The light asymptotic limit of conformal blocks in Toda field theory

We study four types of one-point torus blocks arising in the large central charge regime. According to different limits of conformal dimensions we distinguish between the global block, the light block, the heavy-light block, and the linearized classical block. We show that they are not independent and connected to each other by various links. We find that the global, light, and heavy-light blocks correspond to three different contractions of the Virasoro algebra. Also, we formulate the c-recursive representation of the one-point torus blocks which is relevant in the semiclassical approximation.Comment: 23 page

Section: Light Torus Blockmentioning

confidence: 99%

Various semiclassical limits of torus conformal blocks

Alkalaev

Geiko

Rappoport

2017

“…The Nekrasov partition function can be represented as a sum over Young diagrams [6,8,9] which according to the AGT correspondence can be used to compute conformal blocks in 2d LFT. In [10] the U(N ) Nekrasov partition function in the light asymptotic limit was considered. It was proved that in this limit for a specific choice of fields in the Nekrasov partition function contribute only Young diagrams whose number of rows does not exceed (N − 1).…”

Section: Jhep09(2017)062mentioning

confidence: 99%

“…Introduce also the field that is the highest component of the NS superfield build from Φ α 9) with dimension∆ 10) and as well as the Ramond primary fields defined as…”

Section: The Partition Functions Ofmentioning

confidence: 99%

The light asymptotic limit of conformal blocks in N = 1 $$ \mathcal{N}=1 $$ super Liouville field theory

Poghosyan

2017

Self Cite

Analytic expressions for the two dimensional N = 1 SLFT blocks in the light semi-classical limit are found for both Neveu-Schwarz and Ramond sectors. The calculations are done by using the duality between SU(2) N = 2 super-symmetric gauge theories living on R 4 /Z 2 space and two dimensional N = 1 super Liouville field theory. It is shown that in the light asymptotic limit only a restricted set of Young diagrams contributes to the partition function. This enables us to sum up the instanton series explicitly and find closed expressions for the corresponding N = 1 SLFT four point blocks in the light asymptotic limit.

“…Indeed, from our approach easily follows that the quantity λ 1 ν phq is real-valued for b,Λ,m, ǫ 1 , ξ P R. The eigenvalue λ 1 ν phq in eq. (3.13) is given by the logarithmic derivative of the N f " 1 classical irregular block: 16 A reason we choose this particular change of variable is dictated by experience gained in ref. [23], where this choice led to the coincidence of the expansion of pure gauge three-point degenerate irregular block with similar "weak coupling" expansion of the Mathieu exponent me ν pxq.…”

Section: Single Flavor Case: Solvable Complex Potentialmentioning

confidence: 99%

Classical irregular blocks, Hill’s equation and PT-symmetric periodic complex potentials

Piątek

Pietrykowski

2016

Abstract:The Schrödinger eigenvalue problems for the Whittaker-Hill potential Q 2 (x) = 1 2 h 2 cos 4x + 4hµ cos 2x and the periodic complex potential Q 1 (x) = 1 4 h 2 e −4ix + 2h 2 cos 2x are studied using their realizations in two-dimensional conformal field theory (2dCFT). It is shown that for the weak coupling (small) h ∈ R and non-integer Floquet parameter ν / ∈ Z spectra of hamiltonians H i = −d 2 /dx 2 + Q i (x), i = 1, 2 and corresponding two linearly independent eigenfunctions are given by the classical limit of the "single flavor" and "two flavors" (N f = 1, 2) irregular conformal blocks. It is known that complex nonhermitian hamiltonians which are PT-symmetric (= invariant under simultaneous parity P and time reversal T transformations) can have real eigenvalues. The hamiltonian H 1 is PT-symmetric for h, x ∈ R. It is found that H 1 has a real spectrum in the weak coupling region for ν ∈ R \ Z. This fact in an elementary way follows from a definition of the N f = 1 classical irregular block. Thus, H 1 can serve as yet another new model for testing postulates of PT-symmetric quantum mechanics.