Establishes correspondence between flat, thermal, and defect conformal partial waves via shadow formalism, obtaining thermal blocks from flat four-point and defect two-point functions and reducing the Casimir equation diagonally.
Diagonal Limit for Conformal Blocks in d Dimensions
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abstract
Conformal blocks in any number of dimensions depend on two variables z, zbar. Here we study their restrictions to the special "diagonal" kinematics z = zbar, previously found useful as a starting point for the conformal bootstrap analysis. We show that conformal blocks on the diagonal satisfy ordinary differential equations, third-order for spin zero and fourth-order for the general case. These ODEs determine the blocks uniquely and lead to an efficient numerical evaluation algorithm. For equal external operator dimensions, we find closed-form solutions in terms of finite sums of 3F2 functions.
fields
hep-th 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
Lecture notes develop semiclassical methods to compute large-n scaling dimensions of composite operators in CFTs, recovering known results in free theory and deriving one-loop corrections at the Wilson-Fisher fixed point.
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Thermal conformal partial waves from flat-space and defect CFT
Establishes correspondence between flat, thermal, and defect conformal partial waves via shadow formalism, obtaining thermal blocks from flat four-point and defect two-point functions and reducing the Casimir equation diagonally.
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Lectures on Semiclassical Methods for Composite Operators
Lecture notes develop semiclassical methods to compute large-n scaling dimensions of composite operators in CFTs, recovering known results in free theory and deriving one-loop corrections at the Wilson-Fisher fixed point.