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May 01, 2023 313 likes •786 views

Dipolar Quantization of Conformal Field Theories Tsukasa Tada iTHES RIKEN Nishina Center & iTHES Interdisciplinary Theoretical Science Research Group Sine Square Deformation Recent works include Wen, Ryu, Ludwig, PRB 93 (2016)235119

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Dipolar Quantization

Tsukasa Tada

RIKEN Nishina Center & iTHES

  • f

Conformal Field Theories

iTHES

Interdisciplinary Theoretical Science Research Group
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Sine Square Deformation

Recent works include Wen, Ryu, Ludwig, PRB93 (2016)235119 Okunishi, PTEP(2016)063A02

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Sine Square Deformation

Recent works include Wen, Ryu, Ludwig, PRB93 (2016)235119 Okunishi, PTEP(2016)063A02 SSD ground state for CFT H. Katsura (’12)

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the deformation of CFT

Sine Square Deformation

Ishibashi, T ada, JPA48(2015)315402 Ishibashi, T ada, arXiv:1602.01190

is continuous Virasoro algebra altered Hilbert space

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the deformation of CFT

Sine Square Deformation

Ishibashi, T ada, JPA48(2015)315402 Ishibashi, T ada, arXiv:1602.01190

is

Dipolar Quantization

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Dipolar Quantization

Radial Quantization

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Radial Quantization

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Dipolar Quantization

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Dipolar Quantization

another time foliation is Hamiltonian

c.f. Kiermaier, Sen, Zwiebach (’08)

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Dipolar Quantization

another time foliation is Hamiltonian

c.f. Kiermaier, Sen, Zwiebach (’08) Energy states?

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Dipolar Quantization

another time foliation is conserved charges

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Dipolar Quantization

another time foliation is conserved charges

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Dipolar Quantization

another time foliation is conserved charges

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another time foliation is conserved charges

Dipolar Quantization

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Dipolar Quantization

Define

c.f.

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Dipolar Quantization

Define

c.f.

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Dipolar Quantization

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Dipolar Quantization

Continuous eigenvalues for

Infinite circumference

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Dipolar Quantization

another time foliation is Hermitian conjugate

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Radial Quantization

  • Dipolar

Quantization

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Quantum system Spacetime Symmetry finite space

Difgerent Hilbert Space

infinite space

Dipolar Quantization Radial Quantization

Overview

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Why Dipolar ?

Generators for conformal symmetry [dilation] [translation] [SCT] [rotation] “Time” translation for radial quantization

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Why Dipolar ?

[dilation] [translation] [SCT]

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Why Dipolar ?

Massive Rep. (discrete) Massless Rep. (continuous)

Dipolar Quantization Radial Quantization

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Why Dipolar ?

Dipolar Quantization Radial Quantization

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Why Dipolar ?

Dipolar Quantization Radial Quantization

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Why Dipolar ?

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Why Dipolar ?

Dipolar Quantization

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Why Dipolar ?

Dipolar Quantization

Gap or “Mass”

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Minkowskian CFT

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Minkowskian CFT

SCT

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Minkowskian CFT

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Minkowskian CFT

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Minkowskian CFT

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Minkowskian CFT

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Minkowskian CFT

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Minkowskian CFT

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Minkowskian CFT

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Minkowskian CFT

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Minkowskian CFT

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Summary

Also works for Minkowskian Dipolar quantization for CFT

Sine-square deformation Continuous Virasoro algebra Infinite circumference

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Conformal Quantum Mechanics

de Alfaro, Fubini, Furlan (’76)

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Conformal Quantum Mechanics

de Alfaro, Fubini, Furlan (’76) Claus, Derix, Kallosh, Kumar, T

  • wnsend,

Van Proeyen (’98) Michelson, Strominger (’99)

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