On the large \(N\) limit of Schwinger-Dyson equations of a rank-3 tensor field theory. (English) Zbl 1420.81024
Summary: We analyze in this paper the large \(N\) limit of the Schwinger-Dyson equations in a rank-3 tensor quantum field theory, which are derived with the help of Ward-Takahashi identities. In order to have a well-defined large \(N\) limit, appropriate scalings in powers of \(N\) for the various terms present in the action are explicitly found. A perturbative check of our results is done up to second order in the coupling constant.
©2019 American Institute of Physics
©2019 American Institute of Physics
MSC:
| 81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |
| 81T18 | Feynman diagrams |
| 81T27 | Continuum limits in quantum field theory |
| 81T15 | Perturbative methods of renormalization applied to problems in quantum field theory |
| 60B20 | Random matrices (probabilistic aspects) |
References:
| [1] | Gurau, R., Colored group field theory, Commun. Math. Phys., 304, 69 (2011) · Zbl 1214.81170 · doi:10.1007/s00220-011-1226-9 |
| [2] | Dartois, S.; Rivasseau, V.; Tanasa, A., The 1/N expansion of multi-orientable random tensor models, Ann. Henri Poincare, 15, 965 (2014) · Zbl 1288.81070 · doi:10.1007/s00023-013-0262-8 |
| [3] | Carrozza, S.; Tanasa, A., O(N) random tensor models, Lett. Math. Phys., 106, 1531 (2016) · Zbl 1362.83010 · doi:10.1007/s11005-016-0879-x |
| [4] | Benedetti, D., Carrozza, S., Gurau, R., and Kolanowski, M., “The 1/N expansion of the symmetric traceless and the antisymmetric tensor models in rank three,“ e-print <ext-link ext-link-type=”arxiv“ xlink:href=”http://arxiv.org/abs/1712.00249”>arXiv:1712.00249. · Zbl 1425.81071 |
| [5] | Carrozza, S., Large N limit of irreducible tensor models: O(N) rank-3 tensors with mixed permutation symmetry, J. High Energy Phys., 06, 039 (2018) · Zbl 1395.81155 · doi:10.1007/JHEP06(2018)039 |
| [6] | Klebanov, I. R.; Tarnopolsky, G., On large N limit of symmetric traceless tensor models, J. High Energy Phys., 10, 037 (2017) · Zbl 1383.81239 · doi:10.1007/JHEP10(2017)037 |
| [7] | Tanasa, A., The multi-orientable random tensor model, a review, Symmetry Integrability Geom.: Methods Appl., 12, 056 (2016) · Zbl 1385.60011 · doi:10.3842/sigma.2016.056 |
| [8] | Bonzom, V., Large N limits in tensor models: Towards more universality classes of colored triangulations in dimension d ≥ 2, Symmetry Integrability Geom. Methods Appl., 12, 073 (2016) · Zbl 1343.05059 · doi:10.3842/SIGMA.2016.073 |
| [9] | Sachdev, S.; Ye, J., Gapless spin fluid ground state in a random, quantum Heisenberg magnet, Phys. Rev. Lett., 70, 3339 (1993) · doi:10.1103/physrevlett.70.3339 |
| [10] | Kitaev, A., “A simple model of quantum holography,” Talks at KITP, April 7 and May 27, 2015. |
| [11] | Witten, E., An SYK-like model without disorder · Zbl 1509.81564 |
| [12] | Klebanov, I. R.; Tarnopolsky, G., Uncolored random tensors, melon diagrams, and the Sachdev-Ye-Kitaev models, Phys. Rev, 95, 046004 (2017) · doi:10.1103/PhysRevD.95.046004 |
| [13] | Gurau, R., The complete 1/N expansion of a SYK-like tensor model, Nucl. Phys., B916, 386 (2017) · Zbl 1356.81180 · doi:10.1016/j.nuclphysb.2017.01.015 |
| [14] | Bonzom, V.; Lionni, L.; Tanasa, A., Diagrammatics of a colored SYK model and of an SYK-like tensor model, leading and next-to-leading orders, J. Math. Phys., 58, 052301 (2017) · Zbl 1364.81267 · doi:10.1063/1.4983562 |
| [15] | Bonzom, V.; Nador, V.; Tanasa, A., Diagrammatic proof of the large N melonic dominance in the SYK model · Zbl 1428.81115 |
| [16] | Carrozza, S.; Pozsgay, V., SYK-like tensor quantum mechanics with Sp(N) symmetry, Nucl. Phys. B, 941, 28-52 (2019) · Zbl 1415.81131 · doi:10.1016/j.nuclphysb.2019.02.012 |
| [17] | Klebanov, I. R.; Popov, F.; Tarnopolsky, G., TASI lectures on large N tensor models |
| [18] | Pérez-Sánchez, C. I., The full Ward-Takahashi identity for colored tensor models, Commun. Math. Phys., 358, 589 (2018) · Zbl 1387.83034 · doi:10.1007/s00220-018-3103-2 |
| [19] | Pascalie, R.; Pérez-Sánchez, C. I.; Wulkenhaar, R., Correlation functions of U(N)-tensor models and their Schwinger-Dyson equations, Ann. Inst. Henri Poincaré D: Comb. Phys. Interact. · Zbl 1420.81024 |
| [20] | Ben Geloun, J.; Rivasseau, V., A renormalizable 4-dimensional tensor field theory, Commun. Math. Phys., 318, 69 (2013) · Zbl 1261.83016 · doi:10.1007/s00220-012-1549-1 |
| [21] | Carrozza, S., Tensorial methods and renormalization in group field theories (2013) · Zbl 1338.81004 · doi:10.1007/978-3-319-05867-2 |
| [22] | Eichhorn, A.; Koslowski, T.; Lumma, J.; Pereira, A. D., Towards background independent quantum gravity with tensor models · Zbl 1477.83026 |
| [23] | Eichhorn, A.; Koslowski, T.; Pereira, A. D., Status of background-independent coarse-graining in tensor models for quantum gravity, Universe, 5, 53 (2019) · doi:10.3390/universe5020053 |
| [24] | Disertori, M.; Gurau, R.; Magnen, J.; Rivasseau, V., Vanishing of beta function of non commutative \(\Phi_4^4\) theory to all orders, Phys. Lett. B, 649, 95 (2007) · Zbl 1248.81253 · doi:10.1016/j.physletb.2007.04.007 |
| [25] | Grosse, H.; Wulkenhaar, R., Self-dual noncommutative \(ϕ^4\)-theory in four dimensions is a non-perturbatively solvable and non-trivial quantum field theory, Commun. Math. Phys., 329, 1069 (2014) · Zbl 1305.81129 · doi:10.1007/s00220-014-1906-3 |
| [26] | Samary, D. O., Closed equations of the two-point functions for tensorial group field theory, Class. Quantum Gravity, 31, 185005 (2014) · Zbl 1300.81058 · doi:10.1088/0264-9381/31/18/185005 |
| [27] | Lahoche, V.; Samary, D. O., Ward identity violation for melonic \(T^4\)-truncation, Nucl. Phys. B, 940, 190-213 (2019) · Zbl 1409.83068 · doi:10.1016/j.nuclphysb.2019.01.005 |
| [28] | Krajewski, T.; Toriumi, R., Exact renormalisation group equations and loop equations for tensor models, Symmetry Integrability Geom. Methods Appl., 12, 068 (2016) · Zbl 1343.81179 · doi:10.3842/SIGMA.2016.068 |
| [29] | Perez-Sanchez, C. I., Surgery in colored tensor models, J. Geom. Phys., 120, 262 (2017) · Zbl 1376.83021 · doi:10.1016/j.geomphys.2017.06.009 |
| [30] | Lins, S.; Mulazzani, M., Blobs and flips on gems, J. Knot Theory Ramifications, 15, 1001-1035 (2006) · Zbl 1113.57009 · doi:10.1142/s0218216506004907 |
| [31] | Cassali, R.; Cristofori, P., Cataloguing PL 4-manifolds by gem-complexity, Electron. J. Combin., 22, 4, P4.25 (2015) · Zbl 1332.57020 |
| [32] | Gurau, R.; Ryan, J. P., Colored tensor models: A review, Symmetry Integrability Geom.: Methods Appl., 8, 020 (2012) · Zbl 1242.05094 · doi:10.3842/sigma.2012.020 |
| [33] | Gurau, R.; Schaeffer, G., Regular colored graphs of positive degree, Ann. l’Institut Henri Poincaré D, 3, 257-320 (2016) · Zbl 1352.05090 · doi:10.4171/aihpd/29 |
| [34] | Gurau, R., Random Tensors (2017) · Zbl 1371.81007 |
| [35] | Perez-Sanchez, C. I., Graph calculus and the disconnected-boundary Schwinger-Dyson equations of quartic tensor field theories · Zbl 1457.81090 |
| [36] | Ousmane Samary, D.; Pérez-Sánchez, C. I.; Vignes-Tourneret, F.; Wulkenhaar, R., Correlation functions of a just renormalizable tensorial group field theory: The melonic approximation, Class. Quantum Gravity, 32, 175012 (2015) · Zbl 1327.83122 · doi:10.1088/0264-9381/32/17/175012 |
| [37] | Panzer, E.; Wulkenhaar, R., Lambert-W solves the noncommutative \(Φ^4\)-model · Zbl 1436.81091 |
| [38] | Pascalie, R., A solvable tensor field theory · Zbl 1433.81127 |
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