zbMATH — the first resource for mathematics

Anomalous gravitational TTT vertex, temperature inhomogeneity, and pressure anisotropy. (English) Zbl 1435.81200
Summary: The conformal anomaly in curved spacetime generates a nontrivial anomalous vertex, given by the three-point correlation function TTT of the energy-momentum tensor \(T^{\mu \nu} \). We show that a temperature inhomogeneity in a gas of charged massless particles generates, via the TTT vertex, a pressure anisotropy with respect to the axis of the temperature variation. This very particular signature may provide an experimental access to the elusive gravitational coefficient \(b\) which determines the anomaly contribution of the Weyl tensor to the trace of the energy-momentum tensor in curved spacetime. We present an estimate of the pressure anisotropy both for fermionic quasiparticles in the solid-state environment of Dirac semimetals as well as for a quark-gluon plasma in relativistic heavy-ion collisions. In both cases, the pressure anisotropy is small compared to the mean thermal pressure.
81T50 Anomalies in quantum field theory
81T20 Quantum field theory on curved space or space-time backgrounds
81V10 Electromagnetic interaction; quantum electrodynamics
Full Text: DOI
[1] Nakayama, Y., Scale invariance vs conformal invariance, Phys. Rep., 569, 1 (2015) · Zbl 1202.81191
[2] Duff, M. J., Observations on conformal anomalies, Nucl. Phys. B, 125, 334 (1977)
[3] Duff, M. J., Twenty years of the Weyl anomaly, Class. Quantum Gravity, 11, 1387 (1994) · Zbl 0808.53063
[4] Kharzeev, D. E.; Landsteiner, K.; Schmitt, A.; Yee, H. U., ‘Strongly interacting matter in magnetic fields’: an overview, Lect. Notes Phys., 871, 1 (2013)
[5] Shifman, M. A., Anomalies and low-energy theorems of quantum chromodynamics, Phys. Rep., 209, 341 (1991)
[6] Liu, Z. K.; Zhou, B.; Zhang, Y.; Wang, Z. J.; Weng, H. M.; Prabhakaran, D.; Mo, S-K., Discovery of a three-dimensional topological Dirac semimetal, Na_3Bi, Science, 343, 864 (2014)
[7] Liu, Z. K., A stable three-dimensional topological Dirac semimetal \(C d_3 A s_2\), Nat. Mater., 13, 677 (2014)
[8] Xu, S.-Y., Discovery of a Weyl fermion semimetal and topological Fermi arcs, Science, 349, 613 (2015)
[9] Lv, B. Q., Experimental discovery of Weyl semimetal TaAs, Phys. Rev. X, 5, Article 031013 pp. (2015)
[10] Xu, S.-Y., Discovery of a Weyl fermion state with Fermi arcs in niobium arsenide, Nat. Phys., 11, 748 (2015)
[11] Landsteiner, K., Anomalous transport of Weyl fermions in Weyl semimetals, Phys. Rev. B, 89, Article 075124 pp. (2014)
[12] Isobe, H.; Nagaosa, N., Theory of quantum critical phenomenon in topological insulator - (3+1) D quantum electrodynamics in solids, Phys. Rev. B, 86, Article 165127 pp. (2012)
[13] Yang, B.-J.; Moon, E.-G.; Isobe, H.; Nagaosa, N., Quantum criticality of topological phase transitions in 3d interacting electronic systems, Nat. Phys., 10, 774 (2014)
[14] González, J., Marginal Fermi liquid versus excitonic instability in three-dimensional Dirac semimetals, Phys. Rev. B, 90, Article 121107 pp. (2014)
[15] Roy, B.; Juricic, V.; Herbut, I. F., Emergent Lorentz symmetry near fermionic quantum critical points in two and three dimensions, J. High Energy Phys., 1604, Article 018 pp. (2016)
[16] Pozo, Ó.; Ferreiros, Y.; Vozmediano, M. A.H., Anisotropic fixed points in Dirac and Weyl semimetals, Phys. Rev. B, 98, Article 115122 pp. (2018)
[17] Focus Issue “Topological Semimetals”. Focus Issue “Topological Semimetals”, Nat. Mater., 15, 1139 (2016)
[18] Armitage, N. P.; Mele, E. J.; Vishwanath, A., Weyl and Dirac semimetals in three-dimensional solids, Rev. Mod. Phys., 90, Article 015001 pp. (2018)
[19] Corianò, C.; Maglio, M. M.; Tatullo, A.; Theofilopoulos, D., Exact correlators from conformal ward identities in momentum space and perturbative realizations, PoS, CORFU2018, Article 072 pp. (2019)
[20] Kim, H. J., Dirac versus Weyl fermions in topological insulators: Adler-Bell-Jackiw anomaly in transport phenomena, Phys. Rev. Lett., 111, Article 246603 pp. (2013)
[21] Xiong, J., Evidence for the chiral anomaly in the Dirac semimetal \(N a_3 B i\), Science, 350, 413 (2015) · Zbl 1355.81168
[22] Li, C., Giant negative magnetoresistance induced by the chiral anomaly in individual Cd_3As_2 nanowires, Nat. Commun., 6, Article 10137 pp. (2015)
[23] Zhang, C., Signatures of the Adler-Bell-Jackiw chiral anomaly in a Weyl fermion semimetal, Nat. Commun., 7, Article 10735 pp. (2016)
[24] Fukushima, K.; Kharzeev, D. E.; Warringa, H. J., The chiral magnetic effect, Phys. Rev. D, 78, Article 074033 pp. (2008)
[25] Li, Q., Chiral magnetic effect in ZrTe_5, Nat. Phys., 10, 3648 (2016)
[26] Landsteiner, K.; Megias, E.; Pena-Benitez, F., Gravitational anomaly and transport, Phys. Rev. Lett., 107, Article 021601 pp. (2011)
[27] Chernodub, M. N.; Cortijo, A.; Grushin, A. G.; Landsteiner, K.; Vozmediano, M. A.H., Condensed matter realization of the axial magnetic effect, Phys. Rev. B, 89, Article 081407 pp. (2014)
[28] Gooth, J., Experimental signatures of the mixed axial-gravitational anomaly in the Weyl semimetal NbP, Nature, 547, Article 23005 pp. (2017)
[29] Ferreiros, Y.; Kedem, Y.; Bergholtz, E. J.; Bardarson, J. H., Mixed axial-torsional anomaly in Weyl semimetals, Phys. Rev. Lett., 122, 5, Article 056601 pp. (2019)
[30] Chernodub, M. N., Anomalous transport due to the conformal anomaly, Phys. Rev. Lett., 117, Article 141601 pp. (2016)
[31] Chernodub, M. N.; Cortijo, A.; Vozmediano, M. A.H., Generation of a Nernst current from the conformal anomaly in Dirac and Weyl semimetals, Phys. Rev. Lett., 120, Article 206601 pp. (2018)
[32] Arjona, V.; Chernodub, M. N.; Vozmediano, M. A.H., Fingerprints of the conformal anomaly on the thermoelectric transport in Dirac and Weyl semimetals: result from a Kubo formula, Phys. Rev. B, 99, Article 235123 pp. (2019)
[33] McAvity, D. M.; Osborn, H., A DeWitt expansion of the heat kernel for manifolds with a boundary, Class. Quantum Gravity, 8, 603 (1991) · Zbl 0716.58029
[34] Chu, C. S.; Miao, R. X., Weyl anomaly induced current in boundary quantum field theories, Phys. Rev. Lett., 121, Article 251602 pp. (2018)
[35] Chernodub, M. N.; Goy, V. A.; Molochkov, A. V., Conformal magnetic effect at the edge: a numerical study in scalar QED, Phys. Lett. B, 789, 556 (2019) · Zbl 1406.81087
[36] Chernodub, M. N.; Vozmediano, M. A.H., Direct measurement of a beta function and an indirect check of the Schwinger effect near the boundary in Dirac-Weyl semimetals, Phys. Rev. Res., 1, Article 032002 pp. (2019)
[37] Luttinger, J. M., Theory of thermal transport coefficients, Phys. Rev., 135, Article A1505 pp. (1964)
[38] Stone, M., Gravitational anomalies and thermal hall effect in topological insulators, Phys. Rev. B, 85, Article 184503 pp. (2012)
[39] Tolman, R. C., On the weight of heat and thermal equilibrium in general relativity, Phys. Rev., 35, 904 (1930) · JFM 56.0744.02
[40] Tolman, R. C.; Ehrenfest, P., Temperature equilibrium in a static gravitational field, Phys. Rev., 36, 1791 (1930)
[41] Rovelli, C.; Smerlak, M., Thermal time and Tolman-Ehrenfest effect: temperature as the speed of time, Class. Quantum Gravity, 28, 4 (2010)
[42] Chernodub, M. N.; Vozmediano, M. A.H., Chiral sound waves in strained Weyl semimetals, Phys. Rev. Res., 1 (2019), 032040(R)
[43] Armillis, R.; Corianò, C.; Delle Rose, L., Conformal anomalies and the gravitational effective action: the TJJ correlator for a Dirac fermion, Phys. Rev. D, 81, Article 085001 pp. (2010)
[44] Giannotti, M.; Mottola, E., The trace anomaly and massless scalar degrees of freedom in gravity, Phys. Rev. D, 79, Article 045014 pp. (2009)
[45] Corianò, C.; Maglio, M. M., Renormalization, conformal Ward identities and the origin of a conformal anomaly pole, Phys. Lett. B, 781, 283 (2018) · Zbl 1398.81205
[46] Corianò, C.; Costantini, A.; Delle Rose, L.; Serino, M., Superconformal sum rules and the spectral density flow of the composite dilaton (ADD) multiplet in \(\mathcal{N} = 1\) theories, J. High Energy Phys., 06, Article 136 pp. (2014)
[47] Kobayashi, T.; Afshordi, N., Schwinger effect in 4D de sitter space and constraints on magnetogenesis in the early universe, J. High Energy Phys., 1410, Article 166 pp. (2014) · Zbl 1333.83272
[48] Hayashinaka, T.; Fujita, T.; Yokoyama, J., Fermionic Schwinger effect and induced current in de Sitter space, J. Cosmol. Astropart. Phys., 1607, Article 010 pp. (2016)
[49] Armillis, R.; Corianò, C.; Delle Rose, L., Anomaly poles as common signatures of chiral and conformal anomalies, Phys. Lett. B, 682, 322 (2009)
[50] Riegert, R. J., A nonlocal action for the trace anomaly, Phys. Lett. B, 134, 56 (1984) · Zbl 0966.81550
[51] Corianò, C.; Maglio, M. M., The general 3-graviton vertex (TTT) of conformal field theories in momentum space in \(d = 4\), Nucl. Phys. B, 937, 56 (2018) · Zbl 1402.81199
[52] Corianò, C.; Maglio, M. M., Exact correlators from conformal Ward identities in momentum space and the perturbative TJJ vertex, Nucl. Phys. B, 938, 440-522 (2019) · Zbl 1407.81125
[53] Mazur, P. O.; Mottola, E., Weyl cohomology and the effective action for conformal anomalies, Phys. Rev. D, 64, Article 104022 pp. (2001)
[54] Mottola, E.; Vaulin, R., Macroscopic effects of the quantum trace anomaly, Phys. Rev. D, 74, Article 064004 pp. (2006)
[55] Paneitz, Stephen M., A quartic conformally covariant differential operator for arbitrary pseudo-Riemannian manifolds (summary), SIGMA, 4, Article 036 pp. (2008) · Zbl 1145.53053
[56] Corianò, C.; Delle Rose, L.; Marzo, C.; Serino, M., Higher order dilaton interactions in the nearly conformal limit of the standard model, Phys. Lett. B, 717, 182 (2012)
[57] Corianò, C.; Delle Rose, L.; Marzo, C.; Serino, M., The dilaton Wess-Zumino action in six dimensions from Weyl gauging: local anomalies and trace relations, Class. Quantum Gravity, 31, Article 105009 pp. (2014) · Zbl 1291.81275
[58] Chernodub, M. N.; Cortijo, A.; Vozmediano, M. A.H., Generation of a Nernst current from the conformal anomaly in Dirac and Weyl semimetals, Phys. Rev. Lett., 120, 20, Article 206601 pp. (2018)
[59] Bzowski, A.; McFadden, P.; Skenderis, K., Implications of conformal invariance in momentum space, J. High Energy Phys., 3, Article 111 pp. (2014) · Zbl 1406.81082
[60] Bzowski, A.; McFadden, P.; Skenderis, K., Renormalised 3-point functions of stress tensors and conserved currents in CFT, J. High Energy Phys., 11, Article 153 pp. (2018) · Zbl 1404.81219
[61] Bzowski, A.; McFadden, P.; Skenderis, K., Renormalised CFT 3-point functions of scalars, currents and stress tensors, J. High Energy Phys., 11, Article 159 pp. (2018) · Zbl 1404.83115
[62] Corianò, C.; Maglio, M. M.; Mottola, E., TTT in CFT: trace identities and the conformal anomaly effective action, Nucl. Phys. B, 942, 303-328 (2019) · Zbl 1415.81077
[63] Busza, W.; Rajagopal, K.; van der Schee, W., Heavy ion collisions: the big picture, and the big questions, Annu. Rev. Nucl. Part. Sci., 68, 339 (2018)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.