Integrable quantum field theories with OSP(m/2n) symmetries

TL;DR

This work develops an integrable framework for field theories with orthosymplectic symmetry $OSP(m/2n)$, focusing on supersphere sigma models and Gross Neveu models. It constructs and analyzes factorized $S$-matrices, acknowledging nonunitarity from the supergroup structure, and validates them via thermodynamic Bethe ansatz and finite-field calculations, obtaining central charges and perturbative matches. A key outcome is that the $a_2^{(2)}$ Toda theory underlies the $OSP(1/2)$ case, enabling a precise link to the sigma model limit described by symplectic fermions, and that the supersphere cases generalize to $a_{2n}^{(2)}$ and $OSP(1/2n)$, yielding UV central charges $c_{ m eff}=n$ (sigma models) and $c_{ m eff}=2n+1/2$ (GN-like sectors). The results clarify the continuum limits of integrable superspin chains and challenge simple WZW-based pictures, while opening routes to broader classes of superalgebra–based integrable theories and their finite-size spectra. Overall, the paper provides a consistent S-matrix and TBA framework for a class of nonunitary integrable QFTs with supergroup symmetry and highlights rich connections to symplectic fermions and RSOS/Toda structures.

Abstract

We conjecture the factorized scattering description for OSP(m/2n)/OSP(m-1/2n) supersphere sigma models and OSP(m/2n) Gross Neveu models. The non-unitarity of these field theories translates into a lack of `physical unitarity' of the S matrices, which are instead unitary with respect to the non-positive scalar product inherited from the orthosymplectic structure. Nevertheless, we find that formal thermodynamic Bethe ansatz calculations appear meaningful, reproduce the correct central charges, and agree with perturbative calculations. This paves the way to a more thorough study of these and other models with supergroup symmetries using the S matrix approach.

Figures (9)

• Figure 1: Graphical representation of the invariant tensors appearing in the $S$ matrix.
• Figure 2: Pole structure of $\sigma_2$ as a function of $N$.
• Figure 3: Graphical representation for the defining relations of the BW algebra.
• Figure 4: Dynkin diagrams for $a_2^{(2)}$ and $osp(1/2)^{(1)}$.
• Figure 5: Incidence diagram for the TBA of the (anisotropic) $a_2^{(2)}$ theory. Nodes are associated with the pseudoenergies $\epsilon$, and the cross indicates the presence of a massive asymptotic behavior for $\epsilon_0$.