The Shadow Formalism of Galilean CFT$_2$

Chen, Bin; Liu, Reiko

doi:10.48550/arxiv.2203.10490

Cited by 5 publications

(7 citation statements)

References 123 publications

(219 reference statements)

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“…In establishing the inversion formula for the ξ = 0 sector, we used the alpha-space approach. In [42], the shadow formalism for 2D Galilean CFT was developed, but mainly focusing on the ξ = 0 case. It would be interesting to further develop the shadow formalism in the ξ = 0 sector.…”

Section: Jhep12(2022)019 7 Conclusion and Discussionmentioning

confidence: 99%

On Galilean conformal bootstrap. Part II. ξ = 0 sector

Chen

Hao

Liu

et al. 2022

J. High Energ. Phys.

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In this work, we continue our work on two dimensional Galilean conformal field theory (GCFT2). Our previous work (2011.11092) focused on the ξ ≠ 0 sector, here we investigate the more subtle ξ = 0 sector to complete the discussion. The case ξ = 0 is degenerate since there emerge interesting null states in a general ξ = 0 boost multiplet. We specify these null states and work out the resulting selection rules. Then, we compute the ξ = 0 global GCA blocks and find that they can be written as a linear combination of several building blocks, each of which can be obtained from a sl(2, ℝ) Casimir equation. These building blocks allow us to give an Euclidean inversion formula as well. As a consistency check, we study 4-point functions of certain vertex operators in the BMS free scalar theory. In this case, the ξ = 0 sector is the only allowable sector in the propagating channel. We find that the direct expansion of the 4-point function reproduces the global GCA block and is consistent with the inversion formula.

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Section: Jhep12(2022)019 7 Conclusion and Discussionmentioning

confidence: 99%

On Galilean conformal bootstrap. Part II. ξ = 0 sector

Chen

Hao

Liu

et al. 2022

J. High Energ. Phys.

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show abstract

“…In [42], the shadow formalism for 2D Galilean CFT was developed, but mainly focusing on ξ = 0 case. It would be interesting to further develop the shadow formalism in the ξ = 0 sector.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

On Galilean Conformal Bootstrap II: $ξ=0$ sector

Chen,

Hao,

Liu

et al. 2022

Preprint

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In this work, we continue our work on two dimensional Galilean conformal field theory (GCFT 2 ). Our previous work (2011.11092) focused on the ξ = 0 sector, here we investigate the more subtle ξ = 0 sector to complete the discussion. The case ξ = 0 is degenerate since there emerge interesting null states in a general ξ = 0 boost multiplet. We specify these null states and work out the resulting selection rules. Then, we compute the ξ = 0 global GCA blocks and find that they can be written as a linear combination of several building blocks, each of which can be obtained from a sl(2, R) Casimir equation. These building blocks allow us to give an Euclidean inversion formula as well. As a consistency check, we study four-point functions of certain vertex operators in the BMS free scalar theory. In this case, the ξ = 0 sector is the only allowable sector in the propagating channel. We find that the direct expansion of the 4-point function reproduces the global GCA block and is consistent with the inversion formula.

show abstract

“…In [23,24], the Bondi-Metzner-Sachs(BMS) bootstrap was studied. In [25][26][27], two-dimensional Galilean conformal bootstrap has been initiated.…”

Section: Introductionmentioning

confidence: 99%

On higher-dimensional Carrollian and Galilean conformal field theories

2023

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In this paper, we study the Carrollian and Galilean conformal field theories (CCFT and GCFT) in d>2d>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>2d>2 CCA and GCA carry not only the simple chain structure appeared in logCFT or 2d2d 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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The Shadow Formalism of Galilean CFT$_2$

Cited by 5 publications

References 123 publications

On Galilean conformal bootstrap. Part II. ξ = 0 sector

On Galilean conformal bootstrap. Part II. ξ = 0 sector

On Galilean Conformal Bootstrap II: $ξ=0$ sector

On higher-dimensional Carrollian and Galilean conformal field theories

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