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Petr Hořava1, Christopher J Mogni1

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We explored nonequilibrium quantum systems using the Schwinger-Keldysh method and large-N expansion. This reveals a refined topological genus expansion for dual string theories, separating world sheets into classical and quantum components.

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Area of Science:

  • Theoretical Physics
  • Quantum Field Theory
  • String Theory

Background:

  • Non-equilibrium quantum systems with matrix degrees of freedom are challenging to analyze.
  • The Schwinger-Keldysh formulation provides a framework for studying such systems out of equilibrium.
  • Topological expansions are crucial for understanding the properties of quantum field theories and their duals.

Purpose of the Study:

  • To perform a large-N expansion within the Schwinger-Keldysh formulation for matrix-valued nonequilibrium quantum systems.
  • To investigate universal features of the anticipated dual string theory.
  • To explore a refined topological genus expansion associated with the Schwinger-Keldysh time contour.

Main Methods:

  • Application of the large-N expansion technique.
  • Utilizing the Schwinger-Keldysh formulation for nonequilibrium quantum systems.
  • Performing a Keldysh rotation to analyze world sheet structures.

Main Results:

  • A significant refinement of the topological genus expansion was discovered.
  • The future time instant in the Schwinger-Keldysh contour is associated with a distinct world sheet genus expansion.
  • Post-Keldysh rotation, world sheets naturally decompose into classical and quantum parts.

Conclusions:

  • The study provides new insights into the structure of dual string theories for nonequilibrium quantum systems.
  • The refined genus expansion offers a more detailed understanding of the Schwinger-Keldysh formalism.
  • The decomposition of world sheets highlights fundamental aspects of quantum dynamics in these systems.