Abstract
By using random matrix models we uncover a connection between the low energy sector of four dimensional QCD at finite volume and the Heisenberg XX model in a 1d spin chain. This connection allows to relate crucial properties of QCD with physically meaningful properties of the spin chain, establishing a dictionary between both worlds. We predict for the spin chain a third-order phase transition and a Tracy-Widom law in the transition region. We postulate that this dictionary goes beyond the particular example analyzed here and can be applied to other QFT and spin chain models. We finally comment on possible numerical implications of the connection as well as on possible experimental implementations.
Highlights
The strong interaction is the fundamental force of nature that describes the interaction between quarks and gluons, the elementary constituents of hadronic matter
Low-energy QCD, which is the regime we are interested in, is deeply related to the notion of chiral symmetry breaking and it can be explored with chiral perturbation theory [2,3,4]
We describe the result in Refs. [22,23,24,25] that relates some thermal correlation function of the XX model to a matrix model, which turns out to be the same as before
Summary
The strong interaction is the fundamental force of nature that describes the interaction between quarks and gluons, the elementary constituents of hadronic matter It is described by QCD, a SUð3Þ Yang-Mills theory with a number of distinctive properties, such as asymptotic freedom [1], which correctly describes that the interaction between particles becomes asymptotically weaker as distance decreases and energy increases. The connection allows us to uncover a third-order phase transition in the XX model since, again via random matrix models, one can relate both low-energy QCD and the thermal correlation functions of the XX chain. Number of particles Ket versus bra shift Projection onto momentum θ Different boundary conditions Longer range interactions with the so-called Gross-Witten model, a 2D Yang-Mills theory with gauge group UðNÞ and no matter fields, which has a third-order phase transition in the limit N → ∞ [32]. It opens a way to measure this partition function or to observe the Gross-Witten phase transition experimentally
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