Artículo

Barvinsky, A.O.; Blas, D.; Herrero-Valea, M.; Nesterov, D.V.; Pérez-Nadal, G.; Steinwachs, C.F. "Heat kernel methods for Lifshitz theories" (2017) Journal of High Energy Physics. 2017(6)
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Abstract:

We study the one-loop covariant effective action of Lifshitz theories using the heat kernel technique. The characteristic feature of Lifshitz theories is an anisotropic scaling between space and time. This is enforced by the existence of a preferred foliation of space-time, which breaks Lorentz invariance. In contrast to the relativistic case, covariant Lifshitz theories are only invariant under diffeomorphisms preserving the foliation structure. We develop a systematic method to reduce the calculation of the effective action for a generic Lifshitz operator to an algorithm acting on known results for relativistic operators. In addition, we present techniques that drastically simplify the calculation for operators with special properties. We demonstrate the efficiency of these methods by explicit applications. © 2017, The Author(s).

Registro:

Documento: Artículo
Título:Heat kernel methods for Lifshitz theories
Autor:Barvinsky, A.O.; Blas, D.; Herrero-Valea, M.; Nesterov, D.V.; Pérez-Nadal, G.; Steinwachs, C.F.
Filiación:Theory Department, Lebedev Physics Institute, Leninskii Pr. 53, Moscow, 119991, Russian Federation
Theoretical Physics Department, CERN, Geneva 23, CH-1211, Switzerland
Institute of Physics, LPPC, École Polytechnique Fédérale de Lausanne, Lausanne, CH-1015, Switzerland
Tomsk State University, Department of Physics, Lenin Ave. 36, Tomsk, 634050, Russian Federation
Departamento de Física, FCEN, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón 1, Buenos Aires, 1428, Argentina
Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Hermann-Herder-Strasse 3, Freiburg, 79104, Germany
Palabras clave:Classical Theories of Gravity; Effective Field Theories; Field Theories in Higher Dimensions; Renormalization Group
Año:2017
Volumen:2017
Número:6
DOI: http://dx.doi.org/10.1007/JHEP06(2017)063
Título revista:Journal of High Energy Physics
Título revista abreviado:J. High Energy Phys.
ISSN:11266708
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_11266708_v2017_n6_p_Barvinsky

Referencias:

  • Fradkin, E.H., Field theories of condensed matter physics (2013) Front. Phys., 82, p. 1. , [INSPIRE]
  • Ardonne, E., Fendley, P., Fradkin, E., (2004) Topological order and conformal quantum critical points, Annals Phys.
  • Hořava, P., (2009) Quantum gravity at a Lifshitz point, Phys. Rev.
  • Barvinsky, A.O., Blas, D., Herrero-Valea, M., Sibiryakov, S.M., Steinwachs, C.F., Renormalization of Hořava gravity (2016) Phys. Rev.
  • Blas, D., Sibiryakov, S., Completing Lorentz violating massive gravity at high energies (2015) Zh. Eksp. Teor. Fiz., , [J. Exp. Theor. Phys. 120 (2015) 509]
  • Nicolis, A., Piazza, F., Implications of relativity on nonrelativistic Goldstone theorems: gapped excitations at finite charge density (2013) Phys. Rev. Lett., , [Addendum ibid. 110 (2013) 039901]
  • Watanabe, H., Murayama, H., Effective Lagrangian for nonrelativistic systems (2014) Phys. Rev.
  • Griffin, T., Grosvenor, K.T., Hořava, P., Yan, Z., Cascading multicriticality in nonrelativistic spontaneous symmetry breaking (2015) Phys. Rev. Lett., 115, p. 241601. , [arXiv:1507.06992] [INSPIRE]
  • Goldberger, W.D., Khandker, Z.U., Prabhu, S., OPE convergence in non-relativistic conformal field theories (2015) JHEP, 12, p. 048. , [arXiv:1412.8507] [INSPIRE]
  • Keranen, V., Sybesma, W., Szepietowski, P., Thorlacius, L., Correlation functions in theories with Lifshitz scaling (2017) JHEP, 5, p. 033. , [arXiv:1611.09371] [INSPIRE]
  • Griffin, T., Hořava, P., Melby-Thompson, C.M., Conformal Lifshitz gravity from holography (2012) JHEP, 5, p. 010. , [arXiv:1112.5660] [INSPIRE]
  • Griffin, T., Hořava, P., Melby-Thompson, C.M., Lifshitz gravity for Lifshitz holography (2013) Phys. Rev. Lett.
  • Kachru, S., Liu, X., Mulligan, M., Gravity duals of Lifshitz-like fixed points (2008) Phys. Rev., 500, p. 106005. , [arXiv:0808.1725] [INSPIRE]
  • Nakayama, Y., Holographic renormalization of foliation preserving gravity and trace anomaly (2012) Gen. Rel. Grav., 44, p. 2873. , [arXiv:1203.1068] [INSPIRE]
  • Roychowdhury, D., On anisotropic black branes with Lifshitz scaling (2016) Phys. Lett., B 759, p. 410. , [arXiv:1509.05229] [INSPIRE]
  • Bitaghsir Fadafan, K., Saiedi, F., Holographic Schwinger effect in non-relativistic backgrounds (2015) Eur. Phys. J., 100, p. 612. , [arXiv:1504.02432] [INSPIRE]
  • Taylor, M., (2016) Lifshitz holography, Class. Quant. Grav.
  • Foster, J.W., Liu, J.T., Spatial anisotropy in nonrelativistic holography
  • Adam, I., Melnikov, I.V., Theisen, S., A non-relativistic Weyl anomaly (2009) JHEP, 9, p. 130. , [arXiv:0907.2156] [INSPIRE]
  • Arav, I., Chapman, S., Oz, Y., Lifshitz scale anomalies (2015) JHEP, 2, p. 078. , [arXiv:1410.5831] [INSPIRE]
  • Gomes, P.R.S., Gomes, M., On Ward identities in Lifshitz-like field theories (2012) Phys. Rev. D
  • Baggio, M., de Boer, J., Holsheimer, K., Anomalous breaking of anisotropic scaling symmetry in the quantum Lifshitz model (2012) JHEP, 7, p. 099. , [arXiv:1112.6416] [INSPIRE]
  • Arav, I., Chapman, S., Oz, Y., Non-relativistic scale anomalies (2016) JHEP, 6, p. 158. , [arXiv:1601.06795] [INSPIRE]
  • Pal, S., Grinstein, B., Weyl consistency conditions in non-relativistic quantum field theory (2016) JHEP, 12, p. 012. , [arXiv:1605.02748] [INSPIRE]
  • Auzzi, R., Nardelli, G., Heat kernel for Newton-Cartan trace anomalies (2016) JHEP, 7, p. 047. , [arXiv:1605.08684] [INSPIRE]
  • Pal, S., Grinstein, B., On the heat kernel and Weyl anomaly of Schrödinger invariant theory
  • Nesterov, D., Solodukhin, S.N., Gravitational effective action and entanglement entropy in UV modified theories with and without Lorentz symmetry (2011) Nucl. Phys., B 842, p. 141. , [arXiv:1007.1246] [INSPIRE]
  • D’Odorico, G., Goossens, J.-W., Saueressig, F., Covariant computation of effective actions in Hořava-Lifshitz gravity (2015) JHEP, 10, p. 126. , [arXiv:1508.00590] [INSPIRE]
  • Anselmi, D., Halat, M., Renormalization of Lorentz violating theories (2007) Phys. Rev., 500, p. 125011. , [arXiv:0707.2480] [INSPIRE]
  • Iengo, R., Russo, J.G., Serone, M., Renormalization group in Lifshitz-type theories (2009) JHEP, 11, p. 020. , [arXiv:0906.3477] [INSPIRE]
  • Giribet, G., Nacir, D.L., Mazzitelli, F.D., Counterterms in semiclassical Hořava-Lifshitz gravity (2010) JHEP, 9, p. 009. , [arXiv:1006.2870] [INSPIRE]
  • Lopez Nacir, D.L., Mazzitelli, F.D., Trombetta, L.G., Lifshitz scalar fields: one loop renormalization in curved backgrounds (2012) Phys. Rev. D
  • Griffin, T., Grosvenor, K.T., Melby-Thompson, C.M., Yan, Z., Quantization of Hořava gravity in 2 + 1 dimensions (2017) JHEP, 6, p. 004. , [arXiv:1701.08173] [INSPIRE]
  • Zhou, T., Entanglement entropy of local operators in quantum Lifshitz theory (2016) J. Stat. Mech.
  • Parker, D.E., Vasseur, R., Moore, J.E., Entanglement entropy in excited states of the quantum Lifshitz model (2017) J. Phys., A 50, p. 254003. , [arXiv:1702.07433] [INSPIRE]
  • Karananas, G.K., Monin, A., Gauging nonrelativistic field theories using the coset construction (2016) Phys. Rev. D
  • Pérez-Nadal, G., Anisotropic Weyl invariance
  • DeWitt, B.S., (1965) Dynamical theory of groups and fields, Gordon and Breach
  • McKean, H.P., Singer, I.M., Curvature and eigenvalues of the Laplacian (1967) J. Diff. Geom., 1, p. 43. , [INSPIRE]
  • Gilkey, P.B., theory, I., (1984) the heat equation and the Atiyh-Singer index theorem, , Publish or Perish: Wilmington DE U.S.A
  • Barvinsky, A.O., Heat kernel expansion in the background field formalism (2015) Scholarpedia, 10, p. 31644. , [INSPIRE]
  • Barvinsky, A.O., Vilkovisky, G.A., The generalized Schwinger-Dewitt technique in gauge theories and quantum gravity (1985) Phys. Rept., 119, p. 1. , [INSPIRE]
  • Avramidi, I.G., Heat kernel and quantum gravity (2000) Lect. Notes Phys. Monogr., 64, p. 1. , [INSPIRE]
  • Kirsten, K., (2001) Spectral functions in mathematics and physics, Chapman and Hall, , Boca Raton FL U.S.A. [INSPIRE]
  • Vassilevich, D.V., Heat kernel expansion: user’s manual (2003) Phys. Rept., 388, p. 279. , [hep-th/0306138] [INSPIRE]
  • Fursaev, D., Vassilevich, D., Operators, geometry and quanta: methods of spectral geometry in quantum field theory, Springer Science & Business (2011) The Netherlands
  • Arnowitt, R.L., Deser, S., Misner, C.W., Dynamical structure and definition of energy in general relativity (1959) Phys. Rev., 116, p. 1322. , [INSPIRE]
  • Dowker, J.S., Critchley, R., Effective Lagrangian and energy momentum tensor in de Sitter space (1976) Phys. Rev., 500, p. 3224. , [INSPIRE]
  • Hawking, S.W., Zeta function regularization of path integrals in curved space-time (1977) Commun. Math. Phys., 55, p. 133. , [INSPIRE]
  • Fegan, H.D., Gilkey, P., Invariants of the heat equation (1985) Pacific J. Math., 117, p. 233
  • Birrell, N., Davies, P., Quantum fields in curved space, Cambridge Monogr. Math. Phys (1982) Cambridge U.K.
  • Gilkey, P., (2003) Asymptotic formulae in spectral geometry, Studies in Advanced Mathematics, Chapman and Hall, , Boca Raton FL U.S.A. [INSPIRE]
  • DeWitt, B.S., The global approach to quantum field theory (2003) Int. Ser. Monogr. Phys.
  • Barvinsky, A.O., Nesterov, D.V., Quantum effective action in spacetimes with branes and boundaries (2006) Phys. Rev. D
  • Magnus, W., On the exponential solution of differential equations for a linear operator (1954) Commun. Pure Appl. Math., 7, p. 649. , [INSPIRE]
  • Fradkin, E.S., Tseytlin, A.A., Renormalizable asymptotically free quantum theory of gravity (1981) Phys. Lett., 104B, p. 377. , [INSPIRE]
  • Gusynin, V.P., Seeley-Gilkey coefficients for the fourth order operators on a Riemannian manifold (1990) Nucl. Phys., B 333, p. 296. , [INSPIRE]
  • Zamolodchikov, A.B., Irreversibility of the flux of the renormalization group in a 2D field theory (1986) JETP Lett., , [Pisma Zh. Eksp. Teor. Fiz. 43 (1986) 565]
  • Komargodski, Z., Schwimmer, A., On renormalization group flows in four dimensions (2011) JHEP, 12, p. 099. , [arXiv:1107.3987] [INSPIRE]
  • Nakayama, Y., Scale invariance vs conformal invariance (2015) Phys. Rept., 569, p. 1. , [arXiv:1302.0884] [INSPIRE]
  • Callan, C.G., Jr., Wilczek, F., On geometric entropy (1994) Phys. Lett., B 333, p. 55. , [hep-th/9401072] [INSPIRE]
  • Ryu, S., Takayanagi, T., Holographic derivation of entanglement entropy from AdS/CFT (2006) Phys. Rev. Lett., 96, p. 181602. , [hep-th/0603001] [INSPIRE]
  • Emparan, R., Black hole entropy as entanglement entropy: a holographic derivation (2006) JHEP, 6, p. 012. , [hep-th/0603081] [INSPIRE]
  • Shiba, N., Takayanagi, T., Volume law for the entanglement entropy in non-local QFTs (2014) JHEP, 2, p. 033. , [arXiv:1311.1643] [INSPIRE]
  • Camps, J., Generalized entropy and higher derivative gravity (2014) JHEP, 3, p. 070. , [arXiv:1310.6659] [INSPIRE]
  • Kuchar, K., Kinematics of tensor fields in hyperspace (1976) J. Math. Phys.

Citas:

---------- APA ----------
Barvinsky, A.O., Blas, D., Herrero-Valea, M., Nesterov, D.V., Pérez-Nadal, G. & Steinwachs, C.F. (2017) . Heat kernel methods for Lifshitz theories. Journal of High Energy Physics, 2017(6).
http://dx.doi.org/10.1007/JHEP06(2017)063
---------- CHICAGO ----------
Barvinsky, A.O., Blas, D., Herrero-Valea, M., Nesterov, D.V., Pérez-Nadal, G., Steinwachs, C.F. "Heat kernel methods for Lifshitz theories" . Journal of High Energy Physics 2017, no. 6 (2017).
http://dx.doi.org/10.1007/JHEP06(2017)063
---------- MLA ----------
Barvinsky, A.O., Blas, D., Herrero-Valea, M., Nesterov, D.V., Pérez-Nadal, G., Steinwachs, C.F. "Heat kernel methods for Lifshitz theories" . Journal of High Energy Physics, vol. 2017, no. 6, 2017.
http://dx.doi.org/10.1007/JHEP06(2017)063
---------- VANCOUVER ----------
Barvinsky, A.O., Blas, D., Herrero-Valea, M., Nesterov, D.V., Pérez-Nadal, G., Steinwachs, C.F. Heat kernel methods for Lifshitz theories. J. High Energy Phys. 2017;2017(6).
http://dx.doi.org/10.1007/JHEP06(2017)063