Quantum theory of strings in an Abelian Higgs model

Abstract

Starting from the Abelian Higgs field theory, we construct the theory of quantum Abrikosov-Nielsen-Olesen strings. It is shown that in four space -time dimensions in the limit of infinitely thin strings, the conformal anomaly is absent, and the quantum theory exists. We also study an analogue of the Aharonov-Bohm effect: the corresponding topological interaction is proportional to the linking number of the string world sheet and the particle world trajectory. The creation operators of the strings are explicitly constructed in the path integral and in the Hamiltonian formulation of the theory. We show that the Aharonov-Bohm effect gives rise to several nontrivial commutation relations.

Vortices on the higgs branch of the Seiberg–Witten theory

“…As it is argued in [24,25] its role is to make the ANO string critical in four dimensions. We do not work out J(φ) here.…”

Center vortices as rigid strings

“…The dependence of the bare string tension on the lattice spacing can be explained if one takes into account the contribution of percolating monopole cluster. Interaction between monopoles, which can be approximated by the Yukawa potential with physical mass [21], can also partially account for surface rigidity [11,16,17]. Finally, implications and possible extensions of obtained results are discussed.…”

“…Yukawa-type interaction may be induced if these fermions are coupled to some four-dimensional massive field. Coupling to massive four-dimensional fields also leads to rigidity terms in the effective action [11,16,17], and thus such interaction can be also absorbed in the effective action (1).…”

“…However, even if the model of rigid strings has no continuum limit, it can still serve as an effective model, for which UV cutoff is set by some other fields in the theory. It is known, for instance, that rigidity terms arise in the effective string action after integrating over worldsheet fermions [8,14,15] or some four-dimensional massive fields coupled to the string worldsheet [11,16,17]. The aim of this paper is to fit observed properties of center vortices in the model of rigid strings.…”

Schwinger-Dyson equations and disorder

“…In more realistic models with nontrivial topology i.e. the Schwinger model [21,22] or the abelian Higgs model [23][24][25][26] Green's functions have been studied using semiclassical approximations by introducing dual variables that account for the topological defects. Here instead we will use models in which we can compare SD, semiclassical and exact results.…”