Abstract
Higher-abelian gauge theories associated with Cheeger-Simons differential characters are studied on compact manifolds without boundary. The paper consists of two parts: First the functional integral formulation based on zeta function regularization is revisited and extended in order to provide a general framework for further applications. A field theoretical model - called extended higher-abelian Maxwell theory - is introduced, which is a higher-abelian version of Maxwell theory of electromagnetism extended by a particular topological action. This action is parametrized by two non-dynamical harmonic forms and generalizes the θ-term in usual gauge theories. In the second part the general framework is applied to study the topological Casimir effect in higher-abelian gauge theories at finite temperature at equilibrium. The extended higher-abelian Maxwell theory is discussed in detail and an exact expression for the free energy is derived. A non-trivial topology of the background space-time modifies the spectrum of both the zero-point fluctuations and the occupied states forming the thermal ensemble. The vacuum (Casimir) energy has two contributions: one related to the propagating modes and the second one related to the topologically inequivalent configurations of higher-abelian gauge fields. In the high temperature limit the leading term is of Stefan-Boltzmann type and the topological contributions are suppressed. With a particular choice of parameters extended higher-abelian Maxwell theories of different degrees are shown to be dual. On the n-dimensional torus we provide explicit expressions for the thermodynamic functions in the low- and high temperature regimes, respectively. Finally, the impact of the background topology on the two-point correlation function of a higher-abelian variant of the Polyakov loop operator is analyzed.
Highlights
Higher-abelian gauge theories associated with Cheeger-Simons differential characters are studied on compact manifolds without boundary
The topological Casimir effect at zero and finite temperature has been considered for many years in different contexts1
These areas of applications include for example the impact of the topological Casimir effect in models of a compact universe with non-trivial topology, its role for the stabilization of moduli in multidimensional Kaluza-Klein type theories, its occurrence in brane-world cosmological scenarios or its consequences for compactified condensed matter systems
Summary
We perform our analysis in the functional integral formalism by using zeta function regularization. It is well known that especially in gauge theories at finite temperature particular care has to be taken to obtain a correct functional integral measure including all relevant temperature and volume dependent factors2 This justifies to review the corresponding construction principle before discussing the topological Casimir effect. We determine an exact formula for the regularized free energy and derive a corresponding asymptotic expansion for the hightemperature regime The latter vanishes whenever the topological fields are absent or have integer periods This generalizes our findings obtained previously in Maxwell theory at finite temperature [62], where the effect of these topological contributions was studied.
Sign-in/Register to view highlights & summary 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.
