Irregular Conformal States and Spectral Curve: Irregular Matrix Model Approach

Abstract

We present recent developments of irregular conformal conformal states. Irregular vertex operators and their adjoint in a new formalism are used to define the irregular conformal states and their inner product instead of using the colliding limit procedure. Free field formalism can be augmented by screening operators which provide more degrees of freedom. The inner product is conveniently given as the partition function of an irregular matrix model. (Deformed) spectral curve is the loop equation of the matrix model at Nekrasov-Shatashivili limit. We present the details of analytic structure of the spectral curve for Virasoso symmetry and its extensions, $W$-symmetry and super-symmetry.

References in corpus (10)

• A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories
• Toda Theories, Matrix Models, Topological Strings, and N=2 Gauge Systems
• Asymptotically free N=2 theories and irregular conformal blocks
• On AGT Relations with Surface Operator Insertion and Stationary Limit of Beta-Ensembles
• Topological expansion of beta-ensemble model and quantum algebraic geometry in the sectorwise approach
• Classical irregular block, N=2 pure gauge theory and Mathieu equation
• Quantum Hitchin Systems via beta-deformed Matrix Models
• Virasoro irregular conformal block and beta deformed random matrix model
• Logarithmic potential beta-ensembles and Feynman graphs
• Super-spectral curve of irregular conformal blocks