On the worldsheet theories of strings dual to free large N gauge theories

Abstract

We analyze in detail some properties of the worldsheet of the closed string theories suggested by Gopakumar to be dual to free large N SU(N) gauge theories (with adjoint matter fields). We use Gopakumar's prescription to translate the computation of space-time correlation functions to worldsheet correlation functions for several classes of Feynman diagrams, by explicit computations of Strebel differentials. We compute the worldsheet operator product expansion in several cases and find that it is consistent with general worldsheet conformal field theory expectations. A peculiar property of the construction is that in several cases the resulting worldsheet correlation functions are non-vanishing only on a sub-space of the moduli space (say, for specific relations between vertex positions). Another strange property we find is that for a conformally invariant space-time theory, the mapping to the worldsheet does not preserve the special conformal symmetries, so that the full conformal group is not realized as a global symmetry on the worldsheet (even though it is, by construction, a symmetry of all integrated correlation functions).

60 pages, 17 figures, latex. v2: Added references and a minor correction

Cited by in corpus (13)

• Deriving the ${\text{AdS}}_3/{\text{CFT}}_2$ Correspondence
• Extremal Correlators and Hurwitz Numbers in Symmetric Product Orbifolds
• Higher genus correlators for tensionless ${\mathrm{AdS}}_3$ strings
• String correlators on ${\text{AdS}}_3$: Analytic structure and dual CFT
• From Symmetric Product CFTs to ${\mathrm{AdS}}_3$
• Comments on worldsheet theories dual to free large N gauge theories
• On the AdS Higher Spin / O(N) Vector Model Correspondence: degeneracy of the holographic image
• Cut-and-join operators and N=4 super Yang-Mills
• The space-time operator product expansion in string theory duals of field theories
• Open and Closed String Worldsheets from Free Large N Gauge Theories with Adjoint and Fundamental Matter
• Triangulated Surfaces in Twistor Space: A Kinematical Set up for Open/Closed String Duality
• Moving holographic boundaries
• Boundary Conformal Field Theory and Ribbon Graphs: a tool for open/closed string dualities