Gauge Theory Correlators from Non-Critical String Theory

Gauge Theory Correlators from Non-Critical String Theory

February 1998 | S.S. Gubser, I.R. Klebanov and A.M. Polyakov
The paper by Gubser, Klebanov, and Polyakov explores the connection between gauge theory and non-critical string theory in the context of $\mathcal{N}=4$ supersymmetric Yang-Mills theory with a large number of colors. They propose a method to obtain certain Green's functions in this theory through non-critical string theory, which is related to critical string theory in an anti-deSitter (AdS) background. By introducing a boundary condition on the AdS space, analogous to a cutoff in the Liouville coordinate of two-dimensional string theory, they relate correlation functions of operators in the gauge theory to the dependence of the supergravity action on the boundary conditions. This approach allows them to read off anomalous dimensions from the quadratic terms in supergravity. For operators coupling to massless string states, the anomalous dimensions vanish, and for operators coupling to massive string states at level $n$, the anomalous dimensions grow as $2(n g_{YM} \sqrt{2 N})^{1/2}$ for large 't Hooft coupling. This prediction provides new insights into the strong coupling behavior of large $N$ SYM theory. The paper also discusses the implications of this correspondence for understanding quark confinement and the true "gauge" degrees of freedom in string theories and gravity.The paper by Gubser, Klebanov, and Polyakov explores the connection between gauge theory and non-critical string theory in the context of $\mathcal{N}=4$ supersymmetric Yang-Mills theory with a large number of colors. They propose a method to obtain certain Green's functions in this theory through non-critical string theory, which is related to critical string theory in an anti-deSitter (AdS) background. By introducing a boundary condition on the AdS space, analogous to a cutoff in the Liouville coordinate of two-dimensional string theory, they relate correlation functions of operators in the gauge theory to the dependence of the supergravity action on the boundary conditions. This approach allows them to read off anomalous dimensions from the quadratic terms in supergravity. For operators coupling to massless string states, the anomalous dimensions vanish, and for operators coupling to massive string states at level $n$, the anomalous dimensions grow as $2(n g_{YM} \sqrt{2 N})^{1/2}$ for large 't Hooft coupling. This prediction provides new insights into the strong coupling behavior of large $N$ SYM theory. The paper also discusses the implications of this correspondence for understanding quark confinement and the true "gauge" degrees of freedom in string theories and gravity.
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