Abstract:
We discuss a nonperturbative formulation of the Sachdev–Ye–Kitaev (SYK) model. The partition function of the model can be represented as a well-defined functional integral over Grassmann variables in Euclidean time, but it diverges after the transformation to fermion bilocal fields. We note that the generating functional of the SYK model in real time is well defined even after the transformation to bilocal fields and can be used for nonperturbative investigations of its properties. We study the SYK model in zero dimensions, evaluate its large-NN expansion, and investigate phase transitions.
Citation:
I. Ya. Aref'eva, I. V. Volovich, “Notes on the SYK model in real time”, TMF, 197:2 (2018), 296–310; Theoret. and Math. Phys., 197:2 (2018), 1650–1662
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\by I.~Ya.~Aref'eva, I.~V.~Volovich
\paper Notes on the~SYK model in real time
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\yr 2018
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\pages 296--310
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\jour Theoret. and Math. Phys.
\yr 2018
\vol 197
\issue 2
\pages 1650--1662
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Linking options:
https://www.mathnet.ru/eng/tmf9533
https://doi.org/10.4213/tmf9533
https://www.mathnet.ru/eng/tmf/v197/i2/p296
This publication is cited in the following 11 articles:
V. M. Busovikov, V. Zh. Sakbaev, “Sobolev spaces of functions on a Hilbert space endowed with a translation-invariant measure and approximations of semigroups”, Izv. Math., 84:4 (2020), 694–721
V. V. Belokurov, E. T. Shavgulidze, “Schwarzian functional integrals calculus”, J. Phys. A-Math. Theor., 53:48 (2020), 485201
I. Aref'eva, I. Volovich, “Gas of baby universes in jt gravity and matrix models”, Symmetry-Basel, 12:6 (2020), 975
I. Ya. Aref'eva, I. V. Volovich, “Quasi-averages in Random Matrix Models”, Proc. Steklov Inst. Math., 306 (2019), 1–8
V. V. Belokurov, E. T. Shavgulidze, “Polar decomposition of the Wiener measure: Schwarzian theory versus conformal quantum mechanics”, Theoret. and Math. Phys., 200:3 (2019), 1324–1334
V. V. Zharinov, “Hamiltonian operators with zero-divergence constraints”, Theoret. and Math. Phys., 200:1 (2019), 923–937
I. Ya. Aref'eva, I. V. Volovich, M. A. Khramtsov, “Revealing nonperturbative effects in the SYK model”, Theoret. and Math. Phys., 201:2 (2019), 1585–1605
I. Aref'eva, M. Khramtsov, M. Tikhanovskaya, I. Volovich, “Replica-nondiagonal solutions in the syk model”, J. High Energy Phys., 2019, no. 7, 113
I. Aref'eva, I. Volovich, “Spontaneous symmetry breaking in fermionic random matrix model”, J. High Energy Phys., 2019, no. 10, 114
Aref'eva I., Khramtsov M., Tikhanovskaya M., Xxth International Seminar on High Energy Physics (Quarks-2018), Epj Web of Conferences, 191, eds. Volkova V., Zhezher Y., Levkov D., Rubakov V., Matveev V., E D P Sciences, 2018
Aref'eva I., Khramtsov M., Tikhanovskaya M., Volovich I., Xxth International Seminar on High Energy Physics (Quarks-2018), Epj Web of Conferences, 191, eds. Volkova V., Zhezher Y., Levkov D., Rubakov V., Matveev V., E D P Sciences, 2018
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