Emergent Yang-Mills theory
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Springer
Received: May 7, Revised: August 2, Accepted: September 14, Published: October 15,
2020 2020 2020 2020
Robert de Mello Koch,a,b Jia-Hui Huang,a Minkyoo Kimb and Hendrik J.R. Van Zylb a
Guangdong Provincial Key Laboratory of Nuclear Science, Institute of Quantum Matter, South China Normal University, Higher Education Mega Center, West Waihuan Road No. 378, Guangzhou, China b National Institute for Theoretical Physics, School of Physics and Mandelstam Institute for Theoretical Physics, University of the Witwatersrand, 1 Jan Smuts Avenue, Braamfontein 2000, Johannesburg, South Africa
E-mail: [email protected], [email protected], [email protected], [email protected] Abstract: We study the spectrum of anomalous dimensions of operators dual to giant graviton branes. The operators considered belong to the su(2|3) sector of N = 4 super Yang-Mills theory, have a bare dimension ∼ N and are a linear combination of restricted Schur polynomials with p ∼ O(1) long rows or columns. In the same way that the operator mixing problem in the planar limit can be mapped to an integrable spin chain, we find that our problems maps to particles hopping on a lattice. The detailed form of the model is in precise agreement with the expected world volume dynamics of p giant graviton branes, which is a U(p) Yang-Mills theory. The lattice model we find has a number of noteworthy features. It is a lattice model with all-to-all sites interactions and quenched disorder. Keywords: 1/N Expansion, AdS-CFT Correspondence ArXiv ePrint: 2005.02731
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP10(2020)100
JHEP10(2020)100
Emergent Yang-Mills theory
Contents 1
2 Operators 2.1 Restricted Schur polynomials 2.2 Gauss graph basis
3 3 6
3 Action of the dilatation operator on restricted Schur polynomials
9
4 Dilatation operator on Gauss graphs
13
5 Emergent lattice model
21
6 Emergent Yang-Mills theory
24
7 Mixing with closed string states
27
8 Conclusions and outlook
30
A Field redefinition
32
B N −1 corrections to matrix elements of the dilatation operator
33
1
Introduction
The operator mixing problem in the planar limit of N = 4 super Yang-Mills theory is solved. This dramatic progress was achieved by mapping the dilatation operator of the theory to the Hamiltonian of an integrable spin chain [1]. The mapping identifies each single trace operator with a state of the spin chain and operators of a definite dimension map to spin chain states with a definite energy. The integrable model describes the dynamics of magnons which can scatter with each other. This scattering between the magnons happens in one dimension. As far as the single trace operators are concerned, reordering fields within the trace corresponds to changing their positions in this single dimension. In the integrable spin chain, this dimension is that of the spin chain lattice, while in the holographically dual theory it is the string world sheet. This is precisely what we should have expected from the
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