Fortuity and Complexity in a Simple Quark Model

TL;DR

This paper explores a structural analogy between operator classifications in supersymmetric theories and QCD, using BRST cohomology, and investigates the complexity of meson and baryon states via stabilizer Rényi entropy.

Contribution

It introduces a non-supersymmetric categorization of operators based on BRST cohomology and analyzes the complexity of hadronic states in large-N limits.

Findings

Baryon states are classified as fortuitous, mesons as monotone.

Mesons exhibit power-law complexity, baryons show super-exponential complexity in the Veneziano limit.

The categorization resembles BPS operator classification in supersymmetric theories.

Abstract

We observe and elaborate on a structural similarity between the categorization of monotone and fortuitous BPS operators in supersymmetric theories and gauge invariant quark operators in $SU(N_c)$ QCD. Our designation of fortuity does not rely on supersymmetry and instead uses the BRST cohomology. We argue that within this designation, baryon states are fortuitous while meson states are monotone. We illustrate that in the Veneziano limit of large number of flavors and colors, this designation displays features resembling the fortuitous vs. monotone categorization of BPS operators, e.g., an exponential vs. polynomial dichotomy in the counting of operators. We explore these ideas explicitly in a toy qubit model of quarks. We further investigate the stabilizer R\'enyi entropy of meson and baryon states as a proxy for the complexity of classical simulation for these states. We show that all mesons display power law complexity and present evidence that typical baryons display super-exponential complexity in the Veneziano limit.