Yang–Baxter invariance of the Nappi–Witten model

Hideki Kyono,Kentaroh Yoshida

doi:10.1016/j.nuclphysb.2016.02.017

Abstract

We study Yang–Baxter deformations of the Nappi–Witten model with a prescription invented by Delduc, Magro and Vicedo. The deformations are specified by skew-symmetric classical r-matrices satisfying (modified) classical Yang–Baxter equations. We show that the sigma-model metric is invariant under arbitrary deformations (while the coefficient of B-field is changed) by utilizing the most general classical r-matrix. Furthermore, the coefficient of B-field is determined to be the original value from the requirement that the one-loop β-function should vanish. After all, the Nappi–Witten model is the unique conformal theory within the class of the Yang–Baxter deformations preserving the conformal invariance.

Highlights

The Yang–Baxter sigma-model description, which was originally proposed by Klimcik [1], is a systematic way to consider integrable deformations of 2D non-linear sigma models
The deformations are specified by skew-symmetric classical r-matrices satisfying the modified classical Yang–Baxter equation
Yang–Baxter deformations of the AdS5 × S5 superstring can be studied with the modified classical Yang–Baxter equation (mCYBE)

Summary

Introduction

The Yang–Baxter sigma-model description, which was originally proposed by Klimcik [1], is a systematic way to consider integrable deformations of 2D non-linear sigma models. Yang–Baxter deformations of the AdS5 × S5 superstring can be studied with the mCYBE [4] and the CYBE [5] For the former case, the metric and B-field are derived in [6] and the. Yoshida / Nuclear Physics B 905 (2016) 242–250 full background has recently been studied in [7,8] For the latter case, classical r-matrices are identified with solutions of type IIB supergravity including γ -deformations of S5 [9,10] and gravity duals of non-commutative gauge theories [11,12], in a series of works [13,14,15,16,17,18,19,20] (for a short summary, see [21]). The Nappi–Witten model is the unique conformal theory within the class of the Yang–Baxter deformations preserving the conformal invariance (i.e., Yang–Baxter invariance)

Nappi–Witten model

The overall factor of

A Yang–Baxter deformed classical action

The general deformed background

Yang–Baxter deformations and conformal invariance

Conclusion and discussion