Advertisement

On multi-field flows in gravity and holography

  • Francesco Nitti
  • Leandro Silva Pimenta
  • Danièle A. Steer
Open Access
Regular Article - Theoretical Physics
  • 7 Downloads

Abstract

We perform a systematic analysis of flow-like solutions in theories of Einstein gravity coupled to multiple scalar fields, which arise as holographic RG flows as well as in the context of cosmological solutions driven by scalars. We use the first order formalism and the superpotential formulation to classify solutions close to generic extrema of the scalar potential, and close to “bounces,” where the flow is inverted in some or all directions and the superpotential becomes multi-valued. Although the superpotential formulation contains a large redundancy, we show how this can be completely lift by suitable regularity conditions. We place the first order formalism in the context of Hamilton-Jacobi theory, where we discuss the possibility of non-gradient flows and their connection to non-separable solutions of the Hamilton-Jacobi equation. We argue that non-gradient flows may be useful in the presence of global symmetries in the scalar sector.

Keywords

AdS-CFT Correspondence Gauge-gravity correspondence 

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]
    J.M. Maldacena, The large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].MathSciNetCrossRefMATHGoogle Scholar
  2. [2]
    S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  3. [3]
    E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  4. [4]
    H.J. Boonstra, K. Skenderis and P.K. Townsend, The domain wall/QFT correspondence, JHEP 01 (1999) 003 [hep-th/9807137] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  5. [5]
    L. Girardello, M. Petrini, M. Porrati and A. Zaffaroni, Novel local CFT and exact results on perturbations of N = 4 superYang-Mills from AdS dynamics, JHEP 12 (1998) 022 [hep-th/9810126] [INSPIRE].
  6. [6]
    V. Balasubramanian and P. Kraus, Space-time and the holographic renormalization group, Phys. Rev. Lett. 83 (1999) 3605 [hep-th/9903190] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  7. [7]
    D.Z. Freedman, S.S. Gubser, K. Pilch and N.P. Warner, Renormalization group flows from holography supersymmetry and a c theorem, Adv. Theor. Math. Phys. 3 (1999) 363 [hep-th/9904017] [INSPIRE].MathSciNetCrossRefMATHGoogle Scholar
  8. [8]
    J. de Boer, E.P. Verlinde and H.L. Verlinde, On the holographic renormalization group, JHEP 08 (2000) 003 [hep-th/9912012] [INSPIRE].MathSciNetCrossRefMATHGoogle Scholar
  9. [9]
    M. Bianchi, D.Z. Freedman and K. Skenderis, How to go with an RG flow, JHEP 08 (2001) 041 [hep-th/0105276] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  10. [10]
    S. de Haro, S.N. Solodukhin and K. Skenderis, Holographic reconstruction of space-time and renormalization in the AdS/CFT correspondence, Commun. Math. Phys. 217 (2001) 595 [hep-th/0002230] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  11. [11]
    I. Papadimitriou and K. Skenderis, Correlation functions in holographic RG flows, JHEP 10 (2004) 075 [hep-th/0407071] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  12. [12]
    D. Langlois, S. Renaux-Petel, D.A. Steer and T. Tanaka, Primordial fluctuations and non-Gaussianities in multi-field DBI inflation, Phys. Rev. Lett. 101 (2008) 061301 [arXiv:0804.3139] [INSPIRE].
  13. [13]
    D. Langlois, S. Renaux-Petel, D.A. Steer and T. Tanaka, Primordial perturbations and non-Gaussianities in DBI and general multi-field inflation, Phys. Rev. D 78 (2008) 063523 [arXiv:0806.0336] [INSPIRE].
  14. [14]
    S. Renaux-Petel and K. Turzynki, Geometrical destabilization of inflation, Phys. Rev. Lett. 117 (2016) 141301 [arXiv:1510.01281] [INSPIRE].ADSCrossRefGoogle Scholar
  15. [15]
    A. Celi et al., On the fakeness of fake supergravity, Phys. Rev. D 71 (2005) 045009 [hep-th/0410126] [INSPIRE].
  16. [16]
    K. Skenderis and P.K. Townsend, Gravitational stability and renormalization group flow, Phys. Lett. B 468 (1999) 46 [hep-th/9909070] [INSPIRE].
  17. [17]
    P. Binetruy et al., Universality classes for models of inflation, JCAP 04 (2015) 033 [arXiv:1407.0820] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  18. [18]
    I. Papadimitriou, Multi-trace deformations in AdS/CFT: exploring the vacuum structure of the deformed CFT, JHEP 05 (2007) 075 [hep-th/0703152] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  19. [19]
    D. Martelli and A. Miemiec, CFT/CFT interpolating RG flows and the holographic c function, JHEP 04 (2002) 027 [hep-th/0112150] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  20. [20]
    E. Kiritsis, W. Li and F. Nitti, Holographic RG flow and the quantum effective action, Fortsch. Phys. 62 (2014) 389 [arXiv:1401.0888] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  21. [21]
    J. Bourdier and E. Kiritsis, Holographic RG flows and nearly-marginal operators, Class. Quant. Grav. 31 (2014) 035011 [arXiv:1310.0858] [INSPIRE].
  22. [22]
    E. Kiritsis, F. Nitti and L. Silva Pimenta, Exotic RG Flows from Holography, Fortsch. Phys. 65 (2017) 1600120 [arXiv:1611.05493] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  23. [23]
    U. Gürsoy, E. Kiritsis and F. Nitti, Exploring improved holographic theories for QCD: Part II, JHEP 02 (2008) 019 [arXiv:0707.1349] [INSPIRE].CrossRefGoogle Scholar
  24. [24]
    M. Bianchi, D.Z. Freedman and K. Skenderis, Holographic renormalization, Nucl. Phys. B 631 (2002) 159 [hep-th/0112119] [INSPIRE].
  25. [25]
    I. Papadimitriou, Holographic renormalization of general dilaton-axion gravity, JHEP 08 (2011) 119 [arXiv:1106.4826] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  26. [26]
    J. Sonner and P.K. Townsend, Axion-dilaton domain walls and fake supergravity, Class. Quant. Grav. 24 (2007) 3479 [hep-th/0703276] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  27. [27]
    U. Gürsoy, E. Kiritsis, L. Mazzanti and F. Nitti, Holography and thermodynamics of 5D dilaton-gravity, JHEP 05 (2009) 033 [arXiv:0812.0792] [INSPIRE].
  28. [28]
    J.K. Ghosh, E. Kiritsis, F. Nitti and L.T. Witkowski, Holographic RG flows on curved manifolds and quantum phase transitions, arXiv:1711.08462 [INSPIRE].
  29. [29]
    W. Boucher, Positive energy without supersymmetry, Nucl. Phys. B 242 (1984) 282 [INSPIRE].
  30. [30]
    P.K. Townsend, Positive energy and the scalar potential in higher dimensional (super)gravity theories, Phys. Lett. B 148 (1984) 55.Google Scholar
  31. [31]
    D.Z. Freedman, C. Núñez, M. Schnabl and K. Skenderis, Fake supergravity and domain wall stability, Phys. Rev. D 69 (2004) 104027 [hep-th/0312055] [INSPIRE].
  32. [32]
    I. Papadimitriou and K. Skenderis, AdS/CFT correspondence and geometry, IRMA Lect. Math. Theor. Phys. 8 (2005) 73 [hep-th/0404176] [INSPIRE].MathSciNetMATHGoogle Scholar
  33. [33]
    K. Skenderis and P.K. Townsend, Hamilton-Jacobi method for curved domain walls and cosmologies, Phys. Rev. D 74 (2006) 125008 [hep-th/0609056] [INSPIRE].ADSMathSciNetGoogle Scholar
  34. [34]
    I. Papadimitriou, Holographic renormalization as a canonical transformation, JHEP 11 (2010) 014 [arXiv:1007.4592] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  35. [35]
    I. Papadimitriou, Lectures on holographic renormalization, Springer Proc. Phys. 176 (2016) 131.Google Scholar
  36. [36]
    J. Lindgren, I. Papadimitriou, A. Taliotis and J. Vanhoof, Holographic Hall conductivities from dyonic backgrounds, JHEP 07 (2015) 094 [arXiv:1505.04131] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  37. [37]
    D.S. Salopek and J.R. Bond, Nonlinear evolution of long wavelength metric fluctuations in inflationary models, Phys. Rev. D 42 (1990) 3936 [INSPIRE].
  38. [38]
    K. Skenderis and P.K. Townsend, Hidden supersymmetry of domain walls and cosmologies, Phys. Rev. Lett. 96 (2006) 191301 [hep-th/0602260] [INSPIRE].ADSCrossRefGoogle Scholar
  39. [39]
    J. Diaz Dorronsoro, B. Truijen and T. Van Riet, Comments on fake supersymmetry, Class. Quant. Grav. 34 (2017) 095003 [arXiv:1606.07730] [INSPIRE].
  40. [40]
    T. Banks and L.J. Dixon, Constraints on string vacua with space-time supersymmetry, Nucl. Phys. B 307 (1988) 93 [INSPIRE].
  41. [41]
    J. Garriga, K. Skenderis and Y. Urakawa, Multi-field inflation from holography, JCAP 01 (2015) 028 [arXiv:1410.3290] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar

Copyright information

© The Author(s) 2018

Authors and Affiliations

  • Francesco Nitti
    • 1
  • Leandro Silva Pimenta
    • 1
  • Danièle A. Steer
    • 1
  1. 1.APC, AstroParticule et Cosmologie, Université Paris Diderot, CNRS/IN2P3, CEA/IRFU, Observatoire de Paris, Sorbonne Paris CitéParis Cedex 13France

Personalised recommendations