arXiv subjects

Changhyun Ahn

Publications and source records attributed to Changhyun Ahn.

At least 19 recordsLinked to original sources

arXiv2026

Multi-Particle Contributions to the Celestial Algebra in the ${\cal N}=8$ Supergravity

Recently, Calkins and Pate calculated the multi-particle operator product expansions (OPEs) of single-particle celestial operators with two-particle celestial operators in pure Einstein gravity. We apply their construction to the graviton, gravitinos, graviphotons, graviphotinos and scalars in ${\cal N}=8$ supergravity. By performing various contour integrals on these multi-particle OPEs, we obtain ninety-five (anti)commutators for the single-particle contributions from the celestial soft current algebra (derived from the single-particle OPEs) in a two-dimensional boundary. Moreover, these ninety-five multi-particle OPEs provide nontrivial relations between the corresponding celestial amplitudes. The triple-collinear limits between these bosonic and fermionic particles from the four-dimensional bulk are also described as a double check. Finally, we implicitly propose both the multi-particle OPEs of single-particle celestial operators with $(N-1)$-particle celestial operators and the corresponding (anti)commutators for the modes of celestial operators that have linear terms (or single-particle exchange terms due to the sum of $N$-particle factorization channels from amplitudes) on the right-hand sides.

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arXiv2026

A Charged and Neutral Spin-$4$ Currents in the Grassmannian-like Coset Model

By calculating the second order pole in the operator product expansion (OPE) of the charged spin-$3$ current with the neutral spin-$3$ current in the Grassmannian-like coset model, we determine the primary charged spin-$4$ current. Similarly, by computing the second order pole in the OPE of the neutral spin-$3$ current with itself, we obtain the primary neutral spin-$4$ current. We determine the OPE of the charged spin-$2$ current with the charged spin-$3$ current for generic parameters and the large $k$ (one of the parameters) limit is also obtained for this OPE. In particular, the above primary charged spin-$4$ current appears in the first order pole of this OPE for generic parameters. We also check that the above primary charged and neutral spin-$4$ currents occur at the second order pole in the OPE of the charged spin-$3$ current with itself for fixed parameters.

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arXiv2026

Toward A Celestial Soft Symmetry Algebra in the ${\cal N}=8$ Supergravity

From the classical $SO({\cal N}=8)$ extended superconformal algebra between the lowest ${\cal N}=8$ multiplet in two dimensions obtained by Ademollo et al. (1976), we generalize it for the arbitrary ${\cal N}=8$ multiplet with manifest $SU(8)$ symmetry containing the bosonic $w_{1+\infty}$ algebra. By modifying this ${\cal N}=8$ supersymmetric $w_{1+\infty}$ algebra in two dimensions, we propose a consistent celestial soft current algebra between the graviton, the gravitinos, the graviphotons, the graviphotinos, and the scalars in the ${\cal N}=8$ supergravity theory with $SO(8)$ (or $SU(8)$) global symmetry in four dimensions initiated by de Wit and Freedman (at Stony Brook in 1977). The twenty five couplings in this celestial algebra can be written in terms of eight arbitrary couplings via the Jacobi identity.

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arXiv2025

A Supersymmetric $w_{1+\infty}$ Symmetry, the Extended Supergravity and the Celestial Holography

We determine the ${\cal N}=4$ supersymmetric $W_{1+\infty}^{2,2}[λ=\frac{1}{4}]$ algebra which is an extension of ${\cal N}=4$ $SO(4)$ superconformal algebra with vanishing central charge. We identify the soft current algebra between the graviton, the gravitinos, the vectors, the Majorana fermions, the scalar or the pseudoscalar, from the ${\cal N}=4$ supersymmetric $w_{1+\infty}^{2,2}[λ=\frac{1}{4}]$ algebra, in two dimensions with the ${\cal N}=4$ supergravity theory with $SO(4)$ global symmetry in four dimensions found by Das (at Stony Brook in 1977), via celestial holography. Furthermore, the truncations of ${\cal N}=4$ supersymmetric soft current algebra provide the soft current algebras for the ${\cal N}=2,3$ supergravity theories, the ${\cal N}=2$ supergravity coupled to its Abelian vector multiplet and the ${\cal N}=1$ supersymmetric Maxwell Einstein theory. For the ${\cal N}=2$ supergravity theory, the soft current algebra can be also realized from the ${\cal N}=2$ supersymmetric $w_{1+\infty}^{K,K}[λ=0]$ algebra.

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arXiv2024

A Supersymmetric Extension of $w_{1+\infty}$ Algebra in the Celestial Holography

We determine the ${\cal N}=1$ supersymmetric topological $W_{\infty} $ algebra by using the $λ$ deformed bosons $(β,γ)$ and fermions $(b,c)$ ghost system. By considering the real bosons and the real fermions at $λ=0$ (or $λ=\frac{1}{2}$), the ${\cal N}=1$ supersymmetric $W_{\frac{\infty}{2}}$ algebra is obtained. At $λ=\frac{1}{4}$, other ${\cal N}=1$ supersymmetric $W_{1+\infty}[λ=\frac{1}{4}]$ algebra is determined. We also obtain the extension of Lie superalgebra $PSU(2,2|{\cal N}=4)$ appearing in the worldsheet theory by using the symplectic bosons and the fermions. We identify the soft current algebra between the graviton, the gravitino, the photon (the gluon), the photino (the gluino) or the scalars, equivalent to ${\cal N}=1$ supersymmetric $W_{1+\infty}[λ]$ algebra, in two dimensions with the ${\cal N}=1$ supergravity theory in four dimensions discovered by Freedman, van Nieuwenhuizen and Ferrara in 1976 and its matter coupled theories, via celestial holography.

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arXiv2024

The ${\cal N}=2,4$ Supersymmetric Linear $W_{\infty}[λ]$ Algebras for Generic $λ$ Parameter

The four different kinds of currents are given by the multiple $(β,γ)$ and $(b,c)$ ghost systems with a multiple product of derivatives. We determine their complete algebra where the structure constants depend on the deformation parameter $λ$ appearing in the conformal weights of above fields nontrivially and depend on the generic spins $h_1$ and $h_2$ appearing on the left hand sides in the (anti)commutators. By taking the linear combinations of these currents, the ${\cal N}=4$ supersymmetric linear $W_{\infty}[λ]$ algebra (and its ${\cal N}=4$ superspace description) for generic $λ$ is obtained explicitly. Moreover, we determine the ${\cal N}=2$ supersymmetric linear $W_{\infty}[λ]$ algebra for arbitrary $λ$. As a by product, the $λ$ deformed bosonic $W_{1+\infty}[λ] \times W_{1+\infty}[λ+\frac{1}{2}]$ subalgebra (a generalization of Pope, Romans and Shen's work in $1990$) is obtained. The first factor is realized by $(b,c)$ fermionic fields while the second factor is realized by $(β,γ)$ bosonic fields. The degrees of the polynomials in $λ$ for the structure constants are given by $(h_1+h_2-2)$. Each $w_{1+\infty}$ algebra from the celestial holography is reproduced by taking the vanishing limit of other deformation prameter $q$ at $λ=0$ with the contractions of the currents.

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arXiv2023

The Structure of the ${\cal N}=4$ Supersymmetric Linear $W_{\infty}[λ]$ Algebra

For the vanishing deformation parameter $λ$, the full structure of the (anti)commutator relations in the ${\cal N}=4$ supersymmetric linear $W_{\infty}[λ=0]$ algebra is obtained for arbitrary weights $h_1$ and $h_2$ of the currents appearing on the left hand sides in these (anti)commutators. The $w_{1+\infty}$ algebra can be seen from this by taking the vanishing limit of other deformation parameter $q$ with the proper contractions of the currents. For the nonzero $λ$, the complete structure of the ${\cal N}=4$ supersymmetric linear $W_{\infty}[λ]$ algebra is determined for the arbitrary weight $h_1$ together with the constraint $h_1-3 \leq h_2 \leq h_1+1$. The additional structures on the right hand sides in the (anti)commutators, compared to the above $λ=0$ case, arise for the arbitrary weights $h_1$ and $h_2$ where the weight $h_2$ is outside of above region.

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arXiv2022

A Deformed Supersymmetric $w_{1+\infty}$ Symmetry in the Celestial Conformal Field Theory

By using the $K$-free complex bosons and the $K$-free complex fermions, we construct the ${\cal N}=2$ supersymmetric $W_{\infty}^{K,K}$ algebra which is the matrix generalization of previous ${\cal N}=2$ supersymmetric $W_{\infty}$ algebra. By twisting this ${\cal N}=2$ supersymmetric $W_{\infty}^{K,K}$ algebra, we obtain the ${\cal N}=1$ supersymmetric $W_{\infty}^{K}$ algebra which is the matrix generalization of known ${\cal N}=1$ supersymmetric topological $W_{\infty}$ algebra. From this two-dimensional symmetry algebra, we propose the operator product expansion (OPE) between the soft graviton and gravitino (as a first example), at nonzero deformation parameter, in the supersymmetric Einstein-Yang-Mills theory explicitly. Other six OPEs between the graviton, gravitino, gluon and gluino can be determined completely. At vanishing deformation parameter, we reproduce the known result of Fotopoulos, Stieberger, Taylor and Zhu on the above OPEs via celestial holography.

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arXiv2022

The ${\cal N}=4$ Supersymmetric Linear $W_{\infty}[λ]$ Algebra

From the recently known ${\cal N}=2$ supersymmetric linear $W_{\infty}^{K,K}[λ]$ algebra where $K$ is the dimension of fundamental (or antifundamental) representation of bifundamental $β\, γ$ and $b \, c$ ghost system, we determine its ${\cal N}=4$ supersymmetric enhancement at $K=2$. We construct the ${\cal N}=4$ stress energy tensor, the first ${\cal N}=4$ multiplet and their operator product expansions (OPEs) in terms of above bifundamentals. We show that the OPEs between the first ${\cal N}=4$ multiplet and itself are the same as the corresponding ones in the ${\cal N}=4$ coset $\frac{SU(N+2)}{SU(N)}$ model under the large $(N,k)$ 't Hooft-like limit with fixed $λ_{co} \equiv \frac{(N+1)}{(k+N+2)}$, up to two central terms. The two parameters are related to each other $λ=\frac{1}{2}\, λ_{co}$. We also provide other OPEs by considering the second, the third and the fourth ${\cal N}=4$ multiplets in the ${\cal N}=4$ supersymmetric linear $W_{\infty}[λ]$ algebra.

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arXiv2022

Toward A Supersymmetric $w_{1+\infty}$ Symmetry in the Celestial Conformal Field Theory

The $w_{1+\infty}$ symmetry algebra appears in the Einstein--Yang--Mills theory, proposed recently by Strominger. In this paper, we derive the supersymmetric $w_{1+\infty}$ symmetry by using the known results on the operator product expansions (OPEs) between the graviton, gravitino, gluon, and gluino in the supersymmetric version of the above theory. We calculate the four additional commutator relations between the soft currents explicitly. In addition, we analyze the works of Odake et al. and Pope et al. and introduce the additional symmetry current that corresponds to the celestial gluino operator. Through this procedure, all seven commutator relations can be connected to the ones associated with the supersymmetric $w_{1+\infty}$ algebra with $SU(N)$ symmetry under the restrictions of wedge modes.

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arXiv2022

The ${\cal N}=2$ Supersymmetric $w_{1+\infty}$ Symmetry in the Two-Dimensional SYK Models

We identify the rank $(q_{syk}+1)$ of the interaction of the two-dimensional ${\cal N}=(2,2)$ SYK model with the deformation parameter $λ$ in the Bergshoeff, de Wit and Vasiliev(in 1991)'s linear $W_{\infty}[λ]$ algebra via $λ=\frac{1}{2(q_{syk}+1)}$ by using a matrix generalization. At the vanishing $λ$ (or the infinity limit of $q_{syk}$), the ${\cal N}=2$ supersymmetric linear $W_{\infty}^{N,N}[λ=0]$ algebra contains the matrix version of known ${\cal N}=2$ $W_{\infty}$ algebra, as a subalgebra, by realizing that the $N$-chiral multiplets and the $N$-Fermi multiplets in the above SYK models play the role of the same number of $β\, γ$ and $b\, c$ ghost systems in the linear $W_{\infty}^{N,N}[λ=0]$ algebra. For the nonzero $λ$, we determine the complete ${\cal N}=2$ supersymmetric linear $W_{\infty}^{N,N}[λ]$ algebra where the structure constants are given by the linear combinations of two different generalized hypergeometric functions having the $λ$ dependence. The weight-$1, \frac{1}{2}$ currents occur in the right hand sides of this algebra and their structure constants have the $λ$ factors. We also describe the $λ=\frac{1}{4}$ (or $q_{syk}=1$) case in the truncated subalgebras by calculating the vanishing structure constants.

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arXiv2022

Worldsheet Free Fields, Higher Spin Symmetry and Free ${\cal N}=4$ Super Yang-Mills

By using the free field worldsheet realization described by Gaberdiel and Gopakumar recently, we construct the nontrivial lowest generators of the higher spin superalgebra $hs(2,2|4)$. They consist of cubic terms between the bilinears of ambitwistor-like fields. We also obtain the worldsheet description for the findings of Sezgin and Sundell twenty years ago given by the familiar oscillator construction. The first order poles of the operator product expansions (OPEs), between the conformal weight-$1$ generators of Lie superalgebra $PSU(2,2|4)$ and the above conformal weight-$3$ generators of $hs(2,2|4)$, are determined explicitly and the additional generators appear in the worldsheet theory.

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arXiv2021

Adding Complex Fermions to the Grassmannian-like Coset Model

In the ${\cal N}=2$ supersymmetric coset model, $\frac{SU(N+M)_k \times SO(2 N M)_1}{ SU(N)_{k+M} \times U(1)_{ N M (N+M)(k+N+M)}}$, we construct the $SU(M)$ nonsinglet ${\cal N}=2$ multiplet of spins $(1, \frac{3}{2}, \frac{3}{2}, 2)$ in terms of coset fields. The next $SU(M)$ singlet and nonsinglet ${\cal N}=2$ multiplets of spins $(2, \frac{5}{2}, \frac{5}{2}, 3)$ are determined by applying the ${\cal N}=2$ supersymmetry currents of spin $\frac{3}{2}$ to the bosonic singlet and nonsinglet currents of spin $3$ in the bosonic coset model. We also obtain the operator product expansions(OPEs) between the currents of the ${\cal N}=2$ superconformal algebra and above three kinds of ${\cal N}=2$ multiplets. These currents in two dimensions play the role of the asymptotic symmetry, as the generators of ${\cal N}=2$ "rectangular $W$-algebra", of the $M \times M$ matrix generalization of ${\cal N}=2$ $AdS_3$ higher spin theory in the bulk. The structure constants in the right hand sides of these OPEs are dependent on the three parameters $k, N$ and $M$ explicitly. Moreover, the OPEs between $SU(M)$ nonsinglet ${\cal N}=2$ multiplet of spins $(1, \frac{3}{2}, \frac{3}{2}, 2)$ and itself are analyzed in detail. The complete OPE between the lowest component of the $SU(M)$ singlet ${\cal N}=2$ multiplet of spins $(2, \frac{5}{2}, \frac{5}{2}, 3)$ and itself is described. In particular, when $M=2$, it is known that the above ${\cal N}=2$ supersymmetric coset model provides the realization of the extension of the large ${\cal N}=4$ nonlinear superconformal algebra. We determine the currents of the large ${\cal N}=4$ nonlinear superconformal algebra and the higher spin-$\frac{3}{2}, 2$ currents of the lowest ${\cal N}=4$ multiplet for generic $k$ and $N$ in terms of the coset fields.

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arXiv2021

Fermionic Construction in the Supersymmetric Coset Model

It is known previously that the operator product expansion (OPE) between the first ${\cal N}=3 $ multiplet and itself contains the second ${\cal N}=3$ multiplet in the supersymmetric coset model. In this paper, by using their realizations in terms of various fermions, we compute the four kinds of OPEs between the first and the second ${\cal N}=3$ multiplets for fixed $N$ and $M$ where the group of the coset contains $SU(N+M)$. By supersymmetrizing the above OPEs in ${\cal N}=3$ superspace and using the various Jacobi identities between the currents, we determine the ${\cal N}=3$ supersymmetric OPE between the first and the second ${\cal N}=3$ multiplets completely. The right hand side of this OPE contains the various ${\cal N}=3$ multiplets: the $SO(3)$ singlet ${\cal N}=3$ multiplets of superspin-$\frac{3}{2},2,3,4$ and the $SO(3)$ triplet ${\cal N}=3$ multiplets of superspin-$\frac{5}{2},3,\frac{7}{2}$. The ${\cal N}=2$ superspace description and the decoupling of the spin-$\frac{1}{2}$ current of the ${\cal N}=3$ superconformal algebra are also described.

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arXiv2021

The Grassmannian-like Coset Model and the Higher Spin Currents

In the Grassmannian-like coset model, $\frac{SU(N+M)_k}{SU(N)_k \times U(1)_{k N M (N+M)}}$, Creutzig and Hikida have found the charged spin-$2,3$ currents and the neutral spin-$2,3$ currents previously. In this paper, as an extension of Gaberdiel-Gopakumar conjecture found ten years ago, we calculate the operator product expansion (OPE) between the charged spin-$2$ current and itself, the OPE between the charged spin-$2$ current and the charged spin-$3$ current and the OPE between the neutral spin-$3$ current and itself for generic $N, M$ and $k$. From the second OPE, we obtain the new charged quasi primary spin-$4$ current while from the last one, the new neutral primary spin-$4$ current is found implicitly. The infinity limit of $k$ in the structure constants of the OPEs is described in the context of asymptotic symmetry of $M \times M$ matrix generalization of $AdS_3$ higher spin theory. Moreover, the OPE between the charged spin-$3$ current and itself is determined for fixed $(N,M)=(5,4)$ with arbitrary $k$ up to the third order pole. We also obtain the OPEs between charged spin-$1,2,3$ currents and neutral spin-$3$ current. From the last OPE, we realize that there exists the presence of the above charged quasi primary spin-$4$ current in the second order pole for fixed $(N,M)=(5,4)$. We comment on the complex free fermion realization.

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arXiv2021

The ${\cal N}=4$ Higher Spin Algebra for Generic $μ$ Parameter

The ${\cal N}=4$ higher spin generators for general superspin $s$ in terms of oscillators in the matrix generalization of $AdS_3$ Vasiliev higher spin theory at nonzero $μ$ (which is equivalent to the 't Hooft-like coupling constant $λ$) were found previously. In this paper, by computing the (anti)commutators between these ${\cal N}=4$ higher spin generators for low spins $s_1$ and $s_2$ ($s_1+s_2 \leq 11$) explicitly, we determine the complete ${\cal N}=4$ higher spin algebra for generic $μ$. The three kinds of structure constants contain the linear combination of two different generalized hypergeometric functions. These structure constants remain the same under the transformation $μ\leftrightarrow (1-μ)$ up to signs. We have checked that the above ${\cal N}=4$ higher spin algebra contains the ${\cal N}=2$ higher spin algebra, as a subalgebra, found by Fradkin and Linetsky some time ago.

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arXiv2020

The Small ${\cal N}=4$ Superconformal ${\cal W}_{\infty}$ Algebra

The symmetric orbifold of $\mathbb{T}^4$ is the CFT dual of string theory on AdS$_3\times {\rm S}^3 \times \mathbb{T}^4$ with minimal NS-NS flux. We study its symmetry algebra and provide evidence that it does not have any deformation parameter. This suggests that the symmetric orbifold is (at least locally) the most symmetrical CFT in its moduli space.

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arXiv2019

The ${\cal N}=4$ Coset Model and the Higher Spin Algebra

By computing the operator product expansions between the first two ${\cal N}=4$ higher spin multiplets in the unitary coset model, the (anti)commutators of higher spin currents are obtained under the large $(N,k)$ 't Hooft-like limit. The free field realization with complex bosons and fermions is presented. The (anti)commutators for generic spins $s_1$ and $s_2$ with manifest $SO(4)$ symmetry at vanishing 't Hooft-like coupling constant are completely determined. The structure constants can be written in terms of the ones in the ${\cal N}=2$ ${\cal W}_{\infty}$ algebra found by Bergshoeff, Pope, Romans, Sezgin and Shen previously, in addition to the spin-dependent fractional coefficients and two $SO(4)$ invariant tensors. We also describe the ${\cal N}=4$ higher spin generators, by using the above coset construction results, for general super spin $s$ in terms of oscillators in the matrix generalization of $AdS_3$ Vasiliev higher spin theory at nonzero 't Hooft-like coupling constant. We obtain the ${\cal N}=4$ higher spin algebra for low spins and present how to determine the structure constants, which depend on the higher spin algebra parameter, in general, for fixed spins $s_1$ and $s_2$.

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