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Aspects of \((2,2)\) and \((0,2)\) hybrid models. (English) Zbl 1440.81067

This work is about the study of topological rings of two-dimensional (2, 2) and (0, 2) hybrid models. The first case considered is the \(\eta = (2,2)\) hybrid models that possess enough supersymmetry to admit a well-defined B-twisted version of the hybrid theory provided the conditions for an anomaly-free vector R-symmetry are satisfied. In such case, localisation has been used to derive a formula for the genus-0 correlators of the B-twisted theory. As expected, the expression reduces to a classical integral and instanton corrections are absent. A study of the properties of the correlators are given. The second case considered is the \(\eta = (0,2)\) hybrid models. The conditions for which these models admit a B/2-twist have been studied. In such case, the genus-0 correlators in the zero instanton sector have been computed. The conditions for instanton corrections to vanish have been analysed and the techniques have been applied to an example. The work ends with some open questions.

MSC:

81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
83E30 String and superstring theories in gravitational theory
81T45 Topological field theories in quantum mechanics
81T33 Dimensional compactification in quantum field theory
14D21 Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory)
16W80 Topological and ordered rings and modules
81P40 Quantum coherence, entanglement, quantum correlations
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