Double Field Theory with matter and the generalized Bergshoeff-de Roo identification

TL;DR

This paper explores higher-derivative corrections in Double Field Theory with matter, showing that these corrections can be removed at the supergravity level, implying they only affect the vacuum Lagrangian.

Contribution

It generalizes the scalar field-perfect fluid correspondence to Double Field Theory with matter, revealing that higher-derivative corrections are trivialized at the supergravity level.

Findings

Higher-derivative corrections are removable via field redefinitions.

The sf-pf Lagrangian remains uncorrected to all orders in supergravity.

$\alpha'$-corrections only modify the vacuum Lagrangian.

Abstract

The scalar field-perfect fluid (sf-pf) correspondence shows that the energy-momentum tensor of a scalar field is in correspondence with the dynamics of a perfect fluid. In this work we generalize this concept to study the higher-derivative structure of Double Field Theory with statistical matter. Using the generalized Bergshoeff-de Roo identification we find nontrivial higher-derivative corrections for the generalized scalar field Lagrangian. However, these contributions are removed to any desired order using field redefinitions at the supergravity level. By virtue of the generalized sf-pf correspondence we obtain the higher-derivative dynamics for the perfect fluid in the double geometry, which is also trivialized at the supergravity level. These results imply that the well-known $\alpha'$-corrections obtained by this procedure only correct the effective vacuum Lagrangian, while the sf-pf Lagrangian coupled to the supergravity background remains uncorrected to all orders. Our findings apply for a general (Bosonic-Heterotic-Type II-HSZ) supergravity background.