Gauge Model with Massive Gravitons

Gauge theory of gravity is formulated based on principle of local gauge invariance. Because the model hasstrict local gravitational gauge symmetry, and gauge theory of gravity is a perturbatively renormalizable quantum model.However, in the original model, all gauge gravitons are massless. We want to ask whether there exist massive gravitonsin Nature. In this paper, we will propose a gauge model with massive gravitons. The mass term of gravitational gaugefield is introduced into the theory without violating the strict local gravitational gauge symmetry. Massive gravitons canbe considered to be possible origin of dark energy and dark matter in the Universe.     

One-loop induced topological term in QED3

We consider the 2+1 dimensional massive QED and discuss the induced topological term in the one-loop level by using the higher derivative regularization. We show that the higher derivative regularization, which manifestly preserves the parity invariance when the fermion mass vanishes, automatically leads to a nonvanishing topological term in low energies. Although this higher derivative regularization formally violates the local gauge invariance, we propose a systematic way to recover the gauge invariance by adding local counter terms dictated by Ward-Takahashi identities. In practical applications, this regularization is interesting in connection with the discussion of the dynamical origin of the quantum Hall effect.     

Dimensional regularisation and broken conformal Ward identities

Dimensional regularization is used to give a simple treatment of broken conformal Ward identities. The method reproduces the known answers for standard theories. In addition it permits a derivation of the relevant identities for non-Abelian gauge theories which have not been obtained by other means. For the latter class of theories asymptotic scale invariance is found not to imply asymptotic conformal invariance for gauge variant Green functions. This is due to two gauge dependent insertions occurring in the identities. One can be predicted classically, whereas the other contains a new term dependent on Faddeev-Popov ghosts.     

Invariance of fermion determinant under large gauge transformations

We argue that in the perturbative framework the natural symmetry of the fermionic determinant is the perturbative gauge transformation (p.g.t.) which differs from the usual gauge transformation of the effective action through the absence of terms independent of the coupling constant. Calculated in a non-perturbative framework appropriate for large gauge function, the sum of these latter terms vanish. In three dimensions the invariance of the full fermion determinant under large gauge transformations is thus ensured due to the invariance under p.g.t. of the Chern-Simons term arising in some perturbative regularisations.     

Gauge invariant theories of the generalized chiral Schwinger model

The gauge invariant theories of the generalized chiral Schwinger model are constructed in terms of two schemes with and without Wess-Zumino terms, respectively. Following the former scheme, we calculate the Wess-Zumino term which cancels the gauge anomaly, and then constitute the gauge invariant theory by adding the Wess-Zumino term to the original Lagrangian of the model. According to the latter, we modify the original Hamiltonian by adding a term composed of constraints of the model. It is so designed that the theory described by the modified Hamiltonian and its corresponding first-order Lagrangian maintains gauge invariance. We show by the canonical Dirac method that each of the two gauge invariant theories has the same physical spectrum as that of the original gauge noninvariant formulation.     

Gauge invariant theories of the generalized chiral Schwinger model

The gauge invariant theories of the generalized chiral Schwinger model are constructed in terms of two schemes with and without Wess-Zumino terms, respectively. Following the former scheme, we calculate the Wess-Zumino term which cancels the gauge anomaly, and then constitute the gauge invariant theory by adding the Wess-Zumino term to the original Lagrangian of the model. According to the latter, we modify the original Hamiltonian by adding a term composed of constraints of the model. It is so designed that the theory described by the modified Hamiltonian and its corresponding first-order Lagrangian maintains gauge invariance. We show by the canonical Dirac method that each of the two gauge invariant theories has the same physical spectrum as that of the original gauge noninvariant formulation.     

Vacuum Polarisation Effects in the Lorentz Violating Electrodynamics

In this work we reconsider the one loop calculation for the vacuum polarisation tensor in the Lorentz violating quantum electrodynamics. The electron propagator is “dressed” by a Lorentz breaking extra term in the fermion Lagrangian density. We check gauge invariance and use the Schwinger–Dyson equation to discuss the full photon propagator. After a discussion on a possible photon mass shift, we show how a finite quantum correction can be chosen in a unique way in order to ensure—in the spirit of spontaneously broken theories—the standard normalisation conditions for the vacuum polarisation tensor. Then we comment on possible observable physical consequences on the Lamb-shift.     

Gauge invariance and fermion doubling on the lattice

(1) We consider a possible chiral invariant solution of the lattice fermion doubling problem. This makes the unwanted states decouple in the continuum limit, at least in the non-interacting theory. The introduction of gauge interactions restores doubling. We examine how local gauge invariance makes all the species in a doubled spectrum act alike. (2) We generalise earlier results to show how gauge invariance forces a doubled spectrum on us even when other considerations do not.     

String field theory in the Siegel gauge

We specialize the gauge-fixing procedure for the Witten action of the open bosonic string, given in a preceding paper, choosing the Siegel gauge. We find that the BRST-invariant gauge-fixed action is the gauge invariant one with ghost number unrestricted plus a gauge-fixing term. The BRST invariance of the measure in the functional integral is briefly discussed. As a technical tool the Hodge dual of a string functional is defined.     

N = 4 SYM low-energy effective action in N = 4 harmonic superspace

We apply the N = 4 harmonic superspace with USp(4) harmonic variables for describing the N = 4 SYM low-energy effective action. Scale invariance and gauge symmetry fix the leading term in the low-energy effective action uniquely, up to a constant. The value of the remaining constant can be fixed by the topological quantization condition for the Wess-Zumino term which is present in the component structure of this action.     

Non-abelian gauge dynamics of slowly moving fermions

We study the dynamics generated by local gauge invariance under a non-abelianSU(N) group for two nonrelativistic particles interacting through the effect of the group charges. We describe the local gauge invariant potential which contains the exchange of infinitely many gluons. We discuss the possible implications of our result.     

Gauge invariance based on the extrinsic geometry in the rigid string

The string model with the extrinsic curvature is studied which is a gauge invariant field theory with higher order derivatives. We present an equivalent action without any higher order derivatives which keeps the gauge invariance. We point out the difficulty caused by the second class constraints in Dirac's canonical method. Following a new method for dynamical systems with second class constraints, we construct an equivalent model which has no second class constrants but as a new gauge invariance. This gauge invariance guarantees the equivalence between the original model and the new one. We show that the model can be quantized in this formalism. We find the unitarity violation of the model.     

On the Gauge and BRST Invariance of the Chiral QED with Faddeevian Anomaly

Chiral Schwinger model with the Faddeevian anomaly is considered. It is found that imposing a chiral constraint this model can be expressed in terms of chiral boson. The model when expressed in terms of chiral boson remains anomalous and the Gauss law of which gives anomalous Poisson brackets between itself. In spite of that a systematic BRST quantization is possible. The Wess-Zumino term corresponding to this theory appears automatically during the process of quantization. A gauge invariant reformulation of this model is also constructed. Unlike the former one gauge invariance is done here without any extension of phase space. This gauge invariant version maps onto the vector Schwinger model. The gauge invariant version of the chiral Schwinger model for a=2 has a massive field with identical mass however gauge invariant version obtained here does not map on to that.     

Heterotic string in background gauge fields

The higher order corrections to the two-dimensional nonlinear σ-model for the heterotic string are considered. The divergent parts of the effective action are calculated explicitly to two-loop order in the presence of arbitrary background gauge fields. It is shown that the full gauge Chern-Simons term appears in the divergent terms. We also discuss its relevance to the equations of motion for the massless modes of the heterotic string with emphasis on the local gauge invariance of the heterotic string theory.     

Classification of symmetry breaking by Wilson lines on the Z orbifold

We give a complete classification of gauge symmetry breaking by Wilson lines on the standard Z orbifold by deriving the general formula of the conditions of modular invariance and group invariance in the presence of background gauge fields. All possible E₆×SU(3) breaking in terms of one Wilson line is given. The symmetries of the electroweak and grand unification are obtained by combining two Wilson lines.     

General relativity as a conformally invariant scalar gauge field theory

The global symmetry implied by the fact that one can multiply all masses with a common constant is made into a local, gauge symmetry. The matter action then becomes Conformally invariant and it seems natural to choose for the corresponding scalar gauge field the action for a conformally invariant (massless) scalar field. The resulting conformally invariant theory turns out to be equivalent to general relativity. Since this means that the usual Einstein-Hilbert action is not, in fact, a true gauge action for the space-time geometry, the full theory ought to be supplied with such a term. Gauge-theoretic arguments and conformal invariance requirements dictate its form.     

On the theoretical problems in constructing interactions involving higher-spin massless particles

It is shown that a gauge theory of self-interacting massless spin-3 particles which is analogous to Yang-Mills or the theory of gravity does not exist. A way out may be the existence of an interacting infinite family of massless particles of various spins. The first-order interactions which are possible between such particles show a remarkable structure. This is established by explicit construction. Detailed results are obtained for the possible algebraic structures which one may obtain for gauge theories which are induced from the gauge invariance of free lagrangians.     

Forests, groves and Higgs bosons

We determine the gauge invariance classes of tree level Feynman diagrams in spontaneously broken gauge theories, providing a proof for the formalism of gauge and flavor flips. We find new gauge invariance classes in theories with a nonlinearly realized scalar sector. In unitarity gauge, the same gauge invariance classes correspond to a decomposition of the scattering amplitude into pieces that satisfy the relevant Ward identities individually. In theories with a linearly realized scalar sector in gauge, no additional non-trivial gauge invariance classes exist compared to the unbroken case.Received: 2 June 2003, Revised: 21 July 2003, Published online: 5 September 2003     

D-branes and T-duality

We show how the T-duality between D-branes is realized (i) on p-brane solutions (p = 0,…,9) of IIA/IIB supergravity and (ii) on the D-brane actions (p = 0,…, 3) that act as source terms for the p-brane solutions. We point out that the presence of a cosmological constant in the IIA theory leads, by the requirement of gauge invariance, to a topological mass term for the worldvolume gauge field in the 2-brane case.     

Modified strings in terms of zweibein fields

Possible modifications of the relativistic string which preserves conformal invariance in the conformal gauge is investigated using zweibein fields. A fully reparametrization-invariant action yielding Liouville's equation is then constructed without the introduction of auxiliary fields. This action breaks the local two-dimensional Lorentz invariance and the corresponding extra degree of freedom reduces in the conformal gauge to a free field. For open strings the variation of the action implies that the Liouville field and this free field are connected by a Bäcklund transformation at the boundary. In certain cases it is shown that this extends to hold everywhere. If the local Lorentz invariance is restored, then the reparametrization algebra acquires the anomalous term necessary for the quantization in subcritical dimensions.