This paper presents a method to calculate certain Green's functions in 3+1 dimensional N=4 supersymmetric Yang-Mills (SYM) theory with a large number of colors using non-critical string theory. The non-critical string theory is related to critical string theory in an anti-de Sitter (AdS) background. The authors introduce a boundary of the AdS space analogous to a cutoff in the Liouville coordinate of 2D string theory. Correlation functions of gauge theory operators are related to the dependence of the supergravity action on boundary conditions. From the quadratic terms in supergravity, the anomalous dimensions of operators are derived. For operators coupling to massless string states, the anomalous dimensions vanish, as shown through absorption calculations. Operators coupling to massive string states at level n acquire anomalous dimensions that grow as $2(n g_{YM}\sqrt{2N})^{1/2}$ for large 't Hooft coupling. This is a new prediction about the strong coupling behavior of large N SYM theory. The paper discusses the geometry of N coincident D3-branes, which is described by the metric $ds^2 = \left(1+\frac{R^{4}}{r^{4}}\right)^{-1/2}\left(-dt^2+d\vec{x}^2\right)+\left(1+\frac{R^{4}}{r^{4}}\right)^{1/2}\left(dr^2+r^2d\Omega_5^2\right)$. The near-horizon geometry of N D3-branes is $AdS_5 \times S^5$. The authors identify the generating functional of connected Green's functions in the gauge theory with the minimum of the supergravity action, subject to boundary conditions. They find that the two-point functions of massless vertex operators agree with absorption calculations. The two-point function of the stress-energy tensor is calculated and agrees with the central charge of the N=4 SYM theory. The paper also discusses the two-point functions of massive string states and their relation to the anomalous dimensions of SYM operators. For massive string states, the anomalous dimensions grow as $2(n g_{YM}\sqrt{2N})^{1/2}$ for large 't Hooft coupling. The authors conclude that for large 't Hooft coupling, the anomalous dimensions of vertex operators corresponding to massive string states grow without bound, while those coupling to massless string states do not acquire any anomalous dimensions. This is supported by explicit calculations for gravitons, dilatons, and RR scalars. The paper also discusses the implications of these results for the understanding of gauge theories and string theory.This paper presents a method to calculate certain Green's functions in 3+1 dimensional N=4 supersymmetric Yang-Mills (SYM) theory with a large number of colors using non-critical string theory. The non-critical string theory is related to critical string theory in an anti-de Sitter (AdS) background. The authors introduce a boundary of the AdS space analogous to a cutoff in the Liouville coordinate of 2D string theory. Correlation functions of gauge theory operators are related to the dependence of the supergravity action on boundary conditions. From the quadratic terms in supergravity, the anomalous dimensions of operators are derived. For operators coupling to massless string states, the anomalous dimensions vanish, as shown through absorption calculations. Operators coupling to massive string states at level n acquire anomalous dimensions that grow as $2(n g_{YM}\sqrt{2N})^{1/2}$ for large 't Hooft coupling. This is a new prediction about the strong coupling behavior of large N SYM theory. The paper discusses the geometry of N coincident D3-branes, which is described by the metric $ds^2 = \left(1+\frac{R^{4}}{r^{4}}\right)^{-1/2}\left(-dt^2+d\vec{x}^2\right)+\left(1+\frac{R^{4}}{r^{4}}\right)^{1/2}\left(dr^2+r^2d\Omega_5^2\right)$. The near-horizon geometry of N D3-branes is $AdS_5 \times S^5$. The authors identify the generating functional of connected Green's functions in the gauge theory with the minimum of the supergravity action, subject to boundary conditions. They find that the two-point functions of massless vertex operators agree with absorption calculations. The two-point function of the stress-energy tensor is calculated and agrees with the central charge of the N=4 SYM theory. The paper also discusses the two-point functions of massive string states and their relation to the anomalous dimensions of SYM operators. For massive string states, the anomalous dimensions grow as $2(n g_{YM}\sqrt{2N})^{1/2}$ for large 't Hooft coupling. The authors conclude that for large 't Hooft coupling, the anomalous dimensions of vertex operators corresponding to massive string states grow without bound, while those coupling to massless string states do not acquire any anomalous dimensions. This is supported by explicit calculations for gravitons, dilatons, and RR scalars. The paper also discusses the implications of these results for the understanding of gauge theories and string theory.