Conformal superspace sigma-models
arXiv:1210.8159 · doi:10.1016/j.geomphys.2010.11.004
Abstract
We review recent developments in the context of two-dimensional conformally invariant sigma-models. These quantum field theories play a prominent role in the covariant superstring quantization in flux backgrounds and in the analysis of disordered systems. We present supergroup WZW models as primary examples of logarithmic conformal field theories, whose structure is almost entirely determined by the underlying supergeometry. In particular, we discuss the harmonic analysis on supergroups and supercosets and point out the subtleties of Lie superalgebra representation theory that are responsible for the emergence of logarithmic representations. Furthermore, special types of marginal deformations of supergroup WZW models are studied which only exist if the Killing form is vanishing. We show how exact expressions for anomalous dimensions of boundary fields can be derived using quasi-abelian perturbation theory. Finally, the knowledge of the exact spectrum is used to motivate a duality between the OSP(4|2) symmetric Gross-Neveu model and the S(3|2) supersphere sigma-model.
21 Pages, 7 Figures, 2 Tables. Based on a talk given by Thomas Quella at the Lorentz Center Workshop "The Interface of Integrability and Quantization" (Leiden, 12.-16.4.2010). Version close to that published in Journal of Geometry and Physics
References in corpus (15)
- Conformal Field Theory of AdS Background with Ramond-Ramond Flux
- The GL(1|1) WZW model: From Supergeometry to Logarithmic CFT
- Sigma Model as a Conformal Field Theory
- The su(2)_{-1/2} WZW model and the beta-gamma system
- Conformal Sigma-Models on Supercoset Targets
- Free fermion resolution of supergroup WZNW models
- Logarithmic lift of the su(2)_{-1/2} model
- Boundary Spectra in Superspace Sigma-Models
- The Sigma Model on Complex Projective Superspaces
- Conformal Current Algebra in Two Dimensions
- Principal Chiral Model on Superspheres
- The conformal current algebra on supergroups with applications to the spectrum and integrability
- A lattice approach to the conformal $\OSp(2S+2|2S)$ supercoset sigma model. Part II: The boundary spectrum
- Cohomological Reduction of Sigma Models
- Universality classes of dense polymers and conformal sigma models
Cited by in corpus (8)
- Superspace conformal field theory
- Takiff superalgebras and Conformal Field Theory
- Mock Modular Index of M2-M5 Brane System
- Bott-Borel-Weil theory, BGG reciprocity and twisting functors for Lie superalgebras
- Harmonic Analysis and Free Field Realization of the Takiff Supergroup of GL(1|1)
- On the gl(1|1) Wess-Zumino-Witten Model
- More on (gauged) WZW models over low-dimensional Lie supergroups and their integrable deformations
- Strong gauging or decoupling ghost matter