Eve Mariel Santangelo

We investigate the existence (or lack thereof) of the chiral magnetic effect in the framework of finite temperature field theory, studied through the path integral approach and regularized via the zeta function technique. We show that, independently of the temperature, gauge invariance implies the absence of the effect, a fact proved, at zero temperature and in a Hamiltonian approach, by N. Yamamoto. Indeed, the effect only appears when the manifold is finite in the direction of the magnetic field and gauge-invariance breaking boundary conditions are imposed. We present an explicit calculation for antiperiodic and periodic boundary conditions, which do allow for a CME, since only large gauge transformations are, then, an invariance of the theory. In both cases, the associated current does depend on the temperature, a well as on the size of the sample in the direction of the magnetic field, even for a temperature-independent chiral chemical potential. In particular, for antiperiodic boundary conditions, the value of this current only agrees with the result usually quoted in the literature on the subject in the zero-temperature limit, while it decreases with the temperature in a well-determined way.

We investigate the existence (or lack thereof) of the chiral magnetic effect (CME) in the framework of finite temperature field theory, studied through the path integral approach and regularized via the zeta function technique. We show that, independently of the temperature, gauge invariance implies the absence of the effect, a fact proved, at zero temperature and in a Hamiltonian approach, by Yamamoto. Indeed, the effect only appears when the manifold is finite in the direction of the magnetic field and gauge-invariance breaking boundary conditions are imposed. We present an explicit calculation for antiperiodic and periodic boundary conditions, which do allow for a CME, since only ‘large’ gauge transformations are, then, an invariance of the theory. In both cases, the associated current does depend on the temperature, a well as on the size of the sample in the direction of the magnetic field, even for a temperature-independent chiral chemical potential. In particular, for antiperiodic boundary conditions, the value of this current only agrees with the result usually quoted in the literature on the subject in the zero-temperature limit, while it decreases with the temperature in a well-determined way.

We present a detailed analytic study on the three-dimensional sphere of the most popular candidates for C -functions, both for Dirac and scalar free massive fields. We discuss to which extent the effective action, the Rényi entanglement entropy and the renormalized entanglement entropy fulfill the conditions expected from C -functions. In view of the absence of a good candidate in the case of the scalar field, we introduce a new candidate, which we call the modified effective action, and analyze its pros and cons.

We present a detailed analytic study on the three-dimensional sphere of the most popular candidates for $C$-functions, both for Dirac and scalar free massive fields. We discuss to which extent the effective action, the R\'enyi entanglement entropy and the renormalized entanglement entropy fulfill the conditions expected from $C$-functions. In view of the absence of a good candidate in the case of the scalar field, we introduce a new candidate, which we call the modified effective action, and analyze its pros and cons.

We establish some properties of the zeroes of sums and differences of contiguous Bessel functions of the first kind. As a byproduct, we also prove that the zeroes of the derivatives of Bessel functions of the first kind of different orders are interlaced the same way as the zeroes of Bessel functions themselves. As a physical motivation, we consider gated graphene nanodots subject to Berry-Mondragon boundary conditions. We determine the allowed energy levels and calculate the mean charge at zero temperature. We discuss in detail its dependence on the gate (chemical) potential.Comment: vesrion accepted to Theoretical and Mathematical Physics, 18 pages, 1 figur

We analyze the renormalization group (RG) flow of the temperature independent term of the entropy in the high temperature limit \beta/a< S_top^IR. From a 3-dimensional viewpoint the same term arises in the 3-dimensional Euclidean effective action and has the same monotonic behavior under the RG group flow. We conjecture that such monotonic behavior is generic, which would give rise to a 3-dimensional generalization of the c-theorem, along the lines of the 2-dimensional c-theorem and the 4-dimensional a-theorem. The conjecture is related to recent formulations of the F-theorem. In particular, the holonomy entropy on lens spaces is directly related to the topological R\'enyi entanglement entropy on disks of 2-dimensional flat spaces.