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.
Highlights
We analyze the spectrum of the exactly duality and gauge invariant higherderivative 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
Flat space and reducing to D-dimensional indices i, j, . . ., the metric and two-form fluctuations are encoded in a general second-rank tensor eij, while the additional fields are given by two symmetric tensors aij and aij
As was outlined in [1] and shown in more detail in [10], these extra fields can be treated as auxiliary fields in that they can be eliminated algebraically by iteratively solving their field equations in terms of the massless fields
Summary
We compute the full quadratic Lagrangian and the potential of HSZ theory [1]. We show that the theory admits two vacua with constant backgrounds Both of these vacua have the same number of degrees of freedom; ‘ghost-like’ fields of one vacuum, correspond to ‘healthy’ fields of the other vacuum and vice versa. The Lagrangian L has terms with up to six derivatives, given in equation (3.16) and (3.17) of [13] This Lagrangian can be expanded around a constant background M that can be identified with a constant generalized metric [8]: MMN = HMN + mMN = HMN + mMN + mNM + aM N + aMN. Replace under-barred derivatives by D and barred derivatives by Ddefined as in [8], Di = ∂i − Eik∂ ̃k , Di = ∂i + Eki∂ ̃k ,. 1 2 for each barred contraction and a factor of each under-barred contraction
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