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Line Operators in Chern-Simons-Matter Theories and Bosonization in Three Dimensions.

Barak Gabai1, Amit Sever2, De-Liang Zhong2

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Summary

We analyze Chern-Simons theories with fundamental matter, focusing on mesonic line operators. Both bosonic and fermionic theories exhibit identical evolution equations and boundary operator spectra, simplifying theoretical analysis.

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Area of Science:

  • High-energy physics
  • Quantum field theory
  • String theory

Background:

  • Chern-Simons theories are crucial in understanding topological phases of matter and quantum gravity.
  • Mesonic line operators, like Wilson lines, are fundamental to probing these theories.
  • Understanding their behavior at large N (number of colors) and finite 't Hooft coupling is key.

Purpose of the Study:

  • To classify conformal line operators in Chern-Simons theories with fundamental bosonic or fermionic matter.
  • To determine the spectrum of conformal dimensions and transverse spins for boundary operators.
  • To establish a framework for uniquely determining operator expectation values.

Main Methods:

  • Analysis of mesonic line operators along arbitrary smooth paths.
  • Derivation of first-order chiral evolution equations for these operators.
  • Bootstrapping techniques to calculate operator properties, such as two-point functions.

Main Results:

  • Classification of conformal line operators and their boundary operator spectra.
  • Identification of identical chiral evolution equations for both bosonic and fermionic matter.
  • Demonstration that these equations and spectra uniquely determine operator expectation values.

Conclusions:

  • The behavior of line operators in Chern-Simons theories with fundamental bosons or fermions is unified.
  • The derived evolution equations and spectra provide a powerful tool for theoretical calculations.
  • This work simplifies the study of complex quantum field theories.