3d $$ \mathcal{N} $$ = 4 OPE coefficients from Fermi gas
Shai M. Chester, Rohit R. Kalloor, Adar Sharon
Abstract
A bstract The partition function of a 3d $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 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.