Stress-stress correlator in ϕ4 theory: poles or a cut?

  • Guy D. Moore
Open Access
Regular Article - Theoretical Physics


We explore the analytical properties of the traceless stress tensor 2-point function at zero momentum and small frequency (relevant for shear viscosity and hydrodynamic response) in hot, weakly coupled λϕ4 theory. We show that, rather than one or a small number of poles, the correlator has a cut along the negative imaginary frequency axis. We briefly discuss this result’s relevance for constructing 2’nd order hydrodynamic models of hot relativistic field theories.


Thermal Field Theory Quark-Gluon Plasma 


Open Access

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  1. [1]
    T. Schäfer and D. Teaney, Nearly perfect fluidity: from cold atomic gases to hot quark gluon plasmas, Rept. Prog. Phys. 72 (2009) 126001 [arXiv:0904.3107] [INSPIRE].ADSCrossRefGoogle Scholar
  2. [2]
    D.A. Teaney, Viscous hydrodynamics and the quark gluon plasma, in Quark-gluon plasma 4, R.C. Hwa and X.-N.. Wang eds., World Scientific, Singapore, (2010), pg. 207 [arXiv:0905.2433] [INSPIRE].
  3. [3]
    I. Müller, Zum Paradoxon der Wärmeleitungstheorie (in German), Z. Phys. 198 (1967) 329 [INSPIRE].
  4. [4]
    W.A. Hiscock and L. Lindblom, Stability and causality in dissipative relativistic fluids, Annals Phys. 151 (1983) 466 [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    W.A. Hiscock and L. Lindblom, Generic instabilities in first-order dissipative relativistic fluid theories, Phys. Rev. D 31 (1985) 725 [INSPIRE].ADSMathSciNetGoogle Scholar
  6. [6]
    W. Israel, Nonstationary irreversible thermodynamics: a causal relativistic theory, Annals Phys. 100 (1976) 310 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  7. [7]
    W. Israel and J.M. Stewart, Transient relativistic thermodynamics and kinetic theory, Annals Phys. 118 (1979) 341 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  8. [8]
    R. Baier, P. Romatschke, D.T. Son, A.O. Starinets and M.A. Stephanov, Relativistic viscous hydrodynamics, conformal invariance and holography, JHEP 04 (2008) 100 [arXiv:0712.2451] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    S. Bhattacharyya, V.E. Hubeny, S. Minwalla and M. Rangamani, Nonlinear fluid dynamics from gravity, JHEP 02 (2008) 045 [arXiv:0712.2456] [INSPIRE].ADSCrossRefGoogle Scholar
  10. [10]
    G.S. Denicol, J. Noronha, H. Niemi and D.H. Rischke, Origin of the relaxation time in dissipative fluid dynamics, Phys. Rev. D 83 (2011) 074019 [arXiv:1102.4780] [INSPIRE].
  11. [11]
    P.K. Kovtun and A.O. Starinets, Quasinormal modes and holography, Phys. Rev. D 72 (2005) 086009 [hep-th/0506184] [INSPIRE].
  12. [12]
    S. Grozdanov, N. Kaplis and A.O. Starinets, From strong to weak coupling in holographic models of thermalization, JHEP 07 (2016) 151 [arXiv:1605.02173] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  13. [13]
    T. Koide, E. Nakano and T. Kodama, Shear viscosity coefficient and relaxation time of causal dissipative hydrodynamics in QCD, Phys. Rev. Lett. 103 (2009) 052301 [arXiv:0901.3707] [INSPIRE].ADSCrossRefGoogle Scholar
  14. [14]
    T. Koide and T. Kodama, Transport coefficients of non-Newtonian fluid and causal dissipative hydrodynamics, Phys. Rev. E 78 (2008) 051107 [arXiv:0806.3725] [INSPIRE].
  15. [15]
    P. Romatschke, Retarded correlators in kinetic theory: branch cuts, poles and hydrodynamic onset transitions, Eur. Phys. J. C 76 (2016) 352 [arXiv:1512.02641] [INSPIRE].
  16. [16]
    A. Kurkela and U.A. Wiedemann, Analytic structure of nonhydrodynamic modes in kinetic theory, CERN-TH-2017-255, CERN, Geneva Switzerland, (2017) [arXiv:1712.04376] [INSPIRE].
  17. [17]
    L.P. Kadanoff and G. Baym, Quantum statistical mechanics: Greens function methods in equilibrium and nonequilibrium problems, Front. Phys., W.A. Benjamin, U.S.A., (1962).Google Scholar
  18. [18]
    S. Jeon, Hydrodynamic transport coefficients in relativistic scalar field theory, Phys. Rev. D 52 (1995) 3591 [hep-ph/9409250] [INSPIRE].
  19. [19]
    S. Jeon and L.G. Yaffe, From quantum field theory to hydrodynamics: transport coefficients and effective kinetic theory, Phys. Rev. D 53 (1996) 5799 [hep-ph/9512263] [INSPIRE].
  20. [20]
    P.B. Arnold, D.T. Son and L.G. Yaffe, Effective dynamics of hot, soft non-Abelian gauge fields. Color conductivity and log(1) effects, Phys. Rev. D 59 (1999) 105020 [hep-ph/9810216] [INSPIRE].
  21. [21]
    P.B. Arnold, G.D. Moore and L.G. Yaffe, Transport coefficients in high temperature gauge theories. 1. Leading log results, JHEP 11 (2000) 001 [hep-ph/0010177] [INSPIRE].
  22. [22]
    P.B. Arnold, G.D. Moore and L.G. Yaffe, Transport coefficients in high temperature gauge theories. 2. Beyond leading log, JHEP 05 (2003) 051 [hep-ph/0302165] [INSPIRE].
  23. [23]
    G.D. Moore, Next-to-leading order shear viscosity in λϕ 4 theory, Phys. Rev. D 76 (2007) 107702 [arXiv:0706.3692] [INSPIRE].
  24. [24]
    M. Reed and B. Simon, Methods of modern mathematical physics. 1. Functional analysis, Academic Press, U.S.A., (1972).Google Scholar

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© The Author(s) 2018

Authors and Affiliations

  1. 1.Institut für Kernphysik, Technische Universität DarmstadtDarmstadtGermany

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