摘要:

These lectures give an introduction to duality in Quantum Field Theory. We discuss the phases of gauge theories and the implications of the electric-magnetic duality transformation to describe the mechanism of confinement. We review the exact results ofN=1supersymmetric QCD and the Seiberg-Witten solution ofN=2super Yang-Mills. Some of its extensions to String Theory are also briefly discussed. ©1998 American Institute of Physics.

ISSN:0094-243X    

DOI:10.1063/1.54691

出版商:AIP    

年代:1998

数据来源: AIP

摘要:

In these lectures we present a general introduction to topological quantum field theories. These theories are discussed in the framework of the Mathai-Quillen formalism and in the context of twistedN=2supersymmetric theories. We discuss in detail the recent developments in Donaldson-Witten theory, obtained from the application of results based on duality forN=2supersymmetric Yang-Mills theories. This involves a description of the computation of Donaldson invariants in terms of Seiberg-Witten invariants. Generalizations of Donaldson-Witten theory are reviewed, and the structure of the vacuum expectation values of their observables is analysed in the context of duality for the simplest case. ©1998 American Institute of Physics.

ISSN:0094-243X    

DOI:10.1063/1.54705

出版商:AIP    

年代:1998

数据来源: AIP

摘要:

We use a semiclassical approximation to derive the partition function for an arbitrary potential in one-dimensional Quantum Statistical Mechanics, which we view as an example of finite temperature scalar Field Theory at a point. We rely on Catastrophe Theory to analyze the pattern of extrema of the corresponding path-integral. We exhibit the propagator in the background of the different extrema and use it to compute the fluctuation determinant and to develop a (nonperturbative) semiclassical expansion which allows for the calculation of correlation functions. We discuss the examples of the single and double-well quartic anharmonic oscillators, and the implications of our results for higher dimensions. ©1998 American Institute of Physics.

ISSN:0094-243X    

DOI:10.1063/1.54706

出版商:AIP    

年代:1998

数据来源: AIP

摘要:

The present status of precision electroweak tests of the Standard Model are discussed in Lecture 1, with particular emphasis on the search for the Higgs boson andW+W−production at LEP. Various aspects of supersymmetry phenomenology are discussed in Lecture 2, including models with conservedRparity in which the lightest supersymmetric particle may be a neutralino or the gravitino, and models with brokenRparity, particularly in connection with the large-Q2events recently observed at HERA. Finally, other possible searches for supersymmetric particles are discussed in Lecture 3, including non-accelerator searches for supersymmetric dark matter and future searches at the LHC accelerator. ©1998 American Institute of Physics.

ISSN:0094-243X    

DOI:10.1063/1.54687

出版商:AIP    

年代:1998

数据来源: AIP

摘要:

We review some results recently obtained for the conformal field theories based on the affine Lie superalgebra osp(1|2). In particular, we study the representation theory of the osp(1|2) current algebras and their character formulas. By means of a free field representation of the conformal blocks, we obtain the structure constants and the fusion rules of the model. ©1998 American Institute of Physics.

ISSN:0094-243X    

DOI:10.1063/1.54688

出版商:AIP    

年代:1998

数据来源: AIP

摘要:

I discuss in this talk a bosonization approach recently developed in refs. [1]–[7]. It leads to the (exact) bosonization rule for fermion currents ind⩾2dimensions and also provides a systematic way of constructing the bosonic action in different regimes. ©1998 American Institute of Physics.

ISSN:0094-243X    

DOI:10.1063/1.54689

出版商:AIP    

年代:1998

数据来源: AIP

摘要:

We give an elementary introduction to the recent solution ofN=2supersymmetric Yang-Mills theory. In addition, we review how it can be re-derived from string duality. ©1998 American Institute of Physics.

ISSN:0094-243X    

DOI:10.1063/1.54690

出版商:AIP    

年代:1998

数据来源: AIP

摘要:

The construction of new series of integrable quantum field theories whose equations-of-motion are related to the non-abelian affine Toda equations is summarized. All these theories can be thought of as generalizations of the sine-Gordon theory. They admit (charged) soliton solutions, exhibit a mass-gap, and are described by a unitary (real positive-definite) action. Their quantum integrability and semi-classical spectrum of solitons are also discussed. ©1998 American Institute of Physics.

ISSN:0094-243X    

DOI:10.1063/1.54692

出版商:AIP    

年代:1998

数据来源: AIP

摘要:

Ellipticity of boundary value problems is characterized in terms of the Caldero´n projector. The presence of topological obstructions for the chiral Dirac operator under local boundary conditions in even dimension is discussed. Functional determinants for Dirac operators on manifolds with boundary are considered. The functional determinant for a Dirac operator on a bidimensional disk, in the presence of an Abelian gauge field and subject to global boundary conditions of the type introduced by Atiyah-Patodi-Singer, is evaluated. The relationship with the index theorem is also commented. ©1998 American Institute of Physics.

ISSN:0094-243X    

DOI:10.1063/1.54693

出版商:AIP    

年代:1998

数据来源: AIP

摘要:

The existence of topological invariants analogous to Chern/Pontryagin classes for a standardSO(D)orSU(N)connection, but constructed out of the torsion tensor, is discussed. These invariants exhibit many of the features of the Chern/Pontryagin invariants: they can be expressed as integrals over the manifold of local densities and take integer values on compact spaces without boundary; their spectrum is determined by the homotopy groups&pgr;D−1(SO(D))and&pgr;D−1(SO(D+1)).These invariants are not solely determined by the connection bundle but depend also on the bundle of local orthonormal frames on the tangent space of the manifold. It is shown that in spacetimes with nonvanishing torsion there can occur topologically stable configurations associated with the frame bundle which are independent of the curvature. Explicit examples of topologically stable configurations carrying nonvanishing instanton number in four and eight dimensions are given, and they can be conjectured to exist in dimension4k.It is also shown that the chiral anomaly in a spacetime with torsion receives a contribution proportional to this instanton number and hence, chiral theories in4k-dimensional spacetimes with torsion are potentially anomalous. ©1998 American Institute of Physics.

ISSN:0094-243X    

DOI:10.1063/1.54694

出版商:AIP    

年代:1998

数据来源: AIP