Abstract
We analyze two-dimensional nonlinear sigma models at nonzero chemical potentials, which are governed by a complex action. In the spirit of contour deformations (thimbles), we extend the fields into the complex plane, which allows us to incorporate the chemical potentials $\ensuremath{\mu}$ as twisted boundary conditions. We write down the equations of motion and find exact BPS-like solutions in terms of pairs of (anti)holomorphic functions, in particular generalizations of unit charge and fractional instantons to generic $\ensuremath{\mu}$. The decay of these solutions is controlled by the imaginary part of $\ensuremath{\mu}$ and a vanishing imaginary part causes jumps in the action. We analyze how the total charge is distributed into localized objects and to what extent these are characterized by topology.
Highlights
Two-dimensional nonlinear sigma models have been known for a long time to share nontrivial properties—such as asymptotic freedom, dynamical mass generation, topology, supersymmetric extensions, etc.—with four-dimensional non-Abelian gauge theories; see, e.g., [1]
We focus on the effect of a varying chemical potential μ on this solution
We have analyzed the equations of motion from the complex action of two-dimensional sigma models at nonzero chemical potential
Summary
Two-dimensional nonlinear sigma models have been known for a long time to share nontrivial properties—such as asymptotic freedom, dynamical mass generation, topology, supersymmetric extensions, etc.—with four-dimensional non-Abelian gauge theories; see, e.g., [1]. As examples we analyze analogues of fractional constituents and unit charge instantons in the Oð3Þ ≅ CPð1Þ model at generic μ Their densities turn out to be analytic continuations of the corresponding densities from imaginary μ (i.e., from twisted solutions) to generic μ. From the viewpoint of real μ, an imaginary μ might be viewed as a “regulator.” The limit of vanishing imaginary part of μ, produces an imaginary jump in the total action/charge, similar to lateral Borel resummations of sign-coherent series These jumps appear at branch cuts of the square root function. This work is organized into two main parts, one about the O(3) model and its specific realizations and one about the more general CP(N-1) models In both parts, we first discuss (conventional) BPS solutions, the global symmetries to which chemical potentials couple, the method of pushing the latter into twisted boundary conditions, and the resulting complexity issue. The interesting features of this system are caused by its nonlinearity, which is manifest in the latter two parametrizations; in the η-parametrization it is caused by the constraint
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
