Quantum Global Vortex Strings in a Background Field

We consider quantum global vortex string correlation functions, within the Kalb-Ramond framework, in the presence of a background field-strength tensor and investigate the conditions under which this yields a nontrivial contribution to those correlation functions. We show that a background field must be supplemented to the Kalb-Ramond theory, in order to correctly describe the quantum properties of the vortex strings. The explicit form of this background field and the associated quantum vortex string correlation function are derived. The complete expression for the quantum vortex creation operator is explicitly obtained. We discuss the potential applicability of our results in the physics of superfluids and rotating Bose-Einstein con-densates. Global vortex strings appear as nontrivial excitations in many important physical systems described by the relativistic global U(1) Abelian Higgs model in the spontaneously broken phase. Typical examples are the cosmic strings left as remnants of topological phase transitions occurred in the early universe [1]. Superfluid vortices are similar excitations occurring in nonrelativistic systems such as superfluid helium II [2]. The second case is evidently a completely quantum system and, therefore a full quantum description of the superfluid vortex excitations is necessary. Even for cosmic strings, however, a quantum description is likely to be needed in the early stages of the universe, where quantum effects should be important. Quite interesting works have been devoted to the quantum description of vortices in superfluids [3]. The particular case of vortices in superfluid films has been considered in [4] where a topological coupling between the field associated to the superfluid film and the vortices has been introduced. Yet, a formulation made explicitly in terms of a fully quantized vortex creation operator and its correlation functions would be highly interesting. More recently, it has been found that superfluid vortices are abundantly generated in rotating Bose-Einstein condensates. These are also deeply quantum systems and consequently a quantized framework is required for studying the dynamics of such vortices. An intense research activity has been devoted to these systems in the recent years [5]. The relation between global strings and superfluid vortices has been clarified quite a few years ago. It has been shown that classical superfluid vortices could be described as global strings in the presence of a particular nonrelativistic background field [7, 8]. Assuming that this relationship could be extended up to the quantum level, the potential applicability of a quantum theory of global strings to superfluid vortices becomes …