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Do Instantons and Strings Cluster when the Number of Colors is Large?

G. W. Carter·E. V. Shuryak
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Abstract

We consider the $N_c\to\infty$ limit of QCD using a toy model in which instantons exchange color-singlet scalar fields which do not self-interact. Our main observation is that collective attraction leads the formation of large clusters containing $O(N_c)$ nonperturbative objects. We further show that this clustering of instantons is limited due to a non-trivial repulsion inherent in the ADHM multi-instanton solution. As a result the vacuum is very different from that at low $N_c$, notably being more inhomogeneous, in ways which will affect chiral symmetry breaking of light quarks. We also briefly discuss a similar phenomenon for color strings in baryons made of medium-mass (charm-like) quarks.

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G. W. Carter, E. V. Shuryak. 2001-10-08. Do Instantons and Strings Cluster when the Number of Colors is Large?. https://doi.org/10.1016/s0370-2693(01)01399-5

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