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Short distance properties of cascading gauge theories

Ofer Aharony, Alex Buchel, Amos Yarom

Abstract

We study the short distance (large momentum) properties of correlation functions of cascading gauge theories by performing a tree-level computation in their dual gravitational background. We prove that these theories are holographically renormalizable; the correlators have only analytic ultraviolet divergences, which may be removed by appropriate local counterterms. We find that n-point correlation functions of properly normalized operators have the expected scaling in the semi-classical gravity (large N) limit: they scale as N_{eff}^{2-n} with N_{eff} proportional to ln(k/Lambda) where k is a typical momentum. Our analysis thus confirms the interpretation of the cascading gauge theories as renormalizable four-dimensional quantum field theories with an effective number of degrees of freedom which logarithmically increases with the energy.

Short distance properties of cascading gauge theories

Abstract

We study the short distance (large momentum) properties of correlation functions of cascading gauge theories by performing a tree-level computation in their dual gravitational background. We prove that these theories are holographically renormalizable; the correlators have only analytic ultraviolet divergences, which may be removed by appropriate local counterterms. We find that n-point correlation functions of properly normalized operators have the expected scaling in the semi-classical gravity (large N) limit: they scale as N_{eff}^{2-n} with N_{eff} proportional to ln(k/Lambda) where k is a typical momentum. Our analysis thus confirms the interpretation of the cascading gauge theories as renormalizable four-dimensional quantum field theories with an effective number of degrees of freedom which logarithmically increases with the energy.

Paper Structure

This paper contains 24 sections, 154 equations, 2 tables.

Table of Contents

  1. Introduction and summary
  2. Generalities
  3. Bulk-to-boundary propagators and two-point functions
  4. The AdS bulk-to-boundary propagator
  5. The KT bulk-to-boundary propagator
  6. Non-integer $\nu$
  7. Integer $\nu$
  8. Explicit examples
  9. Two-point functions
  10. Higher $N$-point functions
  11. Tree level $N$-point functions in AdS
  12. General expression for the $N$-point functions
  13. Locality of UV divergences and the $R_{UV} \to 0$ limit
  14. Analysis of leading terms
  15. Examples of correlation functions
  16. ...and 9 more sections