Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Upper bound on the mass anomalous dimension in many-flavor gauge
  theories: a conformal bootstrap approach   We study four-dimensional conformal field theories with an $SU(N)$ global
symmetry by employing the numerical conformal bootstrap. We consider the
crossing relation associated with a four-point function of a spin~$0$
operator~$\phi_i^{\Bar{k}}$ which belongs to the adjoint representation of
$SU(N)$. For~$N=12$ for example, we found that the theory contains a spin~$0$
$SU(12)$-breaking relevant operator when the scaling dimension
of~$\phi_i^{\Bar{k}}$, $\Delta_{\phi_i^{\Bar{k}}}$, is smaller than~$1.71$.
Considering the lattice simulation of many-flavor quantum chromodynamics with
$12$~flavors on the basis of the staggered fermion, the above $SU(12)$-breaking
relevant operator, if it exists, would be induced by the flavor-breaking effect
of the staggered fermion and prevent an approach to an infrared fixed point.
Actual lattice simulations do not show such signs. Thus, assuming the absence
of the above $SU(12)$-breaking relevant operator, we have an upper bound on the
mass anomalous dimension at the fixed point~$\gamma_m^*\leq1.29$ from the
relation~$\gamma_m^*=3-\Delta_{\phi_i^{\Bar{k}}}$. Our upper bound is not so
strong practically but it is strict within the numerical accuracy. We also find
a kink-like behavior in the boundary curve for the scaling dimension of another
$SU(12)$-breaking operator.

21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
24
The categories of this paper are: dg-ga