\(O(D, D)\) and the string \(\alpha '\) expansion: an obstruction

DOI10.1007/JHEP04(2021)013zbMATH Open1462.83073arXiv2012.13410OpenAlexW3113611557WikidataQ125973242 ScholiaQ125973242MaRDI QIDQ2032458

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Publication date: 11 June 2021

Published in: (Search for Journal in Brave)

Abstract: Double Field Theory (DFT) is an attempt to make the O(d,d) T-duality symmetry of string theory manifest, already before reducing on a d-torus. It is known that supergravity can be formulated in an O(D,D) covariant way, and remarkably this remains true to the first order in $alph{a}^{\prime }$. We set up a systematic way to analyze O(D,D) invariants, working order by order in fields, which we carry out up to order $alpha{\text{'}}^3$. At order $alph{a}^{\prime }$ we recover the known Riemann squared invariant, while at order $alpha{\text{'}}^2$ we find no independent invariant. This is compatible with the $alph{a}^{\prime }$ expansion in string theory. However, at order $alpha{\text{'}}^3$ we show that there is again no O(D,D) invariant, in contradiction to the fact that all string theories have a quartic Riemann invariant with coefficient proportional to $zeta(3)$. We conclude that DFT and similar frameworks cannot capture the full $alph{a}^{\prime }$ expansion in string theory.

Full work available at URL: https://arxiv.org/abs/2012.13410

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