  Recently, Ref. [1] reformulated magic-angle twisted bilayer graphene (MATBG)
as a topological heavy fermion problem, and used this reformulation to provide
a deeper understanding for the correlated phases at integer fillings. In this
work, we generalize this heavy-fermion paradigm to magic-angle twisted
symmetric trilayer graphene (MATSTG), and propose a low-energy $f-c-d$ model
that reformulates MATSTG as heavy localized $f$ modes coupled to itinerant
topological semimetalic $c$ modes and itinerant Dirac $d$ modes. Our $f-c-d$
model well reproduces the single-particle band structure of MATSTG at low
energies for displacement field $\mathcal{E}\in[0,300]$meV. By performing
Hartree-Fock calculations with the $f-c-d$ model for $\nu=0,-1,-2$ electrons
per Moir\'e unit cell, we reproduce all the correlated ground states obtain
from the previous numerical Hartree-Fock calculations with the
Bistritzer-MacDonald-type (BM-type) model, and we find additional new
correlated ground states at high displacement field. Based on the numerical
results, we propose a simple rule for the ground states at high displacement
fields by using the $f-c-d$ model, and provide analytical derivation for the
rule at charge neutrality. We also provide analytical symmetry arguments for
the (nearly-)degenerate energies of the high-$\mathcal{E}$ ground states at all
the integer fillings of interest, and make experimental predictions of which
charge-neutral states are stabilized in magnetic fields. Our $f-c-d$ model
provides a new perspective for understanding the correlated phenomena in
MATSTG, suggesting that the heavy fermion paradigm of Ref. [1] should be the
generic underpinning of correlated physics in multilayer moire graphene
structures.
