On the curious spectrum of duality invariant higher-derivative gravity

Abstract

We analyze the spectrum of the exactly duality and gauge invariant higher-derivative double field theory. While this theory is based on a chiral CFT and does not correspond to a standard string theory, our analysis illuminates a number of issues central in string theory. The full quadratic action is rewritten as a two-derivative theory with additional fields. This allows for a simple analysis of the spectrum, which contains two massive spin-2 ghosts and massive scalars, in addition to the massless fields. Moreover, in this formulation, the massless or tensionless limit $\alpha'\rightarrow \infty$ is non-singular and leads to an enhanced gauge symmetry. We show that the massive modes can be integrated out exactly at the quadratic level, leading to an infinite series of higher-derivative corrections. Finally, we present a ghost-free massive extension of linearized double field theory, which employs a novel mass term for the dilaton and metric.Comment: 28 pages. Minor typos corrected. Matches with the published versio

Chiral closed strings: four massless states scattering amplitude

“…(Indeed, ref. [22] presents extra massive scalar states as well that do not take place in the spectra of the work discussed herein.) Contrarily, the schematic KLT analysis without explicit separation of all simple poles from ref.…”

“…Note that this just agrees with the criteria from refs. [21,22] and string field theory. (Indeed, ref.…”

“…Other aspects that can be pursued are the construction of low energy effective actions for the states of the spectrum of chiral strings [21,22]. Since there are a finite number of states, an effective action from field theory can be constructed in principle in order to investigate how the states of the spectrum interact among each other.…”

Second order higher-derivative corrections in Double Field Theory

“…For example, its spectrum contains ghosts and tachyons [20], and the action contains unambiguous Riemann-cubed terms that could lead to causality violations [24]. Given reservations like these, one would be tempted to dismiss the theory altogether.…”

“…To achieve this purpose, the massive modes in HSZ theory must be integrated out, ending with a low-energy effective theory for the generalized metric H M N and generalized dilaton d that contains an infinite series of higher-derivative terms [20][21][22][23]. It is then of interest to elucidate what these corrections look like in terms of the standard gauge covariant massless fields, namely the metric g µν , two-form B µν and dilaton φ, in a manifestly diffeomorphism and gauge invariant form expanded in powers of α ′ .…”