Perturbative deformations of conformal field theories revisited. (English) Zbl 1185.83026
Summary: The purpose of this paper is to revisit the theory of perturbative deformations of conformal field theory from a mathematically rigorous, purely worldsheet point of view. We specifically include the case of \(N = (2,2)\) conformal field theories. From this point of view, we find certain surprising obstructions, which appear to indicate that contrary to previous findings, not all deformations along marginal fields exist perturbatively. This includes the case of deformation of the Gepner model of the Fermat quintic along certain \(cc\) fields. In other cases, including Gepner models of \(K3\)-surfaces and the free field theory, our results coincides with known predictions. We give partial interpretation of our results via renormalization and mirror symmetry.
MSC:
| 83E30 | String and superstring theories in gravitational theory |
| 53D37 | Symplectic aspects of mirror symmetry, homological mirror symmetry, and Fukaya category |
| 81T15 | Perturbative methods of renormalization applied to problems in quantum field theory |
| 81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |
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