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Register a new userInteracting Higher Spins and the High Energy Limit of the Bosonic String
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In this note, we construct a BRST invariant cubic vertex for massless fields of arbitrary mixed symmetry in flat space-time. The construction is based on the vertex given in bosonic Open String Field Theory. The algebra of gauge transformations is closed without any additional, higher than cubic, couplings due to the presence of an infinite tower of massless fields. We briefly discuss the generalization of this result to a curved space-time and other possible implications.
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We study the implications on inflation of an infinite tower of higher-spin states with masses falling exponentially at large field distances, as dictated by the Swampland Distance Conjecture. We show that the Higuchi lower bound on the mass of the tower automatically translates into an upper bound on the inflaton excursion. Strikingly, the mere existence of all spins in the tower forbids any scalar displacement whatsoever, at arbitrarily small Hubble scales, and it turns out therefore incompatible with inflation. A certain field excursion is allowed only if the tower has a cut-off in spin. Finally, we show that this issue is circumvented in the case of a tower of string excitations precisely because of the existence of such a cut-off, which decreases fast enough in field space.
We study the world-volume theory of a bosonic membrane perturbatively and discuss if one can obtain any conditions on the number of space-time dimensions from the consistency of the theory. We construct an action which is suitable for such a study. In order to study the theory perturbatively we should specify a classical background around which perturbative expansion is defined. We will discuss the conditions which such a background should satisfy to deduce the critical dimension. Unfortunately we do not know any background satisfying such conditions. In order to get indirect evidences for the critical dimension of the membrane, we next consider two string models obtained via double dimensional reduction of the membrane. The first one reduces to the Polyakov string theory in the conformal gauge. The second one is described by the Schild action. We show that the critical dimension is 26 for these string theories, which implies that the critical dimension is 27 for the membrane theory.
Two-dimensional fermionic string theory is shown to have a structure of topological model, which is isomorphic to a tensor product of two topological ghost systems independent of each other. One of them is identified with $c=1$ bosonic string theory while the other has trivial physical contents. This fact enables us to regard two-dimensional fermionic string theory as an embedding of $c=1$ bosonic string theory in the moduli space of fermionic string theories. Upon this embedding, the discrete states of $c=1$ string theory are mapped to those of fermionic string theory, which is considered to be the origin of the similarity between the physical spectra of these two theories. We also discuss a novel BRST operator associated with this topological structure.
The simplest higher-spin interactions involve classical external currents and symmetric tensors $phi_{m_1 ... m_s}$, and convey three instructive lessons. The first is a general form of the van Dam-Veltman-Zakharov discontinuity in flat space for this class of fields. The second is the rationale for its disappearance in (A)dS spaces. Finally, the third is a glimpse into an option which is commonly overlooked in Field Theory, and which both higher spins and String Theory are confronting us with: one can well allow in the Lagrangians non-local terms that do not spoil the local nature of physical quantities.
We construct an off-shell extension of cubic interaction vertices between massless bosonic Higher Spin fields on a flat background which can be obtained from perturbative bosonic string theory. We demonstrate how to construct higher quartic interaction vertices using a simple particular example. We examine whether BCFW recursion relations for interacting Higher Spin theories are applicable. We argue that for several interesting examples such relations should exist, but consistency of the theories might require that we supplement Higher Spin field theories with extended and possibly non-local objects.
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