Review talk on symmetric mass generation

• Cenke Xu

Symmetric mass generation of 8 Majorana domain-wall fermions

• Sho Araki (Osaka university)

DMRG study of the Fidkowski-Kitaev model for chiral lattice fermion

• Akira Matsumoto (Graduate School of Science, Osaka Metropolitan University)

We numerically study the Fidkowski-Kitaev (FK) model using the density matrix renormalization group (DMRG), a tensor network method in the Hamiltonian formalism. The 4-fermi interaction of the FK model can generate a mass gap without symmetry-breaking fermion condensation. Thus, it is expected that low-energy modes of one chirality will be decoupled from those of the other by a large mass hierarchy. Our main goals in this work are to obtain low-energy states with a definite chirality and to confirm the absence of symmetry breaking. It is also interesting to understand the effects of the anomaly and its cancellation in the Hamiltonian formalism. We translated the FK model into a spin model and applied the DMRG, in which the sign problem is absent, and the wave functions are directly available. We present our preliminary results and discuss the prospect.

Symmetries and edge modes in 3+1D staggered fermions

• Tatsuya Yamaoka (The University of Osaka)

What can PINN do for lattice fermion formulation?

• Tatsuhiro Misumi (Kindai University)

Physics-Informed Neural Networks (PINNs) have emerged as powerful tools for solving differential equations by incorporating physical constraints directly into the loss function. In this talk, I explore the potential of PINNs in theoretical physics, ranging from non-linear PDEs to lattice field theory. The main focus of this talk is the application of machine learning to lattice fermions. I present a novel approach where neural networks autonomously construct chiral fermions on the lattice. We show that by imposing physical requirements such as the Ginsparg-Wilson (GW) relation and locality, the network successfully learns the spectral operator of Overlap fermions. We verify the topological properties of the learned operator through the Atiyah-Singer index theorem and spectral flow in $U(1)$ gauge fields. Furthermore, I discuss a remarkable result where the NN "rediscovers" the exact GW relation and its generalized variants from physical constraints, suggesting a new data-driven approach to exploring symmetries in quantum field theory.