Asymptotic Analysis of Dotsenko–Fateev Integrals

Lenells, Jonatan; Viklund, Fredrik

doi:10.1007/s00023-019-00849-5

Cited by 5 publications

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“…This technical step involves the computation of rather complicated integral asymptotics. In a separate paper [29], we present an approach for computing such asymptotics and carry out the estimates required for this paper.…”

Section: Introductionmentioning

confidence: 99%

“…(So it is really an SLE κ (2) quantity.) The main difficulty in this case lies in implementing Steps 1 and 2; the latter step is discussed in detail in [29].…”

Section: Introductionmentioning

confidence: 99%

“…In Step 1, we make a prediction for the observable by choosing an appropriate linear combination of the screening integrals such that the leading order term in the asymptotics cancels (thereby matching the asymptotics we expect). In Step 2, which is detailed in [29], we carefully analyze the candidate solution and estimate its boundary behavior. Lastly, given these estimates, we show that the candidate observable enjoys the same probabilistic representation as the Green's function defined as a limitso they must agree.…”

Section: Introductionmentioning

confidence: 99%

“…Even though Dotsenko-Fateev integrals and other generalized hypergeometric functions have been considered before in related contexts (see, e.g., [12,14,20,22,23]), we have not been able to find the required analytic estimates in the literature. We discuss these issues in a separate paper [29] which also includes details of the precise estimates needed here.…”

Section: Introductionmentioning

confidence: 99%

“…In Section 5, we prove rigorously that the predicted Schramm's formula indeed gives the probability that a given point lies to the left of both curves. The proof relies on a number of technical asymptotic estimates; proofs of these estimates are given in [29].…”

Section: Introductionmentioning

confidence: 99%

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Schramm’s Formula and the Green’s Function for Multiple SLE

Lenells

Viklund

2019

J Stat Phys

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We construct martingale observables for systems of commuting SLE curves by applying screening techniques within the CFT framework recently developed by Kang and Makarov extended to admit multiple SLEs. We illustrate this approach by rigorously establishing explicit formulas for the Green's function and Schramm's formula in the case of two curves growing towards infinity. In the special case when the curves are "fused" and start at the same point, some of the formulas we prove were predicted in the physics literature.

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Section: Introductionmentioning

confidence: 99%

“…(So it is really an SLE κ (2) quantity.) The main difficulty in this case lies in implementing Steps 1 and 2; the latter step is discussed in detail in [29].…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Schramm’s Formula and the Green’s Function for Multiple SLE

Lenells

Viklund

2019

J Stat Phys

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The Singularities of Selberg- and Dotsenko–Fateev-Like Integrals

Sussman

2024

Ann. Henri Poincaré

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We discuss the meromorphic continuation of certain hypergeometric integrals modeled on the Selberg integral, including the 3-point and 4-point functions of BPZ’s minimal models of 2D CFT as described by Felder & Silvotti and Dotsenko & Fateev (the “Coulomb gas formalism”). This is accomplished via a geometric analysis of the singularities of the integrands. In the case that the integrand is symmetric (as in the Selberg integral itself) or, more generally, what we call “DF-symmetric,” we show that a number of apparent singularities are removable, as required for the construction of the minimal models via these methods.

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