O(D, D) and the string α′ expansion: an obstruction

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 α′. 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 α′3. At order α′ we recover the known Riemann squared invariant, while at order α′2 we find no independent invariant. This is compatible with the α′ expansion in string theory. However, at order α′3 we show that there is again no O(D, D) invariant, in contradiction to the fact that all string theories have quartic Riemann terms with coefficient proportional to ζ (3). We conclude that DFT and similar frameworks cannot capture the full α′ expansion in string theory.

Cosmology at the top of the α′ tower

“…, O(d, d) is meant to be shorthand notation for O(d, d, R). 2 An alternative approach to finding α corrections by taking advantage of T-duality has been developed thanks to double field theory [19][20][21][22][23][24][25][26][27][28][29][30] (see also [31,32]). This benefits from being a spacetime-covariant approach, which does not have to rely on the assumptions of homogeneity and isotropy.…”

A master exceptional field theory

“…Our construction is limited to the bosonic two-derivative sector. The tree-level string theory effective action is expected to admit the continuous Spin + (10, 10) symmetry to all orders in α [149], so one can possibly construct higher-derivative couplings in DFT [150][151][152][153][154], see however [155] for a recent puzzle in this context. On the contrary, U-duality is a symmetry of the quantum theory [156], and there is no higher-derivative coupling with the continuous symmetry E 11 (R).…”

Supersymmetry, T-duality and heterotic α′-corrections

“…At tree level, these terms are proportional to the transcendental coefficient ζ (3). The analysis of the higher-derivative terms is technically more challenging but also more interesting, since further duality covariant structures, or even a more drastic change of scheme, seem to be necessary as advocated in [81].…”