On the super sigma models and super sine-Gordon model

A study of theO(3) invariant sigma model, theCP ¹ model and the sine-Gordon model in view of their equivalence in the Bose and Fermi-Bose cases is given, using the modern mathematical language of differential forms. On the basis of complex supersymmetry the central charges are shown to exist and interesting properties of complex supersymmetry are studied.     

The effective action for chiral fermions

We present an exact formula for the imaginary part of the effective action for chiral fermions in complex representations of the gauge group G, in the presence of an arbitrary external gauge field configuration. This result provides a unified treatment of both local and global anomalies and a precise characterization of some of the special properties of chiral fermions.     

Un-particle effective action

We study un-particle dynamics in the framework of standard quantum field theory. We obtain the Feynman propagator by supplementing standard quantum field theory definitions with integration over the mass spectrum. Then we use this information to construct effective actions for scalar, gauge vector and gravitational un-particles.     

The local effective action for two-dimensional supergravity

We obtained the local effective actions for (1,0) and (0,1) supergravity. They were shown to be equivalent to the non-local supergravity actions.     

Functional equation for the string effective action

A functional equation for the purely gravitational part of the string effective action is found. Among its solutions are the extended Euler densities and products of Wely tensors. A possible recipe for the Ricci temrs is given.     

The Vilkovisky-DeWitt effective action for quantum gravity

The Vilkovisky-DeWitt effective action for gauge theories is reviewed and then discussed in the context of N-dimensional quantum gravity and quantum Kaluza-Klein theory. The formalism gives an effective action which is gauge-independent and gauge and field-parametrization invariant. These features are illustrated for the vacuum energy of N-dimensional gravity. The Bunch-Parker local momentum space approach is used to calculate also the induced Ricci scalar term in the expansion of the effective action in powers of the curvature. The effective field equations are applied to the self-consistent dimensional reduction of five-dimensional Kaluza-Klein theory. A solution exists, but is found to be physically unacceptable.     

Symmetry-improved CJT effective action

The formalism introduced by Cornwall, Jackiw and Tomboulis (CJT) provides a systematic approach to consistently resumming non-perturbative effects in Quantum Thermal Field Theory. One major limitation of the CJT effective action is that its loopwise expansion introduces residual violations of possible global symmetries, thus giving rise to massive Goldstone bosons in the spontaneously broken phase of the theory. In this paper we develop a novel symmetry-improved CJT formalism for consistently encoding global symmetries in a loopwise expansion. In our formalism, the extremal solutions of the fields and propagators to a loopwise truncated CJT effective action are subject to additional constraints given by the Ward Identities due to global symmetries. By considering a simple O(2)$\mathbb{O}(2)$ scalar model, we show that, unlike other methods, our approach satisfies a number of important field-theoretic properties. In particular, we find that the Goldstone boson resulting from spontaneous symmetry breaking of O(2)$\mathbb{O}(2)$ is massless and the phase transition is a second-order one, already in the Hartree–Fock approximation. After taking the sunset diagrams into account, we show how our approach properly describes the threshold properties of the massless Goldstone boson and the Higgs particle in the loops. Finally, assuming minimal modifications to the Hartree–Fock approximated CJT effective action, we calculate the corresponding symmetry-improved CJT effective potential and discuss the conditions for its uniqueness for scalar-field values away from its minimum.     

An effective action for a variable electromagnetic field

This work consists essentially of two parts. The first part is an analysis of the one-loop effective action using the zeta-function approach. This gives a simple expression for the effective action in terms of the background field propagator. The next-of-kin to the zeta-function, the heat kernel, is given in terms of B. DeWitt's proper time expansion (also known as P. B. Gilkey's theorem). It is calculated in the second part for fermions interacting with an external electromagnetic field to first nonvanishing order in the variations of the gauge field.     

A convergent series for the QED effective action

The one-loop effective action of QED obtained by Heisenberg and Euler and by Schwinger has been expressed by an asymptotic perturbative series which is divergent. In this Letter we present a nonperturbative but convergent series of the effective action. With the convergent series we establish the existence of the manifest electric-magnetic duality in the one-loop effective action of QED.     

Multiloop calculations of effective action for local composite operators

Effective action for local composite operators is described for both the standard loop expansion formulation and an improved two-particle irreducible formulation. Rules for calculating multiloop contributions to the effective action are given in both formulations and are exemplified in the Gross-Neveu model in the large-N limit. Calculation of the exact effective action in the Gross-Neveu model is considerably simplified in the improved formulation. Results obtained from the conventional auxiliary field method, like dynamical symmetry breaking, non-classical solitions, etc., can all be obtained in the present formulation by dealing with the composite operators directly without introducing auxiliary fields. The present method can be applied to models in which the auxiliary field method is difficult to implement.     

Relation between effective couplings for asymptotically free models

For asymptotically free models with two independent couplings asymptotic expansions are constructed which express one effective coupling in terms of the other. The expansions involve powers (including fractional or irrational exponents) and logarithms. All orders of the-functions are taken into account. The expansions found are complete in the sense that they represent solutions (exact to any order) which generalize all the solutions obtained with the-functions approximated to second order. It is shown that higher orders are relevant since it is not possible in general to reparametrize the system such that the-functions become polynomials of the coupling parameters. The simplifications in case of supersymmetric models are discussed.     

Five-brane effective action in M-theory

On the world-volume of an M-theory five-brane propagates a two-form with self-dual field strength. As this field is non-Lagrangian, there is no obvious framework for determining its partition function. An analogous problem exists in Type IIB superstring theory for the self-dual five-form. The resolution of these problems and definition of the partition function is explained. A more complete analysis of perturbative anomaly cancellation for M-theory five-branes is also presented, uncovering some surprising details.     

Covariant effective action for quantum particle with coordinate-dependent mass

Using a covariant background field method we calculate the one-loop quantum effective action for a particle with coordinate-dependent mass moving slowly through a one-dimensional configuration space. The procedure can easily be extended to any desired loop order.