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\( \mathcal{N} = 1 \) SQCD and the transverse field Ising model

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Abstract

We study the dimensions of non-chiral operators in the Veneziano limit of \( \mathcal{N} = 1 \) supersymmetric QCD in the conformal window. We show that when acting on gauge-invariant operators built out of scalars, the 1-loop dilatation operator is equivalent to the spin chain Hamiltonian of the 1D Ising model in a transverse magnetic field, which is a nontrivial integrable system that is exactly solvable at finite length. Solutions with periodic boundary conditions give the anomalous dimensions of flavor-singlet operators and solutions with fixed boundary conditions give the anomalous dimensions of operators whose ends contain open flavor indices.

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  1. Department of Physics, Harvard University, 17 Oxford Street, Cambridge, MA, USA

    David Poland & David Simmons-Duffin

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  1. David Poland
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  2. David Simmons-Duffin
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Correspondence to David Poland.

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ArXiv ePrint: 1104.1425

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Poland, D., Simmons-Duffin, D. \( \mathcal{N} = 1 \) SQCD and the transverse field Ising model. J. High Energ. Phys. 2012, 9 (2012). https://doi.org/10.1007/JHEP02(2012)009

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