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Symmetries of non-maximal supergravities with higher-derivative corrections

Yi Pang, Robert J. Saskowski

Abstract

We consider hidden symmetries arising from U-duality in the dimensional reduction of non-maximal higher-derivative supergravities to three dimensions. In particular, we consider the $G_{2(2)}$ symmetry of minimal five-dimensional supergravity and the $O(d+p+1,d+1)$ symmetry of bosonic and heterotic string theory on $T^d$. Using a group theory argument, we show that the higher-derivative corrections explicitly break all hidden symmetry enhancements. As special cases, this also implies that higher-derivative corrections prevent the symmetry enhancement to $SL(3,\mathbb R)$ in pure five-dimensional gravity and $O(4,4)$ in the STU model.

Symmetries of non-maximal supergravities with higher-derivative corrections

Abstract

We consider hidden symmetries arising from U-duality in the dimensional reduction of non-maximal higher-derivative supergravities to three dimensions. In particular, we consider the symmetry of minimal five-dimensional supergravity and the symmetry of bosonic and heterotic string theory on . Using a group theory argument, we show that the higher-derivative corrections explicitly break all hidden symmetry enhancements. As special cases, this also implies that higher-derivative corrections prevent the symmetry enhancement to in pure five-dimensional gravity and in the STU model.
Paper Structure (8 sections, 70 equations, 2 figures, 1 table)

This paper contains 8 sections, 70 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. $G_{2(2)}$ U-duality
  3. Group structure of $G_{2(2)}$
  4. Two-derivative $G_{2(2)}$ symmetry
  5. Four-derivative $G_{2(2)}$ symmetry
  6. $SL(3,\mathbb R)$ symmetry in pure gravity
  7. $O(d+p+1,d+1)$ U-duality
  8. Discussion

Figures (2)

  • Figure 1: Dynkin diagram of $\mathfrak g_{2(2)}$.
  • Figure 2: Root system of $\mathfrak g_{2(2)}$.