Multiloop modular invariance of the covariant lattice construction of fermionic strings

A simple proof of multiloop modular invariance is given for all ten- and lower-dimensional string theories that can be obtained with the covariant lattice construction.     

Gauge invariant Lagrangian construction for massive higher spin fermionic fields

We formulate a general gauge invariant Lagrangian construction describing the dynamics of massive higher spin fermionic fields in arbitrary dimensions. Treating the conditions determining the irreducible representations of Poincaré group with given spin as the operator constraints in auxiliary Fock space, we built the BRST charge for the model under consideration and find the gauge invariant equations of motion in terms of vectors and operators in the Fock space. It is shown that like in massless case [I.L. Buchbinder, V.A. Krykhtin, A. Pashnev, Nucl. Phys. B 711 (2005) 367, hep-th/0410215], the massive fermionic higher spin field models are the reducible gauge theories and the order of reducibility grows with the value of spin. In compare with all previous approaches, no off-shell constraints on the fields and the gauge parameters are imposed from the very beginning, all correct constraints emerge automatically as the consequences of the equations of motion. As an example, we derive a gauge invariant Lagrangian for massive spin 3/2 field.     

Covariant fermionic vertex in superstrings

A covariant fermionic vertex is constructed in terms of Ramond spinors and ghost operators, starting from the Neveu-Schwarz model. Correlation functions of spinors and ghosts are defined. The supersymmetry algebra is realized as the algebra of massless vertices with zero momentum.     

Loop amplitudes for the fermionic string

We obtain simple formulae for loop amplitudes of the fermionic closed oriented Polyakov string in d= 10, as integrals over moduli and supermoduli space. The integrals over supermoduli may be carried out, leaving an integral over moduli with respect to the Weil-Petersson measure. The integrand consists of Green functions and determinants of laplacians on tensors and spinors.     

Charge density of the fermionic vacuum

We examine the properties of the matter vacuum in the absence of fermion-photon interactions. We calculate the spatial distribution of the vacuum’s charge density associated with model nuclear interactions and show that even in the absence of photons, the fermionic vacuum can screen off the Coulomb field around a nucleus. For force fields that vary on spatial scales larger than the electron’s Compton wavelength, the resulting charge density is proportional to the spatial derivative of the nuclear force field. As a result we can estimate the electric permeability of the one-dimensional fermionic vacuum to be 5.1 × 10^?7.     

Toward the theory of fermionic condensation

The diagrammatic technique elaborated by Belyaev for the theory of a Fermi liquid has been implemented to analyze the behavior of Fermi systems beyond the topological phase transition point, where the fermionic condensate appears. It has been shown that the inclusion of the interaction between the condensate and above-condensate particles leads to the emergence of a gap in the single-particle excitation spectrum of these particles even in the absence of Cooper pairing. Hence, the emergence of this gap in homogeneous electron systems of silicon field-effect structures leads to a metal–insulator phase transition rather than to superconductivity. It has been shown that the same interaction explains the nature of the Fermi arc structure in twodimensional electron systems of cuprates.     

On the interpretation of fermionic zero-modes

We examine the effect of fermionic zero modes on tunneling amplitudes within some simple quantum mechanical models. It is shown that the fermionic zero modes do not cause a total suppression of the tunneling, although it may be reduced. With a θ term present, due to a non-trivial topology, it is shown that the θ dependence is not eliminated by the zero modes. Instead the non-trivial topology introduces a “twist” in the fermionic coordinates which breaks a symmetry of the hamiltonian.     

BRST cohomology of the fermionic string

The BRST cohomology of the first-quantized fermionic string (Ramond model) is explicitly computed by using methods developed in a previous letter. The infinite degeneracy due to the commuting ghost zero mode is shown to be spurious by extending to the BRSt context an argument originally due to Corrigan and Goddard.     

Limiting currents in fermionic superconducting strings

It is usually assumed that the critical current in a fermionic superconducting string is of order em, where m is the in vacuo mass of the charge carrier. It is argued here that in reality the critical current is of order em²R, where R is the string's radius of curvature. This has some important consequences: in particular, scattering amongst the charge carriers can be shown to limit the current to less than roughly 10⁹ GeV.     

p-Wave interactions in low-dimensional fermionic gases

We study a spin-polarized degenerate Fermi gas interacting via a p-wave Feshbach resonance in an optical lattice. The strong confinement available in this system allows us to realize one- and two-dimensional gases and, therefore, to restrict the asymptotic scattering states of atomic collisions. When aligning the atomic spins along (or perpendicular to) the axis of motion in a one-dimensional gas, scattering into channels with the projection of the angular momentum of /m/ = 1 (or m = 0) can be inhibited. In two and three dimensions, we observe the doublet structure of the p-wave Feshbach resonance. For both the one-dimensional and the two-dimensional gases, we find a shift of the position of the resonance with increasing confinement due to the change in collisional energy. In a three-dimensional optical lattice, the losses on the Feshbach resonance are completely suppressed.     

Quasi-two-dimensional superfluid fermionic gases

We study a quasi-two-dimensional superfluid Fermi gas where the confinement in the third direction is due to a strong harmonic trapping. We investigate the behavior of such a system when the chemical potential is varied and find strong modifications of the superfluid properties due to the discrete harmonic oscillator states. We show that such quasi-two-dimensional behavior can be created and observed with current experimental capabilities.     

Vortex-antivortex lattice in ultracold fermionic gases

We discuss ultracold Fermi gases in two dimensions, which could be realized in a strongly confining one-dimensional optical lattice. We obtain the temperature versus effective interaction phase diagram for an s-wave superfluid and show that, below a certain critical temperature Tc, spontaneous vortex-antivortex pairs appear for all coupling strengths. In addition, we show that the evolution from weak-to-strong coupling is smooth, and that the system forms a square vortex-antivortex lattice at a lower critical temperature TM.     

Entanglement entropy in fermionic Laughlin states

We present analytic and numerical calculations on the bipartite entanglement entropy in fractional quantum Hall states of the fermionic Laughlin sequence. The partitioning of the system is done both by dividing Landau-level orbitals and by grouping the fermions themselves. For the case of orbital partitioning, our results can be related to spatial partitioning, enabling us to extract a topological quantity (the "total quantum dimension") characterizing the Laughlin states. For particle partitioning we prove a very close upper bound for the entanglement entropy of a subset of the particles with the rest, and provide an interpretation in terms of exclusion statistics.