Thermally emergent curved spacetime Credit: NASA Masaru Hongo - PowerPoint PPT Presentation

Hayata, Hidaka, MH , Noumi, Phys. Rev. D 92 , 065008 (2015) MH in preparation (2016) Thermally emergent curved spacetime Credit: NASA Masaru Hongo iTHES Research group, RIKEN Big waves of Theoretical Sciences in Okinawa, 2016/7/9, OIST

Question: How to bridge the gap between micro and macro? Motivation Micro Macro by Hashimoto-san ? Quantum Hydrodynamics Field Theory Universal description by Ex. QCD Quark, Gluon T ( x ) , � v ( x ) , µ ( x )

Thermal Field Theory Thermal Field Theory Thermodynamics β 0 ( Matsubara, 1955 ) QFT in the flat spacetime d τ T = const . β 0 Path int. with radius β 0 x ρ G = e − β ( ˆ H − µ ˆ N ) = e − β ( ˆ H − µ ˆ Gibbs distribution: ˆ N ) − Ψ [ β , ν ] Z Thermodynamic potential with Euclidean action � N ) = log Ψ [ β , ν ] = log Tr e − β ( ˆ H − µ ˆ d ϕ � ± ϕ | e − β ( ˆ H − µ ˆ N ) | ϕ � � β � � D ϕ e + S E [ ϕ ] , d 3 x L E ( ϕ , ∂ µ ϕ ) S E [ ϕ ] = d τ = log ϕ ( β )= ± ϕ (0) 0

② ① Local Thermal Field Theory Local Thermal Field Theory Hydro { � ( x ) , � v ( x ) } [Hayata-Hidaka- MH -Noumi (2015)] [ MH in preparation (2016)] QFT in the “curved spacetime” d τ β ( x ) Path int. with “metric” g µ ν = ˜ ˜ g µ ν ( � , � v ) x �� �� � β µ ( x ) ˆ µ ( x ) + ν ( x ) ˆ Ψ [¯ t ; λ ] ≡ log Tr exp J ν ( x ) T ν d Σ ¯ t ν 2 δ T µ ν ( x ) i LG = h ˆ Ψ [ λ ] plays a role as the generating functional: p� g δ g µ ν ( x ) Ψ [ λ ] Ψ [ λ ] is written in terms of QFT in curved spacetime Credit: NASA ds 2 = − e 2 σ ( d ˜ i + γ 0 ¯ ¯ ¯ i dx j t + a ¯ i ) dx j dx ¯ i ¯ Symmetry = Spatial di ff eomorphism + Kaluza-Klein gauge