World-Sheets from N=4 Super Yang-Mills

TL;DR

This paper explores the connection between N=4 super Yang-Mills theory and the AdS_5 x S^5 superstring by comparing their free energies and partition functions, providing insights into how string world-sheets emerge from gauge theory.

Contribution

It introduces a formal free energy for N=4 SYM expanded to all orders, expressed as a sum over discretized surfaces, and compares it with the superstring partition function to shed light on the emergence of string world-sheets.

Findings

Identifies common properties between SYM free energy and superstring partition function.

Suggests a mechanism for the emergence of string world-sheets from gauge theory.

Provides a formal framework for comparing gauge theory and string theory in AdS/CFT.

Abstract

We examine whether the free energy of N=4 super Yang-Mills theory (SYM) in four dimensions corresponds to the partition function of the AdS_5 x S^5 superstring when corresponding operators are inserted into both theories. We obtain a formal free energy of N=4 U(N) SYM in four dimensions generated by the Feynman graph expansion to all orders of the 't Hooft coupling expansion with arbitrary N. This free energy is written as the sum over discretized closed two-dimensional surfaces that are identified with the world-sheets of the string. We compare this free energy with a formal partition function of the discretized AdS_5 x S^5 superstring with the kappa-symmetry fixed in the killing gauge and in the expansion corresponding to the weak 't Hooft coupling expansion in the SYM. We find common properties on both sides, although further studies are required to obtain a more precise comparison. Our result suggests a mechanism for how the world-sheet appears dynamically from N=4 SYM, thus enabling us to derive how the AdS_5 x S^5 superstring is reproduced in the AdS/CFT correspondence.