Mapping between Witten and lightcone string field theories

We propose a transformation between the off-shell field variables of Witten’s open bosonic string field theory and the traditional lightcone string field theory of Kaku and Kikkawa, based on Mandelstam’s interacting string picture. This is accomplished by deforming the Witten vertex into lightcone cubic and quartic vertices, followed by integrating out the ghost and lightcone oscillator excitations from the string field. Surprisingly, the last step does not alter the cubic and quartic interactions and does not generate effective vertices, and leads precisely to Kaku and Kikkawa’s lightcone string field theory.

O(D,D)-covariant two-loop β-functions and Poisson-Lie T-duality

We show that the one- and two-loop β-functions of the closed, bosonic string can be written in a manifestly O(D,D)-covariant form. Based on this result, we prove that1) Poisson-Lie symmetric σ-models are two-loop renormalisable and2) their β-functions are invariant under Poisson-Lie T-duality.Moreover, we identify a distinguished scheme in which Poisson-Lie symmetry is manifest. It simplifies the calculation of two-loop β-functions significantly and thereby provides a powerful new tool to advance into the quantum regime of integrable σ-models and generalised T-dualities. As an illustrating example, we present the two-loop β-functions of the integrable λ- and η-deformation.

Beta functions for the duality-invariant sigma model

The O(d, d) invariant worldsheet theory for bosonic string theory with d abelian isometries is employed to compute the beta functions and Weyl anomaly at one-loop. We show that vanishing of the Weyl anomaly coefficients implies the equations of motion of the Maharana-Schwarz action. We give a self-contained introduction into the required techniques, including beta functions, the Weyl anomaly for two-dimensional sigma models and the background field method. This sets the stage for a sequel to this paper on generalizations to higher loops and α′ corrections.

O(25, 25) symmetry of bosonic string theory at order $$\alpha '^2$$

It has been recently observed that the imposition of the O(1, 1) symmetry on the circle reduction of the classical effective action of string theory, can fix the effective action of the bosonic string theory at order $$\alpha '^2$$ α ′ 2 , up to an overall factor. In this paper, we use the cosmological reduction on the action and show that, up to one-dimensional field redefinitions and total derivative terms, it can be written in the O(25, 25)-invariant form proposed by Hohm and Zwiebach.

Relating the b ghost and the vertex operators of the pure spinor superstring

The OPE between the composite b ghost and the unintegrated vertex operator for massless states of the pure spinor superstring is computed and shown to reproduce the structure of the bosonic string result. The double pole vanishes in the Lorenz gauge and the single pole is shown to be equal to the corresponding integrated vertex operator.

The generalized Bergshoeff-de Roo identification. Part II

We recently introduced a T-duality covariant mechanism to compute all-order higher-derivative interactions in the heterotic string. Here we extend the formalism to account for a two-parameter family of corrections that also include the bosonic string and HSZ theory. We use our result to compute the full second order Double Field Theory (DFT) for generic values of the parameters, including the generalized Green-Schwarz transformation and its invariant action.

Relaxing unimodularity for Yang-Baxter deformed strings

We consider so-called Yang-Baxter deformations of bosonic string sigma- models, based on an R-matrix solving the (modified) classical Yang-Baxter equation. It is known that a unimodularity condition on R is sufficient for Weyl invariance at least to two loops (first order in α′). Here we ask what the necessary condition is. We find that in cases where the matrix (G + B)mn, constructed from the metric and B-field of the undeformed background, is degenerate the unimodularity condition arising at one loop can be replaced by weaker conditions. We further show that for non-unimodular deformations satisfying the one-loop conditions the Weyl invariance extends at least to two loops (first order in α′). The calculations are simplified by working in an O(D, D)-covariant doubled formulation.

Brane with transverse rotation and background fields: boundary state and tachyon condensation

The boundary state corresponding to the Dp-brane with a transverse rotation in the presence of the Kalb–Ramond and tachyon background fields and a U(1) internal field will be constructed. We shall investigate effects of the open string tachyon condensation on this brane via its boundary state. We demonstrate that the background fields and transverse rotation cannot protect the brane against the collapse. Our calculations are in the context of the bosonic string theory.