Quantum corrections to the mass of self-dual vortices

The mass shift induced by one-loop quantum fluctuations on self-dual ANO vortices is computed using heat kernel/generalized zeta function regularization methods. 1. In this Letter we shall compute the one-loop mass shift for Abrikosov-NielsenOlesen self-dual vortices in the Abelian Higgs model. Non-vanishing quantum corrections to the mass of N = 2 supersymmetric vortices were reported during the last year in papers [1] and [2]. In the second paper, a relationship was established between the mass shift and the existence of an anomaly in the central charge of the N = 2 SUSY algebra that we could term a one-loop BPS saturation. This latter result fits in a pattern first conjectured in [3] and then proved in [4] for supersymmetric kinks. Recent work by the authors of the Stony Brook/Viena group, [5], unveils a similar kind of behaviour of supersymmetric BPS monopoles in N = 2 SUSY Yang-Mills theory. We shall focus, however, on the purely bosonic Abelian Higgs model and rely on the heat kernel/generalized zeta function regularization method that we developed in references [6], [7] and [8] to compute the one-loop shift to kink masses. Our approach profits from the high-temperature expansion of the heat function, that is compatible with Dirichlet boundary conditions in purely bosonic theories. In contrast, the application of a similar regularization method to the supersymmetric kink requires SUSY friendly boundary conditions, see [9]. We shall also encounter more difficulties than in the kink case due to the jump from one to two spatial dimensions. Defining non-dimensional space-time variables and fields from the vacuum expectation value of the Higgs field v and the electromagnetic coupling constant e x → 1 ev x ; φ → vφ = v(φ1 + iφ2) ; Aμ → vAμ , the action for the Abelian Higgs model in (2+1)-dimensions reads: S = v e ∫ dx { − 4 FμνF μν + 1 2 (Dμφ) Dφ− β 8 (φφ− 1) }