These lectures introduce some of the basic ideas of e ective eld theories. The topics discussed include: relevant and irrelevant operators and scaling, renormalization in e ective eld theories, decoupling of heavy particles, power counting, and naive dimensional analysis. E ective Lagrangians are used to study the S = 2 weak interactions and chiral perturbation theory.

We analyse the SU(2) k WZNW models beyond the integrable representations and in particular the case of SU(2) 0. We find that these are good examples of logarithmic conformal field theories as indecomposable representations are naturally produced in the fusion of discrete irreducible representations. We also find extra, chiral and non-chiral, multiplet structure in the theory. The chiral fields,...

These lectures introduce some of the basic ideas of effective field theories. The topics discussed include: relevant and irrelevant operators and scaling, renormalization in effective field theories, decoupling of heavy particles, power counting, and naive dimensional analysis. Effective Lagrangians are used to study the ∆S = 2 weak interactions and chiral perturbation theory.

We derive unitarity restrictions on the scaling dimensions of primary quantum operators in a superconformal quantum field theory, in d =3, 4, 5, 6. 1. Introduction Whereas classical massless field theories are often conformally invariant, the same is rarely true of their quantum counterparts. To define a quantum field theory, you need to specify both a Lagrangian and a cutoff. The cutoff introd...

A simple, basic, argument is given, based solely on energy-momentum considerations to recover conditions under which ar affine or conformal Toda field theories can support defects of integrable type. Associated triangle relations are solved to provide expressions for transmission matrices that generalize previously known examples calculated for the sine-Gordon model and the a2 affine Toda model...

An effective field theory (EFT) is a theory of the dynamics of a physical system at energies small compared to a given cut-off. Low-energy states with respect to this cut-off are effectively independent of states at high energies; hence one may study the low-energy dynamics without the need for a detailed description of the high-energy dynamics. Many authors have suggested that, because of the ...

A ‘canonical mapping’ is established between the c = −1 system of bosonic ghosts and the c = 2 complex scalar theory and, a similar mapping between the c = −2 system of fermionic ghosts and the c = 1 Dirac theory. The existence of this mapping is suggested by the identity of the characters of the respective theories. The respective c < 0 and c > 0 theories share the same space of states, wherea...

We define Homotopy quantum field theories (HQFT) as Topological quantum field theories (TQFT) for manifolds endowed with extra structure in the form of a map into some background space X. We also build the category of homotopy cobordisms HCobord(n, X) such that an HQFT is a functor from this category into a category of linear spaces. We then derive some very general properties of HCobord(n, X),...

In this article, written primarily for physicists and geometers, we introduce the notion of TQFT, orbifold, and then we survey the construction of TQFTs originating from orbifolds such as Chen-Ruan cohomology and orbifold string topology.