### Conveners

#### Theoretical Developments: Session 6-1 B

- Akio Tomiya (RIKEN)

#### Theoretical Developments: Session 6-2 A

- Xu Feng (Peking University)

#### Theoretical Developments: Session 7-1 B

- Etsuko Itou (Keio University)

#### Theoretical Developments: Session 7-2 B

- Hidenori Fukaya (Osaka University)

We present numerical results for 3d $\phi^4$ field theory on the $R\times S^2$ manifold in radial quantization using the quantum extension of the finite element method (QFE). The Monte Carlo study supports the QFE ansatz that once counterterms cancel effects from geometric defects in the UV, one reaches the nonperturbative conformal fixed point of the 3d Ising CFT. We demonstrate that...

When the realizations of QFT on quantum computer are discussed, the Kogut-Susskind formulation of lattice Hamiltonian is a popular option. We provide alternative formulations and discuss the pros and cons.

We perform a digital quantum simulation of the Schwinger model with the theta term, which is practically inaccessible by standard lattice Monte Carlo simulations. We construct the true vacuum state of a lattice Schwinger model using adiabatic state preparation which, in turn, allows us to compute an expectation value of the fermion mass operator with respect to the vacuum. Upon taking a...

The efficient digitization required for the quantum simulations of QCD can be obtained by approximating continuous SU(3) gluon fields by discrete subgroups. In this talk, we discuss on-going efforts to develop this program of digitization: deriving improved discrete group lattice actions, classical simulations for quantifying systematic errors, and implementable circuits for digital quantum computers.

We discuss continuous symmetries identities using the tensor formulation of lattice spin and gauge models. We show that the symmetries are encoded in the selection rules of the tensor. This allows truncations that preserve the symmetries exactly. We present the tensorial expression of the transfer matrix for Abelian gauge theories and explain how gauge fixing and Gauss's law relate.

We...

Quantum computing may offer the opportunity to simulate strongly-interacting field theories, such as quantum chromodynamics, with physical time evolution. This would give access to Minkowski signature correlators, in contrast to the Euclidean calculations routinely performed at present. However, as with present-day calculations, quantum computation strategies still require the restriction to a...

In their seminal publication of 1990, Maiani and Testa showed that Euclidean correlators are contaminated by off-shell contributions, limiting a direct extraction of amplitudes away from threshold. In this presentation, we revisit and extend this work, and explore the connection with recent developments on the inverse problem in Lattice QCD.

We review developments in calculating multi-hadron form-factors and transition processes via lattice QCD. Our primary tools are finite-volume scaling relations, which non-perturbatively map spectra and matrix elements to their corresponding infinite-volume amplitudes. We focus on two hadron processes probed by an external current, and provide various checks on the finite-volume formalism in...

Using a non-relativistic EFT, we derive a general relativistic expression for the energy shift in finite volume. This includes the N-particle ground state, and the first two- and three-particle excited states. In addition, we probe the N particle energy shift formula in complex phi^4 theory. We investigate different fit models, that include relativistic effects, exponentially suppressed...

Recently, many studies of quantum field theory with quantum computers have reported. Quantum calculation can only treat unitary evolution, so thermal physics is one of difficulty of it because one needs to produce mixed states within allowed operations. Towards resolving the problem, we attempt to investigate thermal physics with thermal pure quantum(TPQ) state formalism. TPQ state formalism...

Quantum polarization effects associated with the conformal anomaly in a static magnetic field background may generate a transverse electric current in the vacuum of massless particles (either bosons or fermions). The current may be produced either in an unbounded curved spacetime or in flat spacetime in a physically bounded system. In both cases, the magnitude of the electric current is...

We investigate Casimir energy for free fermions on the lattice.

The Casimir energy of fermion fields can be defined with the lattice regularization.

The continuum extrapolation of our results reproduces the Casimir energy known in continuum theory.

We also show the lattice effect for the Casimir energy.

The lattice effect is important as an artifact that should be well-understood in order...

We study the defects that can be defined within the framework of lattice gauge theories, in the presence of anisotropic couplings and try to identify their target space avatars. These are relevant for describing topological insulators.

We suggest that in Yang-Mills theories the ratio R of the mass of the tensor glueball over the mass of the scalar glueball is a universal quantity that depends only on the dimensionality of the space. To support this conjecture, we compute numerically R for Sp(2N) gauge theories for N = 1, 2, 3, 4 in d=4 Euclidean dimensions on a lattice and we analyse our results together with previous...

Tensor network is an attractive approach to field theory with

negative sign problem. The complex \phi^4 theory at finite density is a test bed for numerical algorithms to verify their effectiveness.

The model shows a characteristic feature called the Silver Blaze phenomenon associated with the sign problem in the large volume limit at low temperature. We analyze the four-dimensional model ...

The generalization of Lattice Field Theory targeting in curved Riemann manifolds referred to as Quantum Finite Elements (QFE) requires geometrical tools.

A brief outline for the construction of a Simplicial Complex and

its Delaunay dual, the construction Finite Element of lattice action based on

the elegant Discrete Exterior Calculus (DEC) is given. The focus in on spheres and hyperbolic...

Gauge anomaly in 4-dimensions can be viewed as a current inflow into an extra-dimension, where the total phase of the fermion partition function is given in a gauge invariant way by the Atiyah-Patodi-Singer(APS) eta-invariant of a 5-dimensional Dirac operator. However, this formalism requires a non-local boundary condition, which makes the physical roles of edge/bulk modes unclear and the...

Recently, in the context of the resurgence program, it was conjectured that the perturbative ambiguity caused by the IR renormalon is canceled against the semi-classical object called bion. This conjecture requires the circle compactification with the $Z_N$ twisted boundary condition, in which the bion solution is found. Contrary to this conjecture, we find that there is no IR renormalon in...

Contrary to the common wisdom, local bosonizations of fermionic systems exist in higher dimensions. Interestingly, resulting bosonic variables must satisfy local constraints of a gauge type. They effectively replace long distance exchange interactions. In this work we study in detail the properties of such a system which was proposed a long time ago. In particular, dependence of the...

This talk is about a bosonization procedure based on Clifford algebra-valued degrees of freedom, valid for spaces of any dimension. Its interpretation in terms of lattice Z_2 gauge theory will be presented. Brief comparison with other bosonization proposals will be given.