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The effective action of Double Field Theory

Gerardo Aldazabal, Walter Baron, Diego Marques, Carmen Nunez

TL;DR

This work demonstrates that a generalized Scherk–Schwarz reduction of Double Field Theory on a twisted double torus precisely reproduces the bosonic electric sector of four‑dimensional gauged $\mathcal{N}=4$ supergravity, identifying the 4D gaugings with generalized fluxes $F_{ABC}$ encoded by the internal twist. By extending the internal duality group to $O(D,D+N)$ and exploring rescaling gaugings, the authors show how to realize the full set of electric gaugings within DFT, including additional vectors. The analysis also interprets the internal backgrounds as (non)geometric flux backgrounds connected by T‑duality, and offers Type IIB orientifold and heterotic interpretations that relate the fluxes to conventional string backgrounds and tadpole conditions. The results provide a higher‑dimensional origin for the electric gaugings in $\mathcal{N}=4$ gauged supergravity and highlight the role of the strong constraint and generalized geometry in this correspondence.

Abstract

We perform a generalized Scherk-Schwarz dimensional reduction of Double Field Theory on a twisted double torus. The four dimensional effective action is shown to exactly reproduce the bosonic electric sector of gauged N = 4 supergravity. We present explicit expressions for the gaugings in terms of the twists, and analyze the associated string backgrounds. This framework provides a higher dimensional origin of the gaugings in terms of generalized fluxes.

The effective action of Double Field Theory

TL;DR

This work demonstrates that a generalized Scherk–Schwarz reduction of Double Field Theory on a twisted double torus precisely reproduces the bosonic electric sector of four‑dimensional gauged supergravity, identifying the 4D gaugings with generalized fluxes encoded by the internal twist. By extending the internal duality group to and exploring rescaling gaugings, the authors show how to realize the full set of electric gaugings within DFT, including additional vectors. The analysis also interprets the internal backgrounds as (non)geometric flux backgrounds connected by T‑duality, and offers Type IIB orientifold and heterotic interpretations that relate the fluxes to conventional string backgrounds and tadpole conditions. The results provide a higher‑dimensional origin for the electric gaugings in gauged supergravity and highlight the role of the strong constraint and generalized geometry in this correspondence.

Abstract

We perform a generalized Scherk-Schwarz dimensional reduction of Double Field Theory on a twisted double torus. The four dimensional effective action is shown to exactly reproduce the bosonic electric sector of gauged N = 4 supergravity. We present explicit expressions for the gaugings in terms of the twists, and analyze the associated string backgrounds. This framework provides a higher dimensional origin of the gaugings in terms of generalized fluxes.

Paper Structure

This paper contains 17 sections, 134 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Review of Double Field Theory
  3. Scherk-Schwarz dimensional reduction
  4. The effective action of DFT and gauged ${\cal N} = 4$ supergravity
  5. Review of gauged ${\cal N} = 4$ supergravity
  6. Comparison with the effective action of DFT
  7. The $O(6,6)$ sector
  8. Including vectors
  9. Rescaling symmetry gaugings
  10. (Non)geometric string backgrounds
  11. Reduction on a twisted double torus
  12. Generalized fluxes and superstring compactifications
  13. Type I interpretation
  14. Conclusions
  15. Appendix
  16. ...and 2 more sections

Figures (1)

  • Figure 1: From string supergravity to four dimensional ${\cal N}=4$ gauged supergravity.