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Twisted Holographic Superfluids in External Magnetic Field

Jovan Potrebić, Dragoljub Gočanin

Abstract

Among various applications of the AdS/CFT correspondence in condensed matter physics of particular importance is the realization of the phase transition between the normal and superconducting phase in a holographic QFT. After seminal papers on holographic superconductors that introduced the basic setup, one of the main lines of development focused on capturing the Meissner effect with all the relevant parameters, which requires inclusion of an external magnetic field. Although a complete holographic description of a superconductor is still lacking, the basic elements of the gravitational systems dual to what can be most accurately characterized as a charged superfluid have been established. Using holographic setups for describing three- and four-dimensional superconductors, we investigate the effect of noncommutative twist deformation of bulk fields on the phase transition parameters, such as the critical magnetic field and condensate. In a wider context, our results represent a first systematic attempt to elucidate the role of noncommutative gauge field theory as part of the bulk description of condensed matter systems.

Twisted Holographic Superfluids in External Magnetic Field

Abstract

Among various applications of the AdS/CFT correspondence in condensed matter physics of particular importance is the realization of the phase transition between the normal and superconducting phase in a holographic QFT. After seminal papers on holographic superconductors that introduced the basic setup, one of the main lines of development focused on capturing the Meissner effect with all the relevant parameters, which requires inclusion of an external magnetic field. Although a complete holographic description of a superconductor is still lacking, the basic elements of the gravitational systems dual to what can be most accurately characterized as a charged superfluid have been established. Using holographic setups for describing three- and four-dimensional superconductors, we investigate the effect of noncommutative twist deformation of bulk fields on the phase transition parameters, such as the critical magnetic field and condensate. In a wider context, our results represent a first systematic attempt to elucidate the role of noncommutative gauge field theory as part of the bulk description of condensed matter systems.
Paper Structure (13 sections, 87 equations, 5 figures)

This paper contains 13 sections, 87 equations, 5 figures.

Table of Contents

  1. Introduction
  2. NC Field Theory
  3. Seiberg-Witten Gauge Field Theory
  4. $3$D Twisted Holographic Superfluid in an External Magnetic Field
  5. Numerical Method and Results
  6. 4D Twisted Holographic Superfluid in an External Magnetic Field
  7. Analytical method
  8. Numerical method
  9. Conclusion and Outlook
  10. Acknowledgement
  11. NC expansions
  12. NC gauge field equation
  13. Holographic renormalization

Figures (5)

  • Figure 1: Zero-node and one-node modes of the scalar field with $\mathcal{O}_2$ turned on, shown for both the NC and the commutative cases. The magnetic charge parameter is fixed at $h=0.5$.
  • Figure 2: Allowed values of the magnetic field $B$ and temperature $T$ for condensation to occur, shown for both the NC and the commutative cases.
  • Figure 3: Temperature dependence of the vacuum expectation value of the $\Delta=2$ operator shown for both the NC and the commutative case.
  • Figure 4: Analytical results for temperature dependence of the critical magnetic field for different values of NC parameter $\alpha^2\theta_{xy}={\mathchar'26\mkern-9muk}$.
  • Figure 5: Numerical results for temperature dependence of the critical magnetic field for different values of the NC parameter $\alpha^2\theta_{xy}={\mathchar'26\mkern-9muk}$.