摘要:

A brief review on the progress made in the study of Chern-Simons gauge theory since its relation to knot theory was discovered ten years ago is presented. Emphasis is made on the analysis of the perturbative study of the theory and its connection to the theory of Vassiliev invariants. It is described how the study of the quantum field theory for three different gauge fixings leads to three different representations for Vassiliev invariants. Two of these gauge fixings lead to well known representations: the covariant Landau gauge corresponds to the configuration space integrals while the non-covariant light-cone gauge to the Kontsevich integral. The progress made in the analysis of the third gauge fixing, the non-covariant temporal gauge, is described in detail. In this case one obtains combinatorial expressions, instead of integral ones, for Vassiliev invariants. The approach based on this last gauge fixing seems very promising to obtain a full combinatorial formula. We collect the combinatorial expressions for all the Vassiliev invariants up to order four which have been obtained in this approach. ©1999 American Institute of Physics.

ISSN:0094-243X    

DOI:10.1063/1.59663

出版商:AIP    

年代:1999

数据来源: AIP

摘要:

Recently, the long-standing problem of calculating the quantum mass of supersymmetric and nonsupersymmetric solitons1+1dimensions in an unambiguous way, and the issue of whether or not it satisfies the BPS bound at the quantum level, was solved [1–4]. We discuss here the kink. One basic idea is to compute∂/∂m&hthinsp;∑&ohgr;(which converges) instead of∑&ohgr;,and to fix the integration constant by imposing the renormalization condition that the vacuum energies of the topological sector and the nontopological sector become equal whenmand other dimensional constants (if present) tend to zero. Another new idea is to derive the boundary conditions from the symmetries of the action and the topology of the classical solution. For the bosonic fluctuations about the kink we then find antiperiodic boundary conditions, while for the fermionic fluctuations we find twisted boundary conditions. The almost universally used periodic or antiperiodic boundary conditions are shown to be inconsistent for fermions (!). The central chargeZin the supersymmetry algebra is classically given by the usual total derivative, but at the quantum level an “anomaly” (an extra term of order ℏ) is found inZ. This term is calculated by using a higher-derivative regularization scheme which preserves supersymmetry. Regulating the supersymmetry generators in this way, the BPS bound remains saturated for the supersymmetric kink, but both the mass and the central charge receive (equal) quantum corrections. ©1999 American Institute of Physics.

ISSN:0094-243X    

DOI:10.1063/1.59670

出版商:AIP    

年代:1999

数据来源: AIP

摘要:

We show that the largeNlimit of certain conformal field theories in various dimensions include in their Hilbert space a sector describing supergravity on the product of Anti-deSitter spacetimes, spheres and other compact manifolds. This is shown by taking some branes in the full M/string theory and then taking a low energy limit where the field theory on the brane decouples from the bulk. We observe that, in this limit, we can still trust the near horizon geometry for largeN. The enhanced supersymmetries of the near horizon geometry correspond to the extra supersymmetry generators present in the superconformal group (as opposed to just the super-Poincare group). The ’t Hooft limit of3+1N=4super-Yang-Mills at the conformal point is shown to contain strings: they are IIB strings. We conjecture that compactifications of M/string theory on various Anti-deSitter spacetimes is dual to various conformal field theories. This leads to a new proposal for a definition of M-theory which could be extended to include five non-compact dimensions. ©1999 American Institute of Physics.

ISSN:0094-243X    

DOI:10.1063/1.59653

出版商:AIP    

年代:1999

数据来源: AIP

摘要:

We present D3-brane solutions in type IIB string theory which preserve 1/4 of supersymmetry. Their near-horizon geometry isAdS5×X5whereX5is an appropriate Einstein space and they are candidates for supergravity duals of certain four-dimensional superconformal field theories. ©1999 American Institute of Physics.

ISSN:0094-243X    

DOI:10.1063/1.59654

出版商:AIP    

年代:1999

数据来源: AIP

摘要:

The duality symmetric but non manifestly covariant action proposed by Schwarz and Sen is canonically quantized in the Coulomb gauge. The resulting theory turns out to be, nevertheless, relativistically invariant. It is shown, afterwards, that the Schwarz-Sen model naturally emerges when duality is implemented as a local symmetry of sourceless electrodynamics. This implies in the equivalence of these theories at the quantum level. ©1999 American Institute of Physics.

ISSN:0094-243X    

DOI:10.1063/1.59671

出版商:AIP    

年代:1999

数据来源: AIP

摘要:

We review the developments of a recently proposed approach to study integrable theories in any dimension. The basic idea consists in generalizing the zero curvature representation for two-dimensional integrable models to space-times of dimensiond+1by the introduction of ad-form connection. The method has been used to study several theories of physical interest, like self-dual Yang-Mills theories, Bogomolny equations, non-linear sigma models and Skyrme-type models. The local version of the generalized zero curvature involves a Lie algebra and a representation of it, leading to a number of conservation laws equal to the dimension of that representation. We discuss the conditions a given theory has to satisfy in order for its associated zero curvature to admit an infinite dimensional (reducible) representation. We also present the theory in the more abstract setting of the space of loops, which gives a deeper understanding and a more simple formulation of integrability in any dimension. ©1999 American Institute of Physics.

ISSN:0094-243X    

DOI:10.1063/1.59672

出版商:AIP    

年代:1999

数据来源: AIP

摘要:

There are many reasons to believe the present mass density of the universe is dominated by a weakly interacting massive particle (WIMP), a fossil relic of the early universe. Theoretical ideas and experimental efforts have focused mostly on production and detection ofthermalrelics, with mass typically in the range a few GeV to a hundred GeV. Here, I will review scenarios for production ofnonthermaldark matter. Since the masses of the nonthermalWIMPSare in the range1012to1016&hthinsp;GeV,much larger than the mass of thermal wimpyWIMPS, they may be referred to asWIMPZILLAS. In searches for dark matter it may be well to remember that “size does matter.” ©1999 American Institute of Physics.

ISSN:0094-243X    

DOI:10.1063/1.59655

出版商:AIP    

年代:1999

数据来源: AIP

摘要:

Spectral functions relevant in the context of quantum field theory under the influence of spherically symmetric external conditions are analysed. Examples comprise heat-kernels, determinants and spectral sums needed for the analysis of Casimir energies. First, we summarize that a convenient way of handling them is to use the associated zeta function. A way to determine all its needed properties is derived. Using the connection with the mentioned spectral functions, we provide: i.) a method for the calculation of heat-kernel coefficients of Laplace-like operators on Riemannian manifolds with smooth boundaries and ii.) an analysis of vacuum energies in the presence of spherically symmetric boundaries and external background potentials. ©1999 American Institute of Physics.

ISSN:0094-243X    

DOI:10.1063/1.59656

出版商:AIP    

年代:1999

数据来源: AIP

摘要:

We review some aspects of three-dimensional quantum gravity with emphasis in the‘CFT→Geometry’map that follows from the Brown-Henneaux conformal algebra. The general solution to the classical equations of motion with anti-de Sitter boundary conditions is displayed. This solution is parametrized by two functions which become Virasoro operators after quantization. A map from the space of states to the space of classical solutions is exhibited. Some recent proposals to understand the Bekenstein-Hawking entropy are reviewed in this context. The origin of the boundary degrees of freedom arising in2+1gravity is analyzed in detail using a Hamiltonian Chern-Simons formalism. ©1999 American Institute of Physics.

ISSN:0094-243X    

DOI:10.1063/1.59661

出版商:AIP    

年代:1999

数据来源: AIP

摘要:

We study the non relativistic limit of a Model of Fermions interacting through a Chern-Simons Field, from a perspective that resembles the Wilson’s Renormalization Group approach, instead of the more usual approach found in most texts of Field Theory. The solution of some difficulties, and a new understanding of non relativistic models is given. ©1999 American Institute of Physics.

ISSN:0094-243X    

DOI:10.1063/1.59657

出版商:AIP    

年代:1999

数据来源: AIP