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abelian action algebra analytic approximation asymptotic boundary conditions calculation chiral classical coefficients configurations conformal field theory construction continuum correlation functions corresponding covariant curvature D-branes defined degrees of freedom denote derivative determinant Developments in Quantum dilaton dimension dimensional Dirac operator domain wall Edited by Damgaard eigenvalues ensemble equation expansion fermions Field Theory Edited finite gauge field Gaussian given Hamiltonian hermitian highest-weight holomorphic integral invariant inverse J.J.M. Verbaarschot large N limit lattice Lett loop magnetic field manifold Math matrix model microscopic spectral density Nambu-Goto Nucl obtained parameter partition function path perturbative phase Phys physical polynomial potential Quantum Field Theory quantum gravity quark Random Matrix Theory renormalization representation satisfy scalar scaling sigma model singular solution space spectral correlations spectral density spectrum stress tensor string theory structure symmetry topological universality variables vector Verma modules Virasoro Weyl anomaly zero