Green-Schwarz Mechanism for String Dualities

Recently, it has been shown that the minimum number of gauge invariant couplings for B-field, metric and dilaton at order α′3 is 872. These couplings, in a particular scheme, appear in 55 different structures. In this paper, up to an overall factor, we fix all parameters in type II supertirng theories by requiring the reduction of the couplings on a circle to be invariant under T-duality transformations. We find that there are 445 non-zero couplings which appear in 15 different structures. The couplings are fully consistent with the partial couplings that have been found in the literature by the four-point S-matrix element and by the non-linear Sigma model methods.

Section: Jhep02(2021)157mentioning

confidence: 99%

Effective action of type II superstring theories at order α′3: NS-NS couplings

Garousi

2021

“…Let us emphasize that our results do not imply that there is any problem with the duality symmetry in the compactified theory. Indeed, restricting to backgrounds with d commuting isometries, it should be possible to express everything in an O(d, d) covariant way, as was done at order α in [36] (see also [37,38]). Indeed, this could be very useful to fix the form of higher α -corrections, for example T-duality on a circle has been recently argued to fix the form of the string effective action uniquely to order α 3 [39,40].…”

Section: Jhep04(2021)013mentioning

confidence: 99%

“…Of course, if one compactifies on T d the O(d, d) symmetry should be there to all orders in α [2]. It would be interesting to try to use it to constrain the form of higher α corrections using similar tools to those used here (see [37,38] for a somewhat different approach). Note that in our analysis we have allowed for a general modification of the double Lorentz transformations.…”

Section: Jhep04(2021)013 8 Conclusionmentioning

confidence: 99%

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

Hronek

Wulff

2021

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.

“…SinceΛ is constant the anomalous Lorentz transformation is trivial in this gauge, and also the α -corrections to T-duality will be trivial. 24 (Note that while it is possible to avoid corrections for a single T-duality it is not possible in general for more than one T-duality, as shown in [43].) In [42] this observation was used to obtain the α -corrections to the Tduality rules in the scheme of Bergshoeff and de Roo (BR) [44,45].…”

Section: T-duality and Tst Transformationsmentioning

confidence: 99%

The first α′-correction to homogeneous Yang-Baxter deformations using O(d, d)

Borsato

López

Wulff

2020

We use the O(d, d)-covariant formulation of supergravity familiar from Double Field Theory to find the first α -correction to (unimodular) homogeneous Yang-Baxter (YB) deformations of the bosonic string. A special case of this result gives the α -correction to TsT transformations. In a suitable scheme the correction comes entirely from an induced anomalous double Lorentz transformation, which is needed to make the two vielbeins obtained upon the YB deformation equal. This should hold more generally, in particular for abelian and non-abelian T-duality, as we discuss.