3d N documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$ mathcal{N} $$end{document} = 4 OPE coefficients from Fermi gas

摘要

A bstract The partition function of a 3d N documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$ mathcal{N} $$end{document} = 4 gauge theory with rank N can be computed using supersymmetric localization in terms of a matrix model, which often can be formulated as an ideal Fermi gas with a non-trivial one-particle Hamiltonian. We show how OPE coefficients of protected operators correspond in this formalism to averages of n -body operators in the Fermi gas, which can be computed to all orders in 1 /N using the WKB expansion. We use this formalism to compute OPE coefficients in the U( N )_( k ) × U( N )_( ?k )ABJM theory as well as the U( N ) theory with one adjoint and N _( f )fundamental hypermultiplets, both of which have weakly coupled M-theory duals in the large N and finite k or N _( f )regimes. For ABJM we reproduce known results, while for the N _( f )theory we compute the all orders in 1 /N dependence at finite N _( f )for the coefficient c _( T )of the stress tensor two-point function.