arXiv subjects

Masahito Yamazaki

Publications and source records attributed to Masahito Yamazaki.

At least 55 records · Page 3Linked to original sources

arXiv2023

Conserved charges in the quantum simulation of integrable spin chains

When simulating the time evolution of quantum many-body systems on a digital quantum computer, one faces the challenges of quantum noise and of the Trotter error due to time discretization. The Trotter error in integrable spin chains can be under control if the discrete time evolution preserves integrability. In this work we implement, on a real quantum computer and on classical simulators, the integrable Trotterization of the spin-1/2 Heisenberg XXX spin chain. We study how quantum noise affects the time evolution of several conserved charges, and observe the decay of the expectation values. We in addition study the early time behaviors of the time evolution, which can potentially be used to benchmark quantum devices and algorithms in the future. We also provide an efficient method to generate the conserved charges at higher orders.

quant-ph↗

arXiv2023

Quiver Yangians and Crystal Melting: A Concise Summary

The goal of this short article is to summarize some of the recent developments in the quiver Yangians and crystal meltings. This article is based on a lecture delivered by the author at International Congress on Mathematical Physics (ICMP), Geneva, 2021.

hep-th↗

arXiv2022

Non-unitary TQFTs from 3D $\mathcal{N}=4$ rank 0 SCFTs

We propose a novel procedure of assigning a pair of non-unitary topological quantum field theories (TQFTs), TFT$_\pm [\mathcal{T}_{\rm rank \;0}]$, to a (2+1)D interacting $\mathcal{N}=4$ superconformal field theory (SCFT) $\mathcal{T}_{\rm rank \;0}$ of rank 0, i.e. having no Coulomb and Higgs branches. The topological theories arise from particular degenerate limits of the SCFT. Modular data of the non-unitary TQFTs are extracted from the supersymmetric partition functions in the degenerate limits. As a non-trivial dictionary, we propose that $F = \max_α\left(- \log |S^{(+)}_{0α}| \right) = \max_α\left(- \log |S^{(-)}_{0α}|\right)$, where $F$ is the round three-sphere free energy of $\mathcal{T}_{\rm rank \;0 }$ and $S^{(\pm)}_{0α}$ is the first column in the modular S-matrix of TFT$_\pm$. From the dictionary, we derive the lower bound on $F$, $F \geq -\log \left(\sqrt{\frac{5-\sqrt{5}}{10}} \right) \simeq 0.642965$, which holds for any rank 0 SCFT. The bound is saturated by the minimal $\mathcal{N}=4$ SCFT proposed by Gang-Yamazaki, whose associated topological theories are both the Lee-Yang TQFT. We explicitly work out the (rank 0 SCFT)/(non-unitary TQFTs) correspondence for infinitely many examples.

hep-th↗

arXiv2022

Quantum Simulations of Dark Sector Showers

We consider dark sector scenarios where dark matter is accompanied by a dark photon and multiple-flavor dark fermions charged under the dark gauge group. We study quantum interference effects in dark sector jets, where multiple dark photons are emitted from high-energy dark fermions. We perform fully quantum simulations of dark sector showers and compare the results against those of the classical Monte-Carlo simulations. We find important differences in probability distributions of dark photon countings between quantum and classical computations. When the number of dark-fermion flavors is large, we find significant enhancements in large numbers of dark photon emissions. Such enhancements can provide distinguishing signals for our scenarios at particle colliders.

hep-ph↗

arXiv2022

Boson-fermion duality with subsystem symmetry

We explore an exact duality in $(2+1)$d between the fermionization of a bosonic theory with a $\mathbb{Z}_2$ subsystem symmetry and a fermionic theory with a $\mathbb{Z}_2$ subsystem fermion parity symmetry. A typical example is the duality between the fermionization of the plaquette Ising model and the plaquette fermion model. We first revisit the standard boson-fermion duality in $(1+1)$d with a $\mathbb{Z}_2$ 0-from symmetry, presenting in a way generalizable to $(2+1)$d. We proceed to $(2+1)$d with a $\mathbb{Z}_2$ subsystem symmetry and establish the exact duality on the lattice by using the generalized Jordan-Wigner map, with a careful discussion on the mapping of the twist and symmetry sectors. This motivates us to introduce the subsystem Arf invariant, which exhibits a foliation structure.

cond-mat.str-el↗

arXiv2022

Gauge/Bethe correspondence from quiver BPS algebras

We study the Gauge/Bethe correspondence for two-dimensional $\mathcal{N}=(2,2)$ supersymmetric quiver gauge theories associated with toric Calabi-Yau three-folds, whose BPS algebras have recently been identified as the quiver Yangians. We start with the crystal representations of the quiver Yangian, which are placed at each site of the spin chain. We then construct integrable models by combining the single-site crystals into crystal chains by a coproduct of the algebra, which we determine by a combination of representation-theoretical and gauge-theoretical arguments. For non-chiral quivers, we find that the Bethe ansatz equations for the crystal chain coincide with the vacuum equation of the quiver gauge theory, thus confirming the corresponding Gauge/Bethe correspondence. For more general chiral quivers, however, we find obstructions to the $R$-matrices satisfying the Yang-Baxter equations and the unitarity conditions, and hence to their corresponding Gauge/Bethe correspondence. We also discuss trigonometric (quantum toroidal) versions of the quiver BPS algebras, which correspond to three-dimensional $\mathcal{N}=2$ gauge theories and arrive at similar conclusions. Our findings demonstrate that there are important subtleties in the Gauge/Bethe correspondence, often overlooked in the literature.

hep-th↗

arXiv2022

Quiver Yangian from Crystal Melting

We find a new infinite class of infinite-dimensional algebras acting on BPS states for non-compact toric Calabi-Yau threefolds. In Type IIA superstring compactification on a toric Calabi-Yau threefold, the D-branes wrapping holomorphic cycles represent the BPS states, and the fixed points of the moduli spaces of BPS states are described by statistical configurations of crystal melting. Our algebras are "bootstrapped" from the molten crystal configurations, hence they act on the BPS states. We discuss the truncation of the algebra and its relation with D4-branes. We illustrate our results in many examples, with and without compact $4$-cycles.

hep-th↗

arXiv2022

Toroidal and Elliptic Quiver BPS Algebras and Beyond

The quiver Yangian, an infinite-dimensional algebra introduced recently in arXiv:2003.08909, is the algebra underlying BPS state counting problems for toric Calabi-Yau three-folds. We introduce trigonometric and elliptic analogues of quiver Yangians, which we call toroidal quiver algebras and elliptic quiver algebras, respectively. We construct the representations of the shifted toroidal and elliptic algebras in terms of the statistical model of crystal melting. We also derive the algebras and their representations from equivariant localization of three-dimensional $\mathcal{N}=2$ supersymmetric quiver gauge theories, and their dimensionally-reduced counterparts. The analysis of supersymmetric gauge theories suggests that there exist even richer classes of algebras associated with higher-genus Riemann surfaces and generalized cohomology theories.

hep-th↗

arXiv2021

Peeking into the $θ$ vacuum

We propose a subvolume method to study the $θ$ dependence of the free energy density of the four-dimensional SU($N$) Yang-Mills theory on the lattice. As an attempt, the method is first applied to SU(2) Yang-Mills theory at $T=1.2\,T_c$ to understand the systematics of the method. We then proceed to the calculation of the vacuum energy density and obtain the $θ$ dependence qualitatively different from the high temperature case. The numerical results combined with the theoretical requirements provide the evidence for the spontaneous CP violation at $θ= π$, which is in accordance with the large $N$ prediction and indicates that the similarity between 4d SU($N$) and 2d CP$^{N-1}$ theories does not hold for $N$=2.

hep-lat↗

arXiv2021

Shifted Quiver Yangians and Representations from BPS Crystals

We introduce a class of new algebras, the shifted quiver Yangians, as the BPS algebras for type IIA string theory on general toric Calabi-Yau three-folds. We construct representations of the shifted quiver Yangian from general subcrystals of the canonical crystal. We derive our results via equivariant localization for supersymmetric quiver quantum mechanics for various framed quivers, where the framings are determined by the shape of the subcrystals. Our results unify many known BPS state counting problems, including open BPS counting, non-compact D4-branes, and wall crossing phenomena, simply as different representations of the shifted quiver Yangians. Furthermore, most of our representations seem to be new, and this suggests the existence of a zoo of BPS state counting problems yet to be studied in detail.

hep-th↗

arXiv2021

Chern-Simons Invariants from Ensemble Averages

We discuss ensemble averages of two-dimensional conformal field theories associated with an arbitrary indefinite lattice with integral quadratic form $Q$. We provide evidence that the holographic dual after the ensemble average is the three-dimensional Abelian Chern-Simons theory with kinetic term determined by $Q$. The resulting partition function can be written as a modular form, expressed as a sum over the partition functions of Chern-Simons theories on lens spaces. For odd lattices, the dual bulk theory is a spin Chern-Simons theory, and we identify several novel phenomena in this case. We also discuss the holographic duality prior to averaging in terms of Maxwell-Chern-Simons theories.

hep-th↗

arXiv2021

Is $N=2$ Large?

We study $θ$ dependence of the vacuum energy for the 4d SU(2) pure Yang-Mills theory by lattice numerical simulations. The response of topological excitations to the smearing procedure is investigated in detail, in order to extract topological information from smeared gauge configurations. We determine the first two coefficients in the $θ$ expansion of the vacuum energy, the topological susceptibility $χ$ and the first dimensionless coefficient $b_2$, in the continuum limit. We find consistency of the SU(2) results with the large $N$ scaling. By analytic continuing the number of colors, $N$, to non-integer values, we infer the phase diagram of the vacuum structure of SU(N) gauge theory as a function of $N$ and $θ$. Based on the numerical results, we provide quantitative evidence that 4d SU(2) Yang-Mills theory at $θ= π$ is gapped with spontaneous breaking of the CP symmetry.

hep-lat↗

arXiv2020

Towards Super Teichmüller Spin TQFT

The quantization of the Teichmüller theory has led to the formulation of the so-called Teichmüller TQFT for 3-manifolds. In this paper we initiate the study of "supersymmetrization" of the Teichmüller TQFT, which we call the super Teichmüller spin TQFT. We obtain concrete expressions for the partition functions of the super Teichmüller spin TQFT for a class of spin 3-manifold geometries, by taking advantage of the recent results on the quantization of the super Teichmüller theory. We then compute the perturbative expansions of the partition functions, to obtain perturbative invariants of spin 3-manifolds. We also comment on the relations of the super Teichmüller spin TQFT to 3-dimensional Chern-Simons theories with complex gauge groups, and to a class of 3d N=2 theories arising from the compactifications of the M5-branes.

hep-th↗

arXiv2020

Quiver Yangian and Supersymmetric Quantum Mechanics

The statistical model of crystal melting represents BPS configurations of D-branes on a toric Calabi-Yau three-fold. Recently it has been noticed that an infinite-dimensional algebra, the quiver Yangian, acts consistently on the crystal-melting configurations. We physically derive the algebra and its action on the BPS states, starting with the effective supersymmetric quiver quantum mechanics on the D-brane worldvolume. This leads to remarkable combinatorial identities involving equivariant integrations on the moduli space of the quantum mechanics, which can be checked by numerical computations.

hep-th↗

arXiv2020

Confinement as Analytic Continuation Beyond Infinity

We propose a mechanism for confinement: analytic continuation beyond infinite coupling in the space of the coupling constant. The analytic continuation is realized by renormalization group flows from the weak to the strong coupling regime. We demonstrate this mechanism explicitly for the mass gap in two-dimensional sigma models in the large $N$ limit. Our analysis suggests that the conventional analysis of the operator product expansion in itself does not necessarily guarantee the existence of a classical solution corresponding to renormalons. We discuss how the renormalon puzzle may be resolved by the analytic continuation beyond infinite coupling.

hep-th↗

arXiv2020

Integrability As Duality: The Gauge/YBE Correspondence

The Gauge/YBE correspondence states a surprising connection between solutions to the Yang-Baxter equation with spectral parameters and partition functions of supersymmetric quiver gauge theories. This correspondence has lead to systematic discoveries of new integrable models based on quantum-field-theory methods. We provide pedagogical introduction to the subject and summarizes many recent developments. This is a write-up of the lecture at the String-Math 2018 conference.

hep-th↗

arXiv2020

Fundamental Forces and Scalar Field Dynamics in the Early Universe

Scalar weak gravity conjectures (SWGCs) attempt to pinpoint the ranges of couplings consistent with a fundamental theory of all interactions. We identify a generic dynamical consequence of these conjectures for cosmology and show that SWGCs imply a particular behavior of the scalar fields in the early universe. A scalar field that develops a large expectation value during inflation must relax to the minimum of effective potential at a later time. SWGCs imply that a homogeneous distribution of the field is unstable with respect to fragmentation into localized lumps, which could potentially lead to significant consequences for cosmology.

hep-th↗

arXiv2019

Expanding 3d $\mathcal{N}=2$ Theories around the Round Sphere

We study a perturbative expansion of the squashed 3-sphere ($S^3_b$) partition function of 3d $\mathcal{N}=2$ gauge theories around the squashing parameter $b= 1$. Our proposal gives the coefficients of the perturbative expansion as a finite sum over the saddle points of the supersymmetric-localization integral in the limit $b \rightarrow 0$ (the so-called Bethe vacua), and the contribution from each Bethe vacua can be systematically computed using saddle-point methods. Our expansion provides an efficient and practical method for computing basic CFT data ($F,C_T,C_{JJ}$ and higher-point correlation functions of the stress-energy tensor) of the IR superconformal field theory without performing the localization integrals.

hep-th↗