be easily constructed.

In this work we take a step further towards answering this question, by computing in perturbation theory the 2-loop partition function of $(S)U(N)$ **YM** theory in the large $N$ limit with fixed, small ’t Hooft coupling on $S^3$. We include scalars and chiral fermions in the adjoint representation of the gauge group with arbitrary Yukawa and quartic scalar couplings, only assuming commutator interactions (though our computation can be easily generalized to include non-commutator interactions as well). Our computation follows closely the one of [@Aharony:2006rf] where the same computation was done for pure **YM**.

As an immediate application we can compute the order $\lambda$ corrections to the Hagedorn temperature and to the spectrum of the theory. We check our computation by comparing to the known results for $\cal{N}=4$ **SYM**, which were computed by spin-chain methods in [@Spradlin:2004pp].

The structure of this paper is as follows. In the next subsection we review some of the theoretical background necessary for this work. Section \[sec:Setup\] reviews our conventions for the action, and various mode expansions on $S^3$. In section \[sec:RegCount\] we discuss our renormalization scheme, and present the computation of the various counterterms. In section \[sec:2LoopComputation\] we present the computation of 