Mihail Mintchev

Wilson lines in Chern-Simons theory and link invariants

The vacuum expectation values of Wilson line operators 〈W(L)〉 in the Chern-Simons theory are computed to second order to perturbation theory. The meaning of the framing procedure for knots is analyzed in the context of the Chern-simons field theory. The relation between 〈W(L)〉 and the link invariant polynomials is discussed. We derive an explicit analytic expression for the second coefficient of the Alexander-Conway polynomial, which is related to the Arf- and Casson-invariant. We present also some new relations between the HOMFLY coefficients.

Quantum Field Theory and Link Invariants

Abstract A skein relation for the expectation values of Wilson line operators in three-dimensional SU(N) Chern-Simons gauge theory is derived at first order in the coupling constant. We use a variational method based on the properties of the three-dimensional field theory. The relationship between the above expectation values and the known link invariants is established.

Entanglement entropy of one-dimensional gases.

We introduce a systematic framework to calculate the bipartite entanglement entropy of a spatial subsystem in a one-dimensional quantum gas which can be mapped into a noninteracting fermion system. To show the wide range of applicability of the proposed formalism, we use it for the calculation of the entanglement in the eigenstates of periodic systems, in a gas confined by boundaries or external potentials, in junctions of quantum wires, and in a time-dependent parabolic potential.

Scale invariant sigma models on homogeneous spaces

Abstract A class of two-dimensional scale invariant σ -models on homogeneous spaces is presented. We discuss the symmetry properties of the models and show that they are finite. We compute at two loops the central charge of the Virasoro algebra associated with the energy-momentum tensor.

Chern-Simons Field Theory and Quantum Groups

We study the Gauss constraint of the Chern-Simons theory in presence of sources. We solve this constraint in terms of a matrix-valued gauge connection. The associated holonomies define a representation of the braid group, which commutes with the action of a quantum group.

Beta functions and central charge of supersymmetric sigma models with torsion

Abstract We present a method for the computation of the renormalization group β-functions and the central charge in two-dimensional supersymmetric sigma models in a gravitational background. The two-loops results are exhibited. We use the Pauli-Villars regularization which preserves supersymmetry and permits an unambiguous treatment of the model with torsion. The central charge we derive for a general manifold is in agreement with the expression found on group manifolds.

Luttinger liquid in a non-equilibrium steady state

We propose and investigate an exactly solvable model of non-equilibrium Luttinger liquid on a star graph, modeling a multi-terminal quantum wire junction. The boundary condition at the junction is fixed by an orthogonal matrix , which describes the splitting of the electric current among the leads. The system is driven away from equilibrium by connecting the leads to heat baths at different temperatures and chemical potentials. The associated non-equilibrium steady state depends on and is explicitly constructed. In this context, we develop a non-equilibrium bosonization procedure and compute some basic correlation functions. Luttinger liquids with general anyon statistics are considered. The relative momentum distribution away from equilibrium turns out to be the convolution of equilibrium anyon distributions at different temperatures. Both the charge and heat transport are studied. The exact current–current correlation function is derived and the zero-frequency noise power is determined.

The nonlinear Schrödinger equation on the half line

The nonlinear Schrodinger equation on the half line with mixed boundary condition is investigated. After a brief introduction to the corresponding classical boundary value problem, the exact second quantized solution of the system is constructed. The construction is based on a new algebraic structure, which is called in what follows boundary algebra and which substitutes, in the presence of boundaries, the familiar Zamolodchikov–Faddeev algebra. The fundamental quantum field theory properties of the solution are established and discussed in detail. The relative scattering operator is derived in the Haag–Ruelle framework, suitably generalized to the case of broken translation invariance in space.

QUANTUM FIELD THEORY, BOSONIZATION AND DUALITY ON THE HALF LINE

Abstract We develop a bosonization procedure on the half line. Different boundary conditions, formulated in terms of the vector and axial fermion currents, are implemented by using in general the mixed boundary condition on the bosonic field. The interplay between symmetries and boundary conditions is investigated in this context, with a particular emphasis on duality. As an application, we explicitly construct operator solutions of the massless thirring model on the half line, respecting different boundary conditions.

Chiral anomalies and supersymmetry

Abstract The structure of the chiral anomalies in supersymmetric gauge theories is studied. We discuss in detail the relationship between the two pictures: the manifestly SUSY-covariant approach and the Wess-Zumino gauge. A prescription for the computation of the anomalies in higher dimensions is presented and the resulting expression in six dimensions is reported.