arXiv subjects

Armen Poghosyan

Publications and source records attributed to Armen Poghosyan.

7 recordsLinked to original sources

arXiv2026

A note on Zamolodchikov's recursion relation for the torus conformal block and its light limit

In this paper, we review the Zamolodchikov-like recursion relations for torus one-point conformal blocks in both Liouville and $A_2$ Toda theories. Starting from these relations, we derive the corresponding recursion relations in the light asymptotic limit. In Liouville theory, the light-limit recursion reproduces the known expression for the one-point light conformal block in terms of the Gauss hypergeometric function. For $A_2$ Toda theory, our recursion relation provides a new, efficient method for explicit calculations, and we have verified that it is in full agreement with previously known results in the literature.

hep-th↗

arXiv2026

The $W_n$ Light One-Point Torus Conformal Block

We study the light asymptotic limit of the one-point torus conformal block in $A_{n-1}$ Toda field theory. Through the AGT correspondence, this problem can be translated into the computation of the instanton partition function of four-dimensional ${\cal N}=2^{\ast}$ $U(n)$ supersymmetric Yang--Mills theory, which we then examine in the limit $b\to 0$ at fixed conformal dimensions. We show that, in this regime, the instanton sum simplifies drastically: for each Young diagram, only boxes with specific arm lengths contribute to the bifundamental factors. Exploiting this property, we derive an explicit representation for the light one-point torus $W_n$ conformal block valid for arbitrary $n\ge 2$. As a consistency check, we specialize our construction to the Liouville case $n=2$ and compare it with the previously known hypergeometric representation of the torus block in the light limit. We also discuss the $W_3$ case and its relation to a known alternative representation obtained by the shadow formalism.

hep-th↗

arXiv2023

A note on RG domain wall between successive $A_2^{(p)}$ minimal models

We investigate the RG domain wall between neighboring $A_2^{(p)}$ minimal CFT models and establish the map between UV and IR fields (matrix of mixing coefficients). A particular RG invariant set of six primary and four descendant fields is analyzed in full details. Using the algebraic construction of the RG domain wall we compute the UV/IR mixing matrix. To test our results we show that it diagonalizes the matrix of anomalous dimensions previously known from perturbative analysis. It is important to note that the diagonalizing matrix can not be found from perturbative analysis solely due to degeneracy of anomalous dimensions. The same mixing coefficients are used to explore anomalous W-weights as well.

hep-th↗

arXiv2019

Shaping Lattice through irrelevant perturbation: Ising model

The leading irrelevant perturbation, which controls the deviation of critical square lattice Ising model with periodic boundary conditions from its continuous CFT analog is identified. An explicit expression for the coupling constant in terms of the anisotropy parameter is found. We calculate the next to leading $\sim 1/N^2$ corrections to the spectrum on both lattice theory and the perturbed CFT sides for several classes of states, always getting exact agreement. We discuss also how the perturbing operators and the higher integrals of motion are related.

hep-th↗

arXiv2017

Exact solution of the critical Ising model with special toroidal boundary conditions

The Ising model in two dimensions with special toroidal boundary conditions is analyzed. These boundary condition, which we call duality twisted boundary conditions, may be interpreted as inserting a specific defect line ("seam") in the system, along non-contractible circles of the cylinder, before closing it into a torus. We derive exact expressions for the eigenvalues of the transfer matrix for the critical ferromagnetic Ising model on the M x N square lattice wrapped on the torus with a specific defect line. As result we have obtained analytically the partition function for the Ising model with such boundary conditions. In the case of infinitely long cylinders of circumference L with duality twisted boundary conditions we obtain the asymptotic expansion of the free energy and the inverse correlation lengths. We find that the ratio of subdominant finite-size correction terms in the asymptotic expansion of the free energy and the inverse correlation lengths should be universal. We verify such universal behavior in the framework of perturbating conformal approach by calculating the universal structure constant Cn1n for descendent states generated by the operator product expansion (OPE) of the primary fields. For such states the calculations of the universal structure constants is difficult task, since its involve the knowledge of the four-point correlation function, which in general does not fix by conformal invariance except for some particular cases, including the Ising model.

cond-mat.stat-mech↗

arXiv2015

The critical Ising model on a torus with a defect line

The critical Ising model in two dimensions with a defect line is analyzed to deliver the first exact solution with twisted boundary conditions. We derive exact expressions for the eigenvalues of the transfer matrix and obtain analytically the partition function and the asymptotic expansions of the free energy and inverse correlation lengths for an infinitely long cylinder of circumference $L_x$. We find that finite-size corrections to scaling are of the form $a_k/L^{2k-1}_x$ for the free energy $f$ and $b_k(p)/L_x^{2k-1}$ and $c_k(p)/L_x^{2k-1}$ for inverse correlation lengths $ξ^{-1}_p$ and $ξ^{-1}_{L-p}$, respectively, with integer values of $k$. By exact evaluation we find that the amplitude ratios $b_k(p)/a_k$ and $c_k(p)/a_k$ are universal and verify this universal behavior using a perturbative conformal approach.

cond-mat.stat-mech↗

arXiv2013

Mixing with descendant fields in perturbed minimal CFT models

We extend the analysis of the RG trajectory connecting successive minimal CFT models ${\cal M}_p$ and ${\cal M}_{p-1}$ for $p\gg 1$, performed by A. Zamolodchikov, to the fields $φ_{n,n\pm 3}$. This required a close investigation of mixing with the descendant fields at the level 2. In particular we identify those specific linear combinations of UV fields which flow to the IR fields $φ_{n+3,n}$ and $φ_{n-3,n}$. We report also the results of the calculation of the same mixing coefficients through the recent RG domain wall approach by Gaiotto. These results are in complete agreement with the leading order perturbation theory.

hep-th↗