Massive Gauge Theory Research Articles

Resistivity in the Spin-Gap State of the t-J Model

Being motivated by recent experimental data on YBaCuO, we calculate dc resistivity in the spin-gap state of charge- spin-separated t-J model by using a massive gauge theory of holons and spinons.The result shows it deviates downward from the T-linear behavior below the spin-gap onset temperature.

Vacuum instability in Chern-Simons theory, null vectors and two-dimensional logarithmic operators

A new relation between two-dimensional conformal field theories and three-dimensional topologically massive gauge theories is found, where the dynamical nature of the 3d theory is ultimately important. It is shown that the those primary states in CFT which have non-unitary descendants correspond in the 3d theory to supercritical charges and cause vacuum instability. It is also shown that logarithmic operators separating the unitary sector from a non-unitary one correspond to an exact zero energy ground state in which case the 3d Hamiltonian naturally has a Jordan structure.

Symmetry properties and renormalizability of massive gauge theories in Delbourgo-Jarvis gauge

The massive Curci-Ferrari model in the nonlinear Delbourgo-Jarvis gauge can be renormalized analogously to Yang-Mills theories in linear gauges if besides the (anti-) Slavnov-Taylor and (anti-) Delduc-Sorella identies also the equations of motion for the auxillary field and the (anti-)ghost fields as well as the so-called local Lee identity is required.

Regularization scheme ambiguities in topologically massive gauge theories

It is demonstrated that in the $(2+1)$-dimensional topologically massive gauge theories an agreement of the Pauli-Villars regularization scheme with the other schemes can be achieved by extending it to incorporate pairs of auxiliary fermions with the opposite sign masses. This approach does not introduce additional violation of the discrete $P$ and $T$ symmetries but breaks the local gauge symmetry in the regulator fields sector. However, it is shown that superrenormalizability of the models renders the local gauge symmetry-breaking harmless: the symmetry is restored after the regularization is removed. It is shown also that analogous extension of the Pauli-Villars regularization works in the vector particle sector too.

G/ G models as the strong coupling limit of topologically massive gauge theory

We show that the problem of computing the vacuum expectation values of gauge-invariant operators in the strong coupling limit of topologically massive gauge theory is equivalent to the problem of computing similar operators in the Gk/G model where k is the integer coefficient of the Chem-Simons term. The Gk/G model is a topological field theory and many correlators can be computed analytically. We also show that the effective action for the Polyakov loop operator and static modes of the gauge fields of the strongly coupled theory at finite temperature is a perturbed, non-topological Gk/G model. In this model, we compute the one-loop effective potential for the Polyakov loop operators and explicitly construct the low-lying excited states. In the strong coupling limit the theory is in a deconfined phase.

String winding modes from charge non-conservation in compact Chern-Simons theory

In this letter we show how string winding modes can be constructed using topological membranes. We use the fact that monopole-instantons in compact topologically massive gauge theory lead to charge non-conservation inside the membrane which, in turn, enables us to construct string vertex operators with different left and right momenta. The amount of charge non-conservation inside the membrane is interpreted as giving the momentum associated with the string winding mode and is shown to match precisely the full mass spectrum of compactified string theory. We also argue that if heterotic strings are described by topological membranes, then all space-time dimensions must be compact.

Dissipation and Topologically Massive Gauge Theories in the Pseudo-Euclidean Plane

In pseudo-Euclidean metrics the Chern–Simons gauge theory in the infrared region is found to be associated with dissipative dynamics. In the infrared limit the Lagrangian of (2+1)-dimensional pseudo-euclidean topologically massive electrodynamics has indeed the same form as the Lagrangian of the damped harmonic oscillator. On the hyperbolic plane a set of two damped harmonic oscillators, each time-reversed from the other, is shown to be equivalent to a single undamped harmonic oscillator. The equations for the damped oscillators are proven to be the same as the ones for the Lorentz force acting on two particles carrying opposite charge in a constant magnetic field and in the electric harmonic potential. This provides an immediate link with Chern–Simons-like dynamics of Bloch electrons in solids propagating along the lattice plane with a hyperbolic energy surface. The symplectic structure of the reduced theory is finally discussed in the Dirac constrained canonical formalism and in the Faddeev–Jackiw symplectic formalism.

Canonical quantization of spontaneously broken topologically massive gauge theory

In this paper we investigate the canonical quantization of a non-Abelian topologically massive Chern–Simons theory in which the gauge fields are minimally coupled to a multiplet of scalar fields in such a way that the gauge symmetry is spontaneously broken. Such a model produces the Chern–Simons–Higgs mechanism in which the gauge excitations acquire mass both from the Chern–Simons term and from the Higgs–Kibble effect. The symmetry breaking is chosen to be only partially broken, in such a way that in the broken vacuum there remains a residual non-Abelian symmetry. We develop the canonical operator structure of this theory in the broken vacuum, with particular emphasis on the particle-content of the fields involved in the Chern–Simons–Higgs mechanism. We construct the Fock space and express the dynamical generators in terms of creation and annihilation operator modes. The canonical apparatus is used to obtain the propagators for this theory, and we use the Poincaré generators to demonstrate the effect of Lorentz boosts on the particle states.

Octonionic gauge theory from spontaneously broken SO(8)

An attempt is made to construct a gauge theory based on a bimodular representation of the octonion algebra, the non-associativity of which is manifested as a non-closure of the bimodule algebra. It is found that this fact leads to gauge-non-invariance of the theory. However, the bimodule algebra can be embedded in SO(8), the gauge theory of which can be broken down to give a massless SO(7) theory together with a massive octonionic gauge theory.

Massive loop amplitudes from unitarity

We show, for previously uncalculated examples containing a uniform mass in the loop, that it is possible to obtain complete massive one-loop gauge theory amplitudes solely from unitarity and known ultraviolet or infrared mass singularities. In particular, we calculate four-gluon scattering via massive quark loops in QCD. The contribution of a heavy quark to five-gluon scattering with identical helicities is also presented.

PSEUDOCLASSICAL MODEL FOR CHERN-SIMONS PARTICLES

Pseudoclassical supersymmetrical model to describe massive spin-one particles in (2+1) dimensions is proposed. A quantization of the model leads to the theory of Chern-Simons particles. In particular, one can see that the equations of the topologically massive gauge theory are reproduced in the course of quantization. For comparison a pseudoclassical model for Proca particles in (2+1) dimensions is constructed and discussed.

Bosonization of Thirring Model in Arbitary Dimension

We propose to use a novel master Lagrangian for performing the bosonization of the $D$-dimensional massive Thirring model in $D=d+1 \ge 2$ dimensions. It is shown that our master Lagrangian is able to relate the previous interpolating Lagrangians each other which have been recently used to show the equivalence of the massive Thirring model in (2+1) dimensions with the Maxwell-Chern-Simons theory. Starting from the phase-space path integral representation of the master Lagrangian, we give an alternative proof for this equivalence up to the next-to-leading order in the expansion of the inverse fermion mass. Moreover, in (3+1)-dimensional case, the bosonized theory is shown to be equivalent to the massive antisymmetric tensor gauge theory. As a byproduct, we reproduce the well-known result on bosonization of the (1+1)-dimensional Thirring model following the same strategy. Finally a possibility of extending our strategy to the non-Abelian case is also discussed.

Topologically massive gauge theory with O(2) symmetry

We discuss the structure of the vacua in O(2) topologically massive gauge theory on a torus. Since O(2) has two connected components, there are four classical vacua. The different vacua impose different boundary conditions on the gauge potentials. We also discuss the non-perturbative transitions between the vacua induced by vortices of the theory.

Non-abelian “self-dual” gauge theory in 2 + 1 dimensions

A non-abelian “self-dual” gauge theory describing a massive spin one physical mode is presented. The action is expressed in terms of two independent connections on a principle bundle over 2 + 1 space-time. The kinetic terms are respectively a Chern-Simons and a BF lagrangians, while the gauge invariant interaction is expressed in terms of the difference of the two connections. At the linearized level the theory is equivalent to the Topological Massive gauge theory. The covariant, BRST invariant, effective action of the non-abelian sefl dual gauge theory is constructed.

Integer quantization of the Chern-Simons coefficient in a broken phase

We consider a spontaneously broken nonabelian topologically massive gauge theory in a broken phase possessing a residual nonabelian symmetry. Recently there has been some question concerning the renormalization of the Chern-Simons coefficient in such a broken phase. We show that, in this broken vacuum, the renormalized ratio of the Chern-Simons coupling to the gauge coupling is shifted by 1 4π times an integer, preserving the usual integer quantization condition on the bare parameters.

Topological sectors of spin 1 theories in 2+1 dimensions

It is shown that the topological massive and “self-dual” theories, which are known to provide locally equivalent descriptions of spin 1 theories in 2+1 dimensions, have different global properties when formulated over topologically non-trivial regions of space-time. The partition function of these theories, when constructed on an arbitrary Riemannian manifold, differ by a topological factor, which is equal to the partition function of the pure Chern-Simons theory. This factor is related to the space of solutions of the field equations of the topological massive theory for which the connection is asymptotically flat but not gauge equivalent to zero. A new covariant, first order, gauge action, which generalizes the “self-dual” action, is then proposed. It is obtained by sewing local self-dual theories. Its global equivalence to the topological massive gauge theory is shown.

Reduction of general two-loop self-energies to standard scalar integrals

A method is presented for reducing general two-loop self-energies to standard scalar integrals in massive gauge theories with special emphasis on the electroweak Standard Model (SM). We develop a technique for treating the tensor structure of two-loop integrals appearing in self-energy calculations. It is used together with the symmetry properties of the integrals to obtain a result in terms of a small number of standard scalar integrals. The results are valid for arbitrary values of the invariant momentum p 2, all particle masses, the space-time dimension D and the gauge parameters ζ i ( i = γ Z, W). The algebraic structure of the results clearly displays the gauge dependence of the considered quantities and allows us to perform very stringent checks. We explicitly verify Slavnov-Taylor identities by calculating several thousand Feynman diagrams and adding them up algebraically. As an application of our algorithm we calculate the light fermion contributions to the two-loop gauge boson self-energies of the electroweak SM. We study their gauge dependence and discuss the occurring standard integrals.

Abelian Chern-Simons theory as the strong large-mass limit of topologically massive abelian gauge theory: the Wilson loop

We show that the renormalized vacuum expectation value of the Wilson loop for topologically massive abelian gauge theory in R 3 can be defined so that its large-mass limit is the renormalized vacuum expectation value of the Wilson loop for abelian Chern-Simons theory also in R 3.

Topological mass generation in three-dimensional string theory

The effective action of string theory in three dimensions is investigated, incorporating the Lorentz and gauge Chern-Simons terms in the definition of the Kalb-Ramond axion field strength. Since in three dimensions any three-form is trivial, the action can be reformulated by properly integrating the axion out. The circumstances under which it can be recast in form of topologically massive gravity coupled to a topologically massive gauge theory are pointed out. Finally, the strong coupling limit of the resulting action is inspected, with the focus on the roles played by the axion and dilaton fields.

Chern-Simons states and topologically massive gauge theories

In an abelian topologically massive gauge theory, any eigenstate of the Hamiltonian can be decomposed into a factor describing massive propagating gauge bosons and a Chern-Simons wave function describing a set of nonpropagating “topological” excitations. The energy depends only on the propagating modes, and energy eigenstates thus occur with a degeneracy that can be parametrized by the Hilbert space of the pure Chern-Simons theory. We show that for a nonabelian topologically massive gauge theory, this degeneracy is lifted: although the Gauss law constraint can be solved with a similar factorization, the Hamiltonian couples the propagating and nonpropagating (topological) modes.