Abstract
We construct confluent conformal blocks of the second kind of the Virasoro algebra. We also construct the Stokes transformations which map such blocks in one Stokes sector to another. In the BPZ limit, we verify explicitly that the constructed blocks and the associated Stokes transformations reduce to solutions of the confluent BPZ equation and its Stokes matrices, respectively. Both the confluent conformal blocks and the Stokes transformations are constructed by taking suitable confluent limits of the crossing transformations of the four-point Virasoro conformal blocks.
Highlights
Virasoro conformal blocks [4] are holomorphic building blocks of correlations functions in two-dimensional conformal field theories
In the BPZ limit, we verify explicitly that the constructed blocks and the associated Stokes transformations reduce to solutions of the confluent BPZ equation and its Stokes matrices, respectively
We constructed the Stokes transformations which map such blocks in one Stokes sector to another. Both the confluent conformal blocks and the Stokes transformations were found by taking suitable confluent limits of the crossing transformations of the four-point Virasoro conformal blocks
Summary
Virasoro conformal blocks [4] are holomorphic building blocks of correlations functions in two-dimensional conformal field theories. In the so-called BPZ limit [4], the four-point Virasoro conformal blocks degenerate to solutions of a hypergeometric equation with three regular singular points in the complex plane. These blocks are related by crossing transformations which can be viewed as infinite-dimensional analogs of the connection matrices for the hypergeometric BPZ equation. We will verify explicitly that the constructions of the connection and the Stokes transformations are consistent with the BPZ limit in the sense that (1.5) reduces to (1.4) in this limit and that the following diagram commutes: 4-point Virasoro conformal blocks confluent limit confluent conformal blocks In symbols, this diagram takes the following form: F 0(z), F 1(z), F ∞(z) confluent limit
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