The geometry of the limit of N=2 minimal models

TL;DR

This work analyzes how N=(2,2) minimal models behave as their central charge approaches c=3, uncovering two distinct limiting theories. One limit yields a free theory of two bosons and two fermions, obtained by rescaling U(1) charges and carefully redefining fields; the other limit corresponds to a continuous orbifold of the free theory by the rotation group U(1), interpreted via T-duality from the sigma-model geometry. The authors substantiate both limits by matching partition functions, bulk correlators, and boundary conditions between the minimal models and their respective limit theories, including A- and B-type boundaries. The results illuminate the structure of non-rational theory limits and suggest broader applicability to other N=(2,2) models and holographic contexts.

Abstract

We consider the limit of two-dimensional N=(2,2) superconformal minimal models when the central charge approaches c=3. Starting from a geometric description as non-linear sigma models, we show that one can obtain two different limit theories. One is the free theory of two bosons and two fermions, the other one is a continuous orbifold thereof. We substantiate this claim by detailed conformal field theory computations.

Figures (3)

• Figure 1: Illustration of the boundary condition that corresponds to a one-dimensional brane, and the distance $R$ and the angle $\psi$ that determine its position.
• Figure 2: Ponzano-Regge angles defined in equations (\ref{['PR-angles']}) and (\ref{['def-alphas']}): the $\alpha_i$ are the internal angles of the triangle formed by the $j_i$ labels; the $\beta_i$ are the internal angles of the triangle projected on the xy-plane (where the $\mu_{i}$ measure the z-components of the angular momenta); $\gamma_i$ (not present here) is the angle between the outer normals to the faces adjacent to the edge $j_i$.
• Figure 3: The triangle spanned by $p_{1}$, $p_{2}e^{i\varphi_{2}}$ and $p_{3}e^{i\varphi_{3}}$.