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Abstract
We discuss the effective twisted superpotentials of 2d = (2, 2) theories arising upon the reduction of 4d = 2 gauge theories on the Ω-deformed cigar-like geometry. We explain field-theoretic origins of the gaps in the spectrum in the corresponding quantum mechanical (QM) systems. We find local 2d descriptions of the physics near these gaps by resumming the non-perturbative part of the twisted superpotential and discuss arising wall-crossing phenomena. The interpretation of the associated phenomena in the classical Liouville theory and in the scattering of two heavy states in AdS3 gravity is suggested. Some comments concerning a possible interpretation of the band structure in QM in terms of the Schwinger monopole-pair production in 4d are presented.
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1 Moscow Institute of Physics and Technology, Dolgoprudny, Russia; Institute for Information Transmission Problems of Russian Academy of Science, Moscow, Russia
2 Institute of Theoretical and Experimental Physics, Moscow, Russia; Institute for Information Transmission Problems of Russian Academy of Science, Moscow, Russia; Department of Physics, Princeton University, Princeton, NJ, U.S.A.
3 Institute of Theoretical and Experimental Physics, Moscow, Russia; Moscow Institute of Physics and Technology, Dolgoprudny, Russia; Institute for Information Transmission Problems of Russian Academy of Science, Moscow, Russia