Abstract
We study the thermodynamic properties of a two-site coupled complex Sachdev-Ye-Kitaev (SYK) model in the large $N$ limit by solving the saddle-point Schwinger-Dyson (SD) equations. We find that its phase diagram is richer than in the Majorana case. In the grand canonical ensemble, we identify a region of small chemical potential, and weak coupling between the two SYKs, for which two first order thermodynamic phase transitions occur as a function of temperature. First, we observe a transition from a cold wormhole phase to an intermediate phase that may correspond to a charged wormhole. For a higher temperature, there is another first order transition to the black hole phase. As in the Majorana case, the low temperature wormhole phase is gapped and, for sufficiently large coupling between the two complex SYK, or chemical potential, the first order transitions become crossovers. The total charge is good indicator to study the phase diagram of the model: it is zero in the cold wormhole phase and jumps discontinuously at the temperatures at which the transitions take place. Based on the approximate conformal symmetry of the ground state, expected to be close to a thermofield double state, we identify the effective low energy action of the model. It is a generalized Schwarzian action with $SL(2,R)\times U(1)$ symmetry with an additional potential and a extra degree of freedom related to the charge. In the large $N$ limit, results from this low energy action are consistent with those from the solution of the SD equations. Our findings are a preliminary step towards the characterization of traversable wormholes by its field theory dual, a strongly interacting fermionic system with charger, that is easier to model experimentally.
Highlights
Traversable wormholes are classical solutions of Einstein’s equations representing shortcuts in the geometry that may allow teletransportation among distant regions of space-time
In order to further elucidate the phase diagram of the model, especially the nature of the intermediate phase, we study the energy gap and the charge Q related to the global Uð1Þ symmetry mentioned in previous sections
We have found that, with great accuracy, Ef0 ≈ −μ, which implies that Eg defined in the previous section to characterize the energy gap between the ground state and first excited state in the cold wormhole phase has a simple relation with μ, Eg 1⁄4 E0 − μ where E0 > μ only depends on κ and J and it is a more accurate indicator of the wormhole phase
Summary
Traversable wormholes are classical solutions of Einstein’s equations representing shortcuts in the geometry that may allow teletransportation among distant regions of space-time. The high temperature limit of the two-site SYK model [12], dual to two black hole backgrounds, shares most of these features. The low energy excitations are discrete even in the thermodynamics limit This is consistent with the observation of a transition in level statistics [45], from integrable in the wormhole phase to quantum chaotic in the black hole region. We study a generalization of the two-site SYK model with Majorana fermions, dual of the eternal traversable wormhole [12], to complex fermions with an extra Uð1Þ symmetry. For small chemical potential and low temperature, it has no charge, which is another feature of the traversable wormhole dual to the Majorana two-site SYK model [12].
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
