2023

On Higher-dimensional Carrollian and Galilean Conformal Field Theories

In this paper, we study the Carrollian and Galilean conformal field theories (CCFT and GCFT) in $d>2$ dimensions. We construct the highest weight representations (HWR) of Carrollian and Galilean conformal algebra (CCA and GCA). Even though the two algebras have different structures, their HWRs share similar structure, because their rotation subalgebras are isomorphic. In both cases, we find that the finite dimensional representations are generally reducible but indecomposable, and can be organized into the multiplets. Moreover, it turns out that the multiplet representations in $d>2$ CCA and GCA carry not only the simple chain structure appeared in logCFT or $2d$ GCFT, but also more generally the net structures. We manage to classify all the allowed chain representations. Furthermore we discuss the two-point and three-point correlators by using the Ward identities. We mainly focus on the two-point correlators of the operators in chain representations. Even in this relative simple case, we find some novel features: multiple-level structure, shortage of the selection rule on the representations, undetermined 2-pt coefficients, etc.. We find that the non-trivial correlators could only appear for the representations of certain structure, and the correlators are generally polynomials of time coordinates for CCFT (spacial coordinates for GCFT), whose orders depend on the levels of the correlators.

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