Statistical transmutation of quantum bosonic strings coupled to general four-dimensional Chern-Simons theory

A bosonic string coupled to the generalized Chern-Simons theory in 3+1D acquires a magnetic field along itself, when it is closed, and a topological charge at its extremity, when it is open. We construct the creation operators for the full quantum field states associated to these strings and determine the dual algebra satisfied by them. We show that the creation operator fo the composite state of a quantum closed bosonic string, bearing a magnetic flux, and a topologically charged open bosonic string, possesses generalized statistics. The relation of our results with previous approaches to the problem is also established.Comment: 4 pages, Revtex

Quantized Skyrmion Fields in 2+1 Dimensions

A fully quantized field theory is developped for the skyrmion topological excitations of the O(3) symmetric CP$^1$-Nonlinear Sigma Model in 2+1D. The method allows for the obtainment of arbitrary correlation functions of quantum skyrmion fields. The two-point function is evaluated in three different situations: a) the pure theory; b) the case when it is coupled to fermions which are otherwise non-interacting and c) the case when an electromagnetic interaction among the fermions is introduced. The quantum skyrmion mass is explicitly obtained in each case from the large distance behavior of the two-point function and the skyrmion statistics is inferred from an analysis of the phase of this function. The ratio between the quantum and classical skyrmion masses is obtained, confirming the tendency, observed in semiclassical calculations, that quantum effects will decrease the skyrmion mass. A brief discussion of asymptotic skyrmion states, based on the short distance behavior of the two-point function, is also presented.Comment: Accepted for Physical Review

BF models, Duality and Bosonization on higher genus surfaces

The generating functional of two dimensional $BF$ field theories coupled to fermionic fields and conserved currents is computed in the general case when the base manifold is a genus g compact Riemann surface. The lagrangian density $L=dB{\wedge}A$ is written in terms of a globally defined 1-form $A$ and a multi-valued scalar field $B$. Consistency conditions on the periods of $dB$ have to be imposed. It is shown that there exist a non-trivial dependence of the generating functional on the topological restrictions imposed to $B$. In particular if the periods of the $B$ field are constrained to take values $4\pi n$, with $n$ any integer, then the partition function is independent of the chosen spin structure and may be written as a sum over all the spin structures associated to the fermions even when one started with a fixed spin structure. These results are then applied to the functional bosonization of fermionic fields on higher genus surfaces. A bosonized form of the partition function which takes care of the chosen spin structure is obtainedComment: 17 page

Monopoles and flux strings from SU(2) adjoint scalars

We construct, in an SU(2) gauge theory with two adjoint scalars, flux strings with monopoles attached at the ends. One scalar breaks SU(2) to U(1) and produces monopoles, the other then breaks the U(1) and produces strings. Dualizing, we write the theory in terms of effective string variables and show that the flux in the string is exactly saturated by the monopoles at the ends.Comment: 12 pp. v2: added several references and reworded some statement

High TcT_c Superconductivity, Skyrmions and the Berry Phase

It is here pointed out that the antiferromagnetic spin fluctuation may be associated with a gauge field which gives rise to the antiferromagnetic ground state chirality. This is associated with the chiral anomaly and Berry phase when we consider the two dimensional spin system on the surface of a 3D sphere with a monopole at the centre. This realizes the RVB state where spinons and holons can be understood as chargeless spins and spinless holes attached with magnetic flux. The attachment of the magnetic flux of the charge carrier suggest, that this may be viewed as a skyrmion. The interaction of a massless fermion representing a neutral spin with a gauge field along with the interaction of a spinless hole with the gauge field enhances the antiferromagnetic correlation along with the pseudogap at the underdoped region. As the doping increases the antiferromagnetic long range order disappears for the critical doping parameter $\delta_{sc}$. In this framework, the superconducting pairing may be viewed as caused by skyrmion-skyrmion bound states.Comment: 10 pages, accepted in Phys. Rev.

Relativistic particle dynamics in D=2+1

We propose a SUSY variant of the action for a massless spinning particles via the inclusion of twistor variables. The action is constructed to be invariant under SUSY transformations and $\tau$-reparametrizations even when an interaction field is including. The constraint analysis is achieved and the equations of motion are derived. The commutation relations obtained for the commuting spinor variables $\lambda$ show that the particle states have fractional statistics and spin. At once we introduce a possible massive term for the non-interacting model.Comment: 11 page

Quantum Criticality and Superconductivity in Quasi-Two-Dimensional Dirac Electronic Systems

We present a theory describing the superconducting (SC) interaction of Dirac electrons in a quasi-two-dimensional system consisting of a stack of N planes. The occurrence of a SC phase is investigated both at T=0 and T\neq 0, in the case of a local interaction, when the theory must be renormalized and also in the situation where a natural physical cutoff is present in the system. In both cases, at T=0, we find a quantum phase transition connecting the normal and SC phases at a certain critical coupling. The phase structure is shown to be robust against quantum fluctuations. The SC gap is determined for T=0 and T\neq 0, both with and without a physical cutoff and the interplay between the gap and the SC order parameter is discussed. Our theory qualitatively reproduces the SC phase transition occurring in the underdoped regime of the high-Tc cuprates. This fact points to the possible relevance of Dirac electrons in the mechanism of high-Tc superconductivity.Comment: To be published in Nuclear Physics, Section B. 24 pages, 4 figure

A Geometric Approach to Massive p-form Duality

Massive theories of abelian p-forms are quantized in a generalized path-representation that leads to a description of the phase space in terms of a pair of dual non-local operators analogous to the Wilson Loop and the 't Hooft disorder operators. Special atention is devoted to the study of the duality between the Topologically Massive and the Self-Dual models in 2+1 dimensions. It is shown that these models share a geometric representation in which just one non local operator suffices to describe the observables.Comment: 26 pages, LaTeX. The discussion about the equivalence between the Proca model and two seldual models, with opposite spins, was eliminated. Typos correcte

Superconductivity in graphene stacks: from the bilayer to graphite

We study the superconducting phase transition, both in a graphene bilayer and in graphite. For that purpose we derive the mean-field effective potential for a stack of graphene layers presenting hopping between adjacent sheets. For describing superconductivity, we assume there is an on-site attractive interaction between electrons and determine the superconducting critical temperature as a function of the chemical potential. This displays a dome-shaped curve, in agreement with previous results for two-dimensional Dirac fermions. We show that the hopping between adjacent layers increases the critical temperature for small values of the chemical potential. Finally, we consider a minimal model for graphite and show that the transition temperature is higher than that for the graphene bilayer for small values of chemical potential. This might explain why intrinsic superconductivity is observed in graphite

Effective Action for QED with Fermion Self-Interaction in D=2 and D=3 Dimensions

In this work we discuss the effect of the quartic fermion self-interaction of Thirring type in QED in D=2 and D=3 dimensions. This is done through the computation of the effective action up to quadratic terms in the photon field. We analyze the corresponding nonlocal photon propagators nonperturbatively in % \frac{k}{m}, where k is the photon momentum and m the fermion mass. The poles of the propagators were determined numerically by using the Mathematica software. In D=2 there is always a massless pole whereas for strong enough Thirring coupling a massive pole may appear . For D=3 there are three regions in parameters space. We may have one or two massive poles or even no pole at all. The inter-quark static potential is computed analytically in D=2. We notice that the Thirring interaction contributes with a screening term to the confining linear potential of massive QED_{2}. In D=3 the static potential must be calculated numerically. The screening nature of the massive QED$_{3}$ prevails at any distance, indicating that this is a universal feature of % D=3 electromagnetic interaction. Our results become exact for an infinite number of fermion flavors.Comment: Latex, 13 pages, 3 figure