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On Two-Loop Effective Action of 2D Sigma Model

P. V. Akacevich, A. V. Ivanov

Abstract

In this paper, we study two-loop contribution to the effective action of a two-dimensional sigma model. We derive a new formula, which can be applicable to a regularization of general type. As examples, we obtain known results for dimensional regularization and investigate new types of cutoff one. Also, we discuss non-local contributions and restrictions on the regularization.

On Two-Loop Effective Action of 2D Sigma Model

Abstract

In this paper, we study two-loop contribution to the effective action of a two-dimensional sigma model. We derive a new formula, which can be applicable to a regularization of general type. As examples, we obtain known results for dimensional regularization and investigate new types of cutoff one. Also, we discuss non-local contributions and restrictions on the regularization.
Paper Structure (7 sections, 44 equations, 3 figures)

This paper contains 7 sections, 44 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Sigma model
  3. Two-loop divergent part
  4. Applications
  5. Dimensional regularization
  6. Cutoff regularization
  7. Conclusion

Figures (3)

  • Figure 1: Diagram technique elements.
  • Figure 2: Diagram representation of $W_{a}[B]$.
  • Figure 3: Diagram representation of $W_{b}[B]$.