Holomorphic Constraints Research Articles

Effective field theory of relativistic quantum hall systems

Motivated by the observation of the fractional quantum Hall effect in graphene, we consider the effective field theory of relativistic quantum Hall states. We find that, beside the Chern-Simons term, the effective action also contains a term of topological nature, which couples the electromagnetic field with a topologically conserved current of $2+1$ dimensional relativistic fluid. In contrast to the Chern-Simons term, the new term involves the spacetime metric in a nontrivial way. We extract the predictions of the effective theory for linear electromagnetic and gravitational responses. For fractional quantum Hall states at the zeroth Landau level, additional holomorphic constraints allow one to express the results in terms of two dimensionless constants of topological nature.

Low-energy Kähler potentials in supersymmetric gauge theories with (almost) flat directions

We derive the supersymmetric low-energy effective theory of the D-flat directions of a supersymmetric gauge theory. The Kähler potential of Affleck, Dine and Seiberg is derived by applying holomorphic constraints which manifestly maintain supersymmetry. We also present a simple procedure for calculating all derivatives of the Kähler potential at points on the flat direction manifold. Together with knowledge of the superpotential, these are sufficient for a complete determination of the spectrum and the interactions of the light degrees of freedom. We illustrate the method on the example of a chiral abelian model, and comment on its application to more complicated calculable models with dynamical supersymmetry breaking.

Harmonic BRST quantization of systems with irreducible holomorphic bosonic and fermionic constraints.

We consider systems with second-class constraints or, equivalently, first-class holomorphic constraints. We show that the harmonic Becchi-Rouet-Stora-Tyutin method of quantizing systems with bosonic holomorphic constraints extends to systems having both bosonic and fermionic holomorphic constraints. The ghosts for bosonic holomorphic constraints in the harmonic BRST method have a Poisson brackets structure different from that of the ghosts in the usual BRST method, which applies to systems with real first-class constraints. Apart from this exotic ghost structure for bosonic constraints, the new feature of the harmonic BRST method is the introduction of two new holomorphic BRST charges \ensuremath{\bigominus} and $\overline{\ensuremath{\bigominus}}$ and the addition of an extra term $\ensuremath{-}\ensuremath{\beta}{\ensuremath{\bigominus}, \overline{\ensuremath{\bigominus}}}$ to the BRST-invariant Hamiltonian. We apply the Fradkin-Vilkovisky theorem to general systems with mixed bosonic and fermionic holomorphic constraints and show that, taking an appropriate limit, the extra term in the harmonic BRST-modified path integral reproduces the correct Senjanovic measure.

BRST formulation of the Gupta–Bleuler quantization method

In this paper it is shown how an algebra of mixed first- and second-class constraints can be transformed into an algebra of the Gupta–Bleuler type, consisting of holomorphic and antiholomorphic constraints. Its quantization is performed by BRST methods. A second-level BRST operator Ω is constructed by introducing a new ghost sector (the second-level ghosts), in addition to the ghosts of the standard BRST operator. An inner product in this ghost sector is found such that the operator Ω is Hermitean. The physical states, as defined by the non-Hermitean holomorphic constraints, are shown to be given in terms of the cohomology of this Hermitean BRST charge.

Calabi-Yau manifolds as complete intersections in products of complex projective spaces

We consider constructions of manifolds withSU(3) holonomy as embedded in products of complex projective spaces by imposing certain homogeneous holomorphic constraints. We prove that every such construction leads to one deformation class of manifolds withSU(3) holonomy. For a subset of these manifolds we prove simple connectedness, address the problem of calculating the second Betti number and explicitly calculate it for a class of constructions. This establishes a very wide class of manifolds withSU(3) holonomy, that can give rise to yet many more constructions via dividing out the action of suitably chosen discrete groups. Some of the examples studied may yield phenomenologically acceptable models.

CP(N−1)model with holomorphic constraints inD=2andD=4dimensions

We introduce additional holomorphic constraints in the $\mathrm{CP}(N\ensuremath{-}1)$ model and derive, in the $\frac{1}{N}$ expansion, the effective action for neutral and charged composite fields. Then we discuss in four dimensions the generalized $\mathrm{CP}(N\ensuremath{-}1)$ model with four-linear Lagrangian and additional constraints. We also present a supersymmetric generalization of the model.