Axel Perez-Obiol, Kochi Univ. of Technology

Coulomb 1D problem with general connection condition at the origin and non-Rydberg spectra

##### We consider the solution of the quantum Coulomb problem in one dimension with the most general connection condition at the origin. The divergence of the derivative of the wave function at the origin invalidates the standard current conservation approach. We explore two approaches, Wronskian self-adjoint extension method and cutoff regularization method, and establish their mutual relations, thereby clarifying the physical contents of the connection parameters. We show how to realize exotic non-Loudon connection conditions, entailing the realization of non-Rydberg spectrum.

Masafumi Fukuma, Kyoto University

Tempered Lefschetz thimble method: the basics and applications

##### The tempered Lefschetz thimble method (TLTM) [arXiv:1703.00861] is a parallel-tempering algorithm towards solving the numerical sign problem. It uses the flow time of the antiholomorphic gradient flow as a tempering parameter, and is expected to tame both the sign and ergodicity problems simultaneously that exist intrinsically in thimble methods. In this talk, we elaborate on the basics of TLTM, and apply the method to various problems, including the (0+1)-dimensional finite-density Thirring model and the quantum Monte Carlo simulation of the Hubbard model away from half filling.

Masafumi Fukuma, Kyoto University

Sign problem in Monte Carlo simulations and the tempered Lefschetz thimble method

##### When numerically estimating observables on a large-scale system with a complex-valued action, one needs an exponentially long computational time for precise estimation. After reviewing various approaches to this “sign problem”, we explain “the tempered Lefschetz thimble method”, which was introduced by MF and N. Umeda in [arXiv:1703.00861]. We argue that this has a potential to be a universal solution to the sign problem, by explicitly showing that this algorithm gives correct estimates for problems that have been difficult by other algorithms.

Matthew Dodelson, IPMU

High energy behavior of Mellin amplitudes

##### I will describe recent work with Ooguri, in which we obtained bounds on the Mellin amplitude at high energies. I’ll start with a general overview of Mellin space, and then move on to our derivation of the bounds. The bounds are obtained by demanding that position space correlators don’t have spurious singularities. At the end I might talk about related ongoing work on black holes, if I have time.

Tomomi Sunayama, IPMU

Cosmology with Subaru Prime Focus Spectrograph (PFS)

##### PFS (Prime Focus Spectrograph), a next generation facility instruments on the Subaru telescope, is a wide-field, massively multiplexed, and optical & near-infrared spectrograph. In the PFS cosmology survey, emission line galaxies (ELGs) in the wide redshift range from z= 0.6to2.4 over 1400 square-degree will be observed. The unique redshift range for the PFS cosmology survey is at z>2. We envision that we will start our survey from 2022, and I will describe strategies to achieve the scientific goals as well as the possible systematic problems for future fiber-fed spectroscopic surveys.

Po-Yen Tseng, Yonsei University

Light gauge boson interpretation for muon g-2 and J-PARC KOTO anomalies

##### We discuss a list of possible light gauge boson interpretations for the long-standing experimental anomaly in $(g-2)\mu$ and also recent anomalous excess in $KL \rightarrow \pi^0 + \text{(invisible)}$ events at the J-PARC KOTO experiment. We consider two models: i) $L\mu – L\tau$ gauge boson with heavy vector-like quarks and ii) $(L\mu – L\tau) + \epsilon (B3 – L\tau)$ gauge boson in the presence of right-handed neutrinos. When the light gauge boson has mass close to the neutral pion in order to satisfy the Grossman-Nir bound, the models successfully explain the anomalies simultaneously while satisfying all known experimental constraints. We extensively provide the future prospect of suggested models.

Tatsuhiro Misumi, Akita University

Central-branch Wilson fermion, Spin chain and Aoki phase

##### In this talk, we first discuss the central-branch Wilson fermion, which is defined by imposing a specific relation between the mass and the Wilson parameter [1]. This setup gives two massless Dirac fermions in the continuum limit, and it turns out that no fine-tuning of m is required because the extra U(1) symmetry at the central branch prohibits the additive mass renormalization [2,3]. We show that Dirac determinant is positive semi-definite and this formulation is free from the sign problem, so the Monte Carlo simulation of the path integral is possible. By identifying the symmetry at low energy, we find that this lattice model has the mixed ’t Hooft anomaly between the extra U(1) symmetry, lattice translation, and lattice rotation, which means that the trivially gapped phase is forbidden at the central branch [4]. We discuss its relation to the anomaly of half-integer anti-ferromagnetic spin chains, so our lattice gauge theory is suitable for numerical simulation of Haldane conjecture. We also argue that it gives new and strict understanding on parity-broken phase (Aoki phase) of 2d Wilson fermion [4]. Furthermore, we show that our study can be extended to 4d lattice QCD with Wilson fermion, leading to a novel insight into the question which of Aoki-phase or Sharpe-Singleton scenarios is valid.

[References]

[1] M. Creutz, T. Kimura, T. Misumi, Phys. Rev. D83 (2011) 094506, [arXiv:1101.4239].

[2] T. Kimura, S. Komatsu, T. Misumi, T. Noumi, S. Torii, S. Aoki, JHEP 01 (2012) 048, [arXiv:1111.0402].

[3] T. Misumi, PoS LATTICE2012 (2012) 005, [arXiv:1211.6999].

[4] T. Misumi, Y. Tanizaki, [arXiv:1910:09604].

Sanefumi Moriyama, Osaka City University

ABJM Matrix Model and 2D Toda Lattice Hierarchy