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Sigma-Models and Strings

  • M. T. Grisaru
Part of the The Subnuclear Series book series (SUS, volume 25)

Abstract

The modern covariant approach to string theory is based on the Polyakov ansatz: The dual model scattering amplitude is given by an expression
$$ \sum\limits_{topo\log ies}{\int{\left[ {{d}_{{{\gamma }_{\mu \nu }}}} \right]}}\left[ d{{X}^{m}} \right]\,\exp \left[ \frac{1}{2}\int{d\zeta d\tau \sqrt{\gamma }{{\gamma }^{\mu \nu }}{{\partial }_{\mu }}{{X}_{m}}{{\partial }_{\nu }}{{X}^{m}}} \right]\cdot V\left( {{k}_{1}},{{s}_{1}} \right)V\left( {{k}_{2}},{{s}_{2}} \right)\cdots \,V\left( {{k}_{n}},{{s}_{n}} \right) $$
(1)
where \( \int{\left[ {{d}_{{{\gamma }_{\mu \nu }}}} \right]\left[ d{{X}^{m}} \right]} \) represents functional integration over all possible embeddings of the two-dimensional world-sheet with coordinates (ζ, τ) into D-dimensional space-time with coordinates X m , and over all possible (gauge-inequivalent) metrics on the world-sheet, and the sum is over all topologies of the world-sheet. The V’s are vertex functions \( V\left( {{k}_{i}},{{s}_{i}} \right)=\int{d{{\zeta }_{i}}d{{\tau }_{i}}V\left( {{k}_{i}},{{s}_{i}},{{X}_{i}} \right)} \) for emission of particle species s i with momentum k i [1].

Keywords

Conformal Invariance Operator Product Expansion Dimensional Regularization Background Field Dual Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Plenum Press, New York 1990

Authors and Affiliations

  • M. T. Grisaru
    • 1
  1. 1.Physics DepartmentBrandeis UniversityWalthamUSA

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