Higher-spin Massive String Interactions

This thesis develops a systematic and fully covariant framework for constructing and studying interactions of massive higher-spin states in bosonic string theory. Central to this work is a reformulation of the traditional DDF (Del Giudice–Di Vecchia–Fubini) construction in terms of framed DDF operators, defined using a local Lorentz frame (vielbein) that cleanly separates global and gauge degrees of freedom. This approach yields DDF and Brower operators with genuine zero conformal dimension, independent of the auxiliary tachyon momentum, and provides a transparent mapping between covariant, light-cone, and BRST formulations of physical string states. Using this framed formalism, the thesis derives the general covariant solution to the Virasoro constraints—both on-shell and minimally off-shell—clarifying the role of lightcone degrees of freedom, gauge redundancies, and null (Brower) states. Building on this, the Sciuto–Della Selva–Saito (SDS) operator formalism is extended to an arbitrary number of arbitrarily excited DDF states (the DDF Reggeon), enabling the computation of massive string scattering amplitudes in a manifestly covariant way. Explicit three- and four-point amplitudes involving massive scalar and spin-2 states are obtained, illustrating the practicality and naturalness of the formalism. Finally, by comparing the DDF interaction vertices to their light-cone counterparts, we establish a direct and detailed correspondence between DDF amplitudes and light-cone amplitudes. This leads to a derivation of the Mandelstam mapping from purely covariant data and provides new insight into the geometric structure of multi-string interactions. Overall, this work provides a coherent operator-based framework for massive higherspin string interactions, bridging covariant and light-cone approaches, and providing tools relevant for applications ranging from Regge physics and high-spin interactions to the string–black-hole correspondence