Integrable Open Spin Chains and the Doubling Trick in N = 2 SYM with Fundamental Matter

TL;DR

This paper shows that the one-loop anomalous dimension matrix in N=2 SYM with fundamental matter forms an integrable open spin chain and explores its relation to closed chains in N=4 SYM via the doubling trick, with implications for AdS/CFT.

Contribution

It demonstrates the integrability of open spin chains in N=2 SYM with fundamental matter and relates them to closed chains in N=4 SYM using the doubling trick.

Findings

The anomalous dimension matrix is an integrable open spin chain.

The doubling trick relates open and closed spin chains, with differences vanishing semiclassically.

Closed strings are sometimes simpler to analyze than open strings in this context.

Abstract

We demonstrate that the one-loop anomalous dimension matrix in N = 2 SYM with a single chiral hypermultiplet of fundamental matter, which is dual to AdS_5 X S^5 with a D7-brane filling AdS_5 and wrapped around an $^3 in the S^5, is an integrable open spin chain Hamiltonian. We also use the doubling trick to relate these open spin chains to closed spin chains in pure N = 4 SYM. By using the AdS/CFT correspondence, we find a relation between the corresponding open and closed strings that differs from a simple doubling trick by terms that vanish in the semiclassical limit. We also demonstrate that in some cases the closed string is simpler and easier to study than the corresponding open string, and we speculate on the nature of corrections due to the presence of D-branes that this implies.