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

Masaru Hongo

iTHES Research group, RIKEN Big waves of Theoretical Sciences in Okinawa, 2016/7/9, OIST

Credit: NASA

Motivation

Hydrodynamics Macro Quantum Field Theory Micro

by Hashimoto-san

• Ex. QCD

Quark, Gluon

?

Question: How to bridge the gap between micro and macro?

Universal description by T(x), v(x), µ(x)

Thermal Field Theory

T = const.

Thermodynamics β0

x

β0

dτ

β0

QFT in the flat spacetime with radius

Thermal Field Theory

Path int.

( Matsubara, 1955 )

Gibbs distribution: ˆ ρG = e−β( ˆ

H−µ ˆ N)

Z = e−β( ˆ

H−µ ˆ N)−Ψ[β,ν]

Thermodynamic potential with Euclidean action

Ψ[β, ν] = log Tr e−β( ˆ

H−µ ˆ N) = log

• dϕ±ϕ|e−β( ˆ

H−µ ˆ N)|ϕ

SE[ϕ] = β dτ

• d3x LE(ϕ, ∂µϕ)

= log

• ϕ(β)=±ϕ(0)

Dϕ e+SE[ϕ],

Hydro {(x),

v(x)}

β(x)

x

dτ

[Hayata-Hidaka-MH-Noumi (2015)] [MH in preparation (2016)]

˜ gµν = ˜ gµν(, v)

QFT in the “curved spacetime” with “metric”

Local Thermal Field Theory

Path int.

Local Thermal Field Theory

Ψ[¯ t; λ] ≡ log Tr exp

• dΣ¯

tν

• βµ(x) ˆ

T ν

µ(x) + ν(x) ˆ

Jν(x)

• Symmetry = Spatial diffeomorphism + Kaluza-Klein gauge

① plays a role as the generating functional:

Ψ[λ]

h ˆ T µν(x)iLG = 2 pg δ δgµν(x)Ψ[λ]

ds2 = −e2σ(d˜ t + a¯

i)dx ¯ i + γ0 ¯ i¯ jdx ¯ idx ¯ j

is written in terms of QFT in curved spacetime

Ψ[λ]

②

Credit: NASA