Schramm-Loewner evolution with Lie superalgebra symmetry
arXiv:1803.09579 · doi:10.1142/S0217751X18501178
Abstract
We propose a generalization of Schramm-Loewner evolution (SLE) that has internal degrees of freedom described by an affine Lie superalgebra. We give a general formulation of SLE corresponding to representation theory of an affine Lie superalgebra whose underlying finite dimensional Lie superalgebra is basic classical type, and write down stochastic differential equations on internal degrees of freedom in case that the corresponding affine Lie superalgebra is . We also demonstrate computation of local martingales associated with the solution from a representation of .
arXiv comment15pages, to appear in IJMPA
References in corpus (21)
- Vertex Algebras and Algebraic Curves
- Critical Percolation in Finite Geometries
- 2D growth processes: SLE and Loewner chains
- Conformal Field Theories of Stochastic Loewner Evolutions
- Multiple Schramm-Loewner Evolutions and Statistical Mechanics Martingales
- SLE_k growth processes and conformal field theories
- On the SU(2|1) WZW model and its statistical mechanics applications
- Continuum Limit of the Integrable sl(2/1) 3-\bar{3} Superspin Chain
- SLE martingales and the Virasoro algebra
- Conformal restriction, highest-weight representations and SLE
- On Conformal Field Theory and Stochastic Loewner Evolution
- Stochastic Loewner evolution for conformal field theories with Lie-group symmetries
- Multiple Schramm-Loewner evolutions for conformal field theories with Lie algebra symmetries
- SLE and Virasoro representations: Fusion
- Virasoro Module Structure of Local Martingales of SLE Variants
- Stochastic evolutions in superspace and superconformal field theory
- Note on SLE and logarithmic CFT
- On Stochastic Evolutions and Superconformal Field Theory
- Logarithmic Conformal Null Vectors and SLE
- On SLE martingales in boundary WZW models
- SLE-type growth processes and the Yang-Lee singularity