String theory is the most promising candidate to describe quantum gravity. Its properties and applications have been explored now for over 50 years, showing an admirable self-consistency and mathematical richness. This project is dedicated to gaining a deeper understanding of fundamental aspects of string theory. In the first part we will investigate the string spectrum in AdS backgrounds and try to develop a spectrum generating algebra in parallel to the DDF operators in flat space, aiming also to extend the current knowledge of the famous AdS/CFT correspondence. The massless vertex operators are key ingredients and will be thoroughly investigated. In the second part of the project, our aim is to understand the underlying gauge theory of the socalled pure spinor (PS) formalism of the superstring. Although successful in all tests against the main string formalisms, the PS superstring lacks a fundamental description of its own foundations. We will investigate and extend the current proposal of the twistor-like constraint by Berkovits, trying to determine the gauge algebra involved.
Fundamental aspects of superstrings