Abstract
We study the ground state instability of a strongly coupled QFT with the z=2 Schrödinger symmetry in a constant electric field using probe branes holography. The system is N_f{mathcal {N}}=2 hypermultiplet fermions at zero charge density in the supergravity Schrödinger background. We show that the instability occurs due to Schwinger-like effect and an insulator state will undergo a transition to a conductor state. We calculate the decay rate of instability and pair production probability by using the gauge / gravity duality. At zero temperature for massive fermions, we suggest that the instability occurs if the critical electric field is larger than the confining force between fermions, which is proportional to an effective mass. We demonstrate that, at zero temperature, the Schrödinger background simulates the role of a crystal lattice for massive particles. We also show that at finite ’t Hooft coupling for particles with a mass higher than frac{sqrt{lambda }}{pi beta }, in this background, instability does not occur, no matter how large the external electric field is, meaning that we have a perfect insulator. Moreover, we derive Euler–Heisenberg effective Lagrangian for the non-relativistic strongly correlated quantum theory from probe branes holography in Schrödinger spacetime.
Highlights
E Schrödinger background simulates the role of a crystal lattice for massive particles
By using null Melvin twist(N M T ) transformations [12], or T sT [13] or the Ad S geometry solution of the type I I B supergravity, which has a dual QFT with conformal symmetry, the spacetime can be generated with the Schrödinger symmetry which has a dual non-relativistic QFT
We study the breakdown of the vacuum of strongly coupled systems with the z = 2 Schrödinger symmetry at the presence of an external electric field via probe branes holography
Summary
Let embed the D7 branes in 10 dimension space–time as follows : The dual theory would live on intersection of D3 and D7 branes at r = 0 which is denoted by the (x+, x−, x) As it clear, there is a O(2) symmetry in (χ , θ ) direction which clarify the shape of D7 branes relative to the background. For the non-zero electric field on the probe branes, we have another class of embedding [17,20] which known as Minkowski embedding with the horizon (MEH). At the non-zero electric field, the probe D-branes would have the world-volume horizon which, in general, differs from the background event horizon. We investigate the instability which causes the phase transitions in schrödinger geometry from type IIB supergravity
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