Advertisement

An entropy current in superspace

  • Kristan JensenEmail author
  • Raja Marjieh
  • Natalia Pinzani-Fokeeva
  • Amos Yarom
Open Access
Regular Article - Theoretical Physics
  • 22 Downloads

Abstract

We provide a mechanism by which an entropy current can be constructed in a supersymmetric formulation of the low-energy effective action for the Schwinger-Keldysh generating functional. This mechanism allows us to define an entropy current quantum mechanically by coupling it to an external source. Such an entropy current is given by the bottom component of an entropy current superfield which is conserved in superspace, but when restricted to real space satisfies a non-conservation law. We demonstrate the validity of our mechanism in a probe limit which allows us to fully treat quantum fluctuations.

Keywords

Effective Field Theories Global Symmetries 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

References

  1. [1]
    L.D. Landau and E.M. Lifshitz, A course in theoretical physics — fluid mechanics, volume 6, Pergamon, U.K., (1987).Google Scholar
  2. [2]
    K. Jensen, M. Kaminski, P. Kovtun, R. Meyer, A. Ritz and A. Yarom, Parity-violating hydrodynamics in 2 + 1 dimensions, JHEP 05 (2012) 102 [arXiv:1112.4498] [INSPIRE].
  3. [3]
    N. Banerjee, J. Bhattacharya, S. Bhattacharyya, S. Jain, S. Minwalla and T. Sharma, Constraints on fluid dynamics from equilibrium partition functions, JHEP 09 (2012) 046 [arXiv:1203.3544] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    K. Jensen, M. Kaminski, P. Kovtun, R. Meyer, A. Ritz and A. Yarom, Towards hydrodynamics without an entropy current, Phys. Rev. Lett. 109 (2012) 101601 [arXiv:1203.3556] [INSPIRE].ADSCrossRefGoogle Scholar
  5. [5]
    D.T. Son and P. Surowka, Hydrodynamics with triangle anomalies, Phys. Rev. Lett. 103 (2009) 191601 [arXiv:0906.5044] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  6. [6]
    F.M. Haehl, R. Loganayagam and M. Rangamani, The eightfold way to dissipation, Phys. Rev. Lett. 114 (2015) 201601 [arXiv:1412.1090] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  7. [7]
    F.M. Haehl, R. Loganayagam and M. Rangamani, Adiabatic hydrodynamics: the eightfold way to dissipation, JHEP 05 (2015) 060 [arXiv:1502.00636] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    J. de Boer, M.P. Heller and N. Pinzani-Fokeeva, Effective actions for relativistic fluids from holography, JHEP 08 (2015) 086 [arXiv:1504.07616] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    M. Crossley, P. Glorioso, H. Liu and Y. Wang, Off-shell hydrodynamics from holography, JHEP 02 (2016) 124 [arXiv:1504.07611] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    S.-I. Sasa and Y. Yokokura, Thermodynamic entropy as a Noether invariant, Phys. Rev. Lett. 116 (2016) 140601 [arXiv:1509.08943] [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    P. Glorioso and H. Liu, The second law of thermodynamics from symmetry and unitarity, arXiv:1612.07705 [INSPIRE].
  12. [12]
    P. Glorioso, M. Crossley and H. Liu, Effective field theory of dissipative fluids (II): classical limit, dynamical KMS symmetry and entropy current, JHEP 09 (2017) 096 [arXiv:1701.07817] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  13. [13]
    F.M. Haehl, R. Loganayagam and M. Rangamani, The fluid manifesto: emergent symmetries, hydrodynamics and black holes, JHEP 01 (2016) 184 [arXiv:1510.02494] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  14. [14]
    M. Crossley, P. Glorioso and H. Liu, Effective field theory of dissipative fluids, JHEP 09 (2017) 095 [arXiv:1511.03646] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  15. [15]
    F.M. Haehl, R. Loganayagam and M. Rangamani, Topological σ-models & dissipative hydrodynamics, JHEP 04 (2016) 039 [arXiv:1511.07809] [INSPIRE].
  16. [16]
    F.M. Haehl, R. Loganayagam and M. Rangamani, Schwinger-Keldysh formalism. Part I: BRST symmetries and superspace, JHEP 06 (2017) 069 [arXiv:1610.01940] [INSPIRE].
  17. [17]
    F.M. Haehl, R. Loganayagam and M. Rangamani, Schwinger-Keldysh formalism. Part II: thermal equivariant cohomology, JHEP 06 (2017) 070 [arXiv:1610.01941] [INSPIRE].
  18. [18]
    K. Jensen, N. Pinzani-Fokeeva and A. Yarom, Dissipative hydrodynamics in superspace, JHEP 09 (2018) 127 [arXiv:1701.07436] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  19. [19]
    F.M. Haehl, R. Loganayagam and M. Rangamani, Two roads to hydrodynamic effective actions: a comparison, arXiv:1701.07896 [INSPIRE].
  20. [20]
    M. Geracie, F.M. Haehl, R. Loganayagam, P. Narayan, D.M. Ramirez and M. Rangamani, Schwinger-Keldysh superspace in quantum mechanics, Phys. Rev. D 97 (2018) 105023 [arXiv:1712.04459] [INSPIRE].
  21. [21]
    K. Jensen, R. Loganayagam and A. Yarom, Chern-Simons terms from thermal circles and anomalies, JHEP 05 (2014) 110 [arXiv:1311.2935] [INSPIRE].ADSCrossRefGoogle Scholar
  22. [22]
    F.M. Haehl, R. Loganayagam and M. Rangamani, Inflow mechanism for hydrodynamic entropy, Phys. Rev. Lett. 121 (2018) 051602 [arXiv:1803.08490] [INSPIRE].
  23. [23]
    K. Jensen, R. Marjieh, N. Pinzani-Fokeeva and A. Yarom, A panoply of Schwinger-Keldysh transport, SciPost Phys. 5 (2018) 053 [arXiv:1804.04654] [INSPIRE].ADSCrossRefGoogle Scholar
  24. [24]
    R. Loganayagam, Anomaly induced transport in arbitrary dimensions, arXiv:1106.0277 [INSPIRE].
  25. [25]
    S. Bhattacharyya, Entropy current and equilibrium partition function in fluid dynamics, JHEP 08 (2014) 165 [arXiv:1312.0220] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  26. [26]
    S. Bhattacharyya, Entropy current from partition function: one example, JHEP 07 (2014) 139 [arXiv:1403.7639] [INSPIRE].ADSCrossRefGoogle Scholar

Copyright information

© The Author(s) 2019

Authors and Affiliations

  • Kristan Jensen
    • 1
    Email author
  • Raja Marjieh
    • 2
  • Natalia Pinzani-Fokeeva
    • 3
  • Amos Yarom
    • 2
  1. 1.Department of Physics and AstronomySan Francisco State UniversitySan FranciscoU.S.A.
  2. 2.Department of Physics, TechnionHaifaIsrael
  3. 3.Institute for Theoretical Physics, KU LeuvenLeuvenBelgium

Personalised recommendations