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Scattering and duality in the 2 dimensional OSP(2|2) Gross Neveu and sigma models

H. Saleur, B. Pozsgay

TL;DR

This work develops a comprehensive thermodynamic Bethe Ansatz framework for massive osp(2|2) GN and supersphere sigma models, providing nonperturbative support for the GN S-matrix proposed by Bassi and Leclair and revealing a deep duality between osp(2|2) and SO(4) GN/sigma systems. It further uncovers unconventional features in the sigma-model S-matrix and connects the q-deformed osp(2|2) sigma model to complex sine-Gordon-type theories, suggesting broader integrable structures. The authors also analyze massless flows to the random bond Ising model and argue against the proposed SUSY flow S-matrix, highlighting subtle issues in massless and noncompact sectors. Collectively, the paper links lattice regularizations, S-matrix properties, and nonperturbative TBA results to map massive and massless flows in these supersymmetric theories, while outlining important open questions related to UV behavior, dualities, and AdS/CFT connections.

Abstract

We write the thermodynamic Bethe ansatz for the massive OSp(2|2) Gross Neveu and sigma models. We find evidence that the GN S matrix proposed by Bassi and Leclair [12] is the correct one. We determine features of the sigma model S matrix, which seem highly unconventional; we conjecture in particular a relation between this sigma model and the complex sine-Gordon model at a particular value of the coupling. We uncover an intriguing duality between the OSp(2|2) GN (resp. sigma) model on the one hand, and the SO(4) sigma (resp. GN model) on the other, somewhat generalizing to the massive case recent results on OSp(4|2). Finally, we write the TBA for the (SUSY version of the) flow into the random bond Ising model proposed by Cabra et al. [39], and conclude that their S matrix cannot be correct.

Scattering and duality in the 2 dimensional OSP(2|2) Gross Neveu and sigma models

TL;DR

This work develops a comprehensive thermodynamic Bethe Ansatz framework for massive osp(2|2) GN and supersphere sigma models, providing nonperturbative support for the GN S-matrix proposed by Bassi and Leclair and revealing a deep duality between osp(2|2) and SO(4) GN/sigma systems. It further uncovers unconventional features in the sigma-model S-matrix and connects the q-deformed osp(2|2) sigma model to complex sine-Gordon-type theories, suggesting broader integrable structures. The authors also analyze massless flows to the random bond Ising model and argue against the proposed SUSY flow S-matrix, highlighting subtle issues in massless and noncompact sectors. Collectively, the paper links lattice regularizations, S-matrix properties, and nonperturbative TBA results to map massive and massless flows in these supersymmetric theories, while outlining important open questions related to UV behavior, dualities, and AdS/CFT connections.

Abstract

We write the thermodynamic Bethe ansatz for the massive OSp(2|2) Gross Neveu and sigma models. We find evidence that the GN S matrix proposed by Bassi and Leclair [12] is the correct one. We determine features of the sigma model S matrix, which seem highly unconventional; we conjecture in particular a relation between this sigma model and the complex sine-Gordon model at a particular value of the coupling. We uncover an intriguing duality between the OSp(2|2) GN (resp. sigma) model on the one hand, and the SO(4) sigma (resp. GN model) on the other, somewhat generalizing to the massive case recent results on OSp(4|2). Finally, we write the TBA for the (SUSY version of the) flow into the random bond Ising model proposed by Cabra et al. [39], and conclude that their S matrix cannot be correct.

Paper Structure

This paper contains 15 sections, 124 equations, 17 figures, 1 table.

Table of Contents

  1. Introduction
  2. Solving the monodromy problem: the Bethe ansatz for integrable SL(2$|$1) vertex models and spin chains
  3. The Bethe equations in the fermionic grading
  4. The solutions for large chains
  5. TBA for the $3,\bar{3}$ and the $4$ (fundamental of OSp(2$|$2)) spin chains
  6. TBA for OSp(2$|$2) scattering: the fundamental representation case and the GN model
  7. The OSp(2$|$2) supersphere sigma model TBA.
  8. Do the massive flows exist?
  9. The q-deformed case
  10. Application: flow in the Random Bond Ising model
  11. Conclusion
  12. $O(3)$ sigma-model with $\theta=\pi$: a reminder
  13. The conjectured massless flow in the $OSP(2|2)$ case
  14. CDD-factors
  15. $S_{LR}$ being a pure CDD factor

Figures (17)

  • Figure 1: Graphical representation of the invariant tensors appearing in the $S$ matrix.
  • Figure 2: Pole structure of $\sigma_2$ as a function of $N$. Except for a finite region at small $N$, the generic S matrix with $\sigma_2^+$ describes the sigma model and the one with $\sigma_2^-$ the GN model.
  • Figure 3: Dynkin diagram leading to our Bethe equations
  • Figure 9: TBA diagram for the $sl(2/1)$ chain with alternating $3$ and $\bar{3}$ representations.
  • Figure 10: TBA diagram for the $OSP(2/2)$ chain (four dimensional fundamental representation).
  • ...and 12 more figures