We study the thermal phase transition of the bosonic BMN model which is a mass deformed version of the bosonic part of the BFSS model. Our results connect the massless region of the phase diagram described by the bosonic BFSS model with the large-mass region, where the model is analytically solvable. We observe that at finite value of the matrix size $N$, the critical region is smeared over a small temperature range. The model has a single critical temperature, which arises as the large $N$ limit of two apparent transitions at finite $N$. We emphasise the vital role played by finite $N$ corrections in the confined phase and illustrate this with a novel treatment of the noninteracting Gaussian model.
As a continuation of our previous works studying the holographic principle in the plane-wave limit, we discuss the 3-point correlation functions of BMN operators with bosonic excitations when impurities are not conserved. We show that our proposal for a holographic mapping between the conformal OPE coefficients of super Yang-Mills theory and the 3-point vertex of the holographic string field theory is valid to the leading order in the large $μ$ limit. Our results provide for the first time a direct holographic relation for the 3-point correlators of BMN operators including impurity non-preserv…
We test a conjecture by Maldacena and Milekhin for the ungauged version of the Berenstein-Maldacena-Nastase (BMN) matrix model by lattice Monte Carlo simulation. The numerical results reproduce the perturbative and gravity results in the limit of large and small flux parameter, respectively, and are consistent with the conjecture.
In this thesis we provide the results obtained through lattice Monte Carlo simulations of the bosonic BMN and the bosonic BFSS matrix models. The simulations are performed using Hybrid Monte Carlo (HMC) algorithm. The BMN matrix model is expected to have a Hagedorn/deconfinement type phase transition as the temperature is varied in the system. The Polyakov loop is used as an order parameter for detecting the phase transition. Besides the Polyakov loop, other prime observables such as the internal energy and the extent of space were also computed. We also check the validity of numerical simulat…
Several reductions of the bosonic BMN matrix model equations to ordinary point particle Hamiltonian dynamics in the plane (or R^3) are given - as well as a few explicit solutions (some of which, as N->infinity, correspond to membranes rotating with constant angular velocity, others to higher dimensional objects).
We study the bosonic part of the BMN matrix model for wide ranges of temperatures, values of the deformation parameter, and numbers of colors $16 \leq N \leq 48$. Using lattice computations, we analyze phase transitions in the model, observing a single first-order transition from a uniform to a gapped phase for all values of the deformation parameter. We study the functional form of the dependence of the critical temperature on the deformation parameter, to describe how our results smoothly interpolate between the limits of the bosonic BFSS model and the gauged Gaussian model.
We study the confining/deconfining phase transition in the mass deformed Yang-Mills matrix model which is obtained by the dimensional reduction of the bosonic sector of the four-dimensional maximally supersymmetric Yang-Mills theory compactified on the three sphere, i.e. the bosonic BMN model. The $1/D$ (with $D$ the number of matrices) expansion suggests that the model may have two closely separated transitions. However, using a second order lattice formulation of the model we find that for the small value of the mass parameter, $μ=2$, those two apparent critical temperatures merge at large $…
One-instanton contributions to the correlation functions of two gauge-invariant single-trace operators in N=4 SU(N) Yang-Mills theory are studied in semi-classical approximation in the BMN limit. The most straightforward examples involve operators with four bosonic impurities. The explicit form for the correlation functions, which determine the anomalous dimensions, follows after integration over the large number of bosonic and fermionic moduli. Our results demonstrate that the instanton contributions scale appropriately in the BMN limit. We find impressive agreement with the D-instanton contr…
Yau Mathematical Sciences Center (YMSC), Tsinghua University（清华大学丘成桐数学科学中心）；Beijing Institute of Mathematical Sciences and Applications (BIMSA)（北京国际数学研究中心）
Quantization of the bosonic string around the classical, perturbative vacuum is not consistent for spacetime dimensions 2<d<26. Recently we have showed that at large d there is another so-called mean field vacuum. Here we extend this mean field calculation to finite d and show that the corresponding mean field vacuum is stable under quadratic fluctuations for 2<d<26. We point out the analogy with the two-dimensional O(N)-symmetric sigma-model, where the 1/N-vacuum is very close to the real vacuum state even for finite N, in contrast to the perturbative vacuum.
In this paper, following the work of Hohm and Zwiebach [arXiv:1905.06583], we show that in bosonic string theory nonperturbative anti-de Sitter (AdS) vacua could exist with all $α^{\prime}$ corrections included. We also discuss the possibility of the coexistence of nonperturbative dS and AdS vacua.
Using analytical methods, a nonpertubative vacuum is constructed recursively in the field theory for the open bosonic string. Evidence suggests it corresponds to the Lorentz-invariant endpoint of tachyon condensation on a D25-brane. The corresponding string field is a twisted squeezed state.
Mass-Flow Invariance of $Q$-Cohomology in BMN Matrix Quantum Mechanics
Yau Mathematical Sciences Center (YMSC), Tsinghua University（清华大学丘成桐数学科学中心）；Beijing Institute of Mathematical Sciences and Applications (BIMSA)（北京国际数学研究中心）；Department of Mathematical Sciences, Tsinghua University（清华大学数学科学系）
We compute the action of closed bosonic string field theory at quartic order with fields up to level ten. After level four, the value of the potential at the minimum starts oscillating around a nonzero negative value, in contrast with the proposition made in [5]. We try a different truncation scheme in which the value of the potential converges faster with the level. By extrapolating these values, we are able to give a rather precise value for the depth of the potential.
We employ machine learning techniques to provide accurate variational wavefunctions for matrix quantum mechanics, with multiple bosonic and fermionic matrices. Variational quantum Monte Carlo is implemented with deep generative flows to search for gauge invariant low energy states. The ground state, and also long-lived metastable states, of an $\mathrm{SU}(N)$ matrix quantum mechanics with three bosonic matrices, as well as its supersymmetric `mini-BMN' extension, are studied as a function of coupling and $N$. Known semiclassical fuzzy sphere states are recovered, and the collapse of these geo…
Nonperturbative Stabilization of D-Instantons in the Bosonic IIB Matrix Model
National Taiwan University（国立台湾大学）；Nambu Yoichiro Institute of Theoretical and Experimental Physics (NITEP), Osaka Metropolitan University（大阪公立大学南村亮郎理论实验物理研究所(NITEP)）；Department of Physics, National Sun Yat-Sen University（国立中山大学物理系）；KEK Theory Center, Institute of Particle and Nuclear Studies, High Energy Accelerator Research Organization（高能加速器研究机构粒子核研究所学部理论中心）；Graduate Institute for Advanced Studies, SOKENDAI（SOKENDAI高等研究院）
Type-IIB supersymmetric theories have an SL(2,Z) invariance, known as U-duality, which controls the non-perturbative behavior of the theory. Under SL(2,Z) the supercharges are doublets, implying that the bosonic charges would be singlets or triplets. However, among the bosonic charges there are doublet strings and doublet fivebranes which are in conflict with the doublet property of the supercharges. It is shown that the conflict is resolved by structure constants that depend on moduli, such as the tau parameter, which transform under the same SL(2,Z). The resulting superalgebra encodes the no…
Using the formalism of superconnections, we show the existence of a bosonic action functional for the standard K-cycle in noncommutative geometry, giving rise, through the spectral action principle, only to the Einstein gravity and Standard Model Yang-Mills-Higgs terms. It provides an effective nonminimal coupling in the bosonic sector of the Lagrangian.
The IIB matrix model has been suggested as a particular formulation of nonperturbative superstring theory (M-theory). It has now been realized that an emerging classical spacetime may reside in its large-$N$ master field. This bosonic master field can, in principle, give rise to Minkowski and Robertson-Walker spacetimes. The outstanding task is to solve the bosonic master-field equation, which is essentially an algebraic equation. In this article, we present new results for the $(D,\,N)=(10,\,4)$ bosonic master-field equation of the IIB matrix model, where $D$ is the number of bosonic matrices…
The cubic interaction vertex of light-cone string field theory in the plane-wave background has a simple effective form when considering states with only bosonic excitations. This simple effective interaction vertex is used in this paper to calculate the three string interaction matrix elements for states of arbitrary bosonic excitation and these results are used to examine certain decay modes on the mass-shell. It is shown that the matrix elements of one string to two string decays involving only bosonic excitations will vanish to all orders in 1/mu on the mass-shell when the number of excita…
We obtain analytic, nonperturbative, approximate solutions of Yukawa theory in the one-fermion sector using light-front quantization. The theory is regulated in the ultraviolet by the introduction of heavy Pauli-Villars scalar and fermion fields, each with negative norm. In order to obtain a directly soluble problem, fermion-pair creation and annihilation are neglected, and the number of bosonic constituents is limited to one of either type. We discuss some of the features of the wave function of the eigensolution, including its endpoint behavior and spin and orbital angular momentum content. …
We show how Monte Carlo approach can be used to study the double scaling limit in matrix models. As an example, we study a solvable hermitian one-matrix model with the double-well potential, which has been identified recently as a dual description of noncritical string theory with worldsheet supersymmetry. This identification utilizes the nonperturbatively stable vacuum unlike its bosonic counterparts, and therefore it provides a complete constructive formulation of string theory. Our data with the matrix size ranging from 8 to 512 show a clear scaling behavior, which enables us to extract the…
We propose a nonperturbative framework for the O(32) type I open and closed string theory. The short distance degrees of freedom are bosonic and fermionic hermitian matrices belonging respectively to the adjoint and fundamental representations of the special unitary group SU(N). We identify a closed matrix algebra at finite N which corresponds to the Lorentz, gauge, and supersymmetry algebras of the large N continuum limit. The planar reduction of our matrix theory coincides with the low energy spacetime effective action of the d=10 type I O(32) unoriented open and closed string theory. We sho…
We study a 4d supersymmetric matrix model with a cubic term, which incorporates fuzzy spheres as classical solutions, using Monte Carlo simulations and perturbative calculations. The fuzzy sphere in the supersymmetric model turns out to be always stable if the large-N limit is taken in such a way that various correlation functions scale. This is in striking contrast to analogous bosonic models, where the fuzzy sphere decays into the pure Yang-Mills vacuum due to quantum effects when the coefficient of the cubic term becomes smaller than a critical value. We also find that the power-law tail of…
Bosonization allows one to describe the low-energy physics of one-dimensional quantum fluids within a bosonic effective field theory formulated in terms of two fields: the "density" field $φ$ and its conjugate partner, the phase $\vartheta$ of the superfluid order parameter. We discuss the implementation of the nonperturbative functional renormalization group in this formalism, considering a Luttinger liquid in a periodic potential as an example. We show that in order for $\vartheta$ and $φ$ to remain conjugate variables at all energy scales, one must dynamically redefine the field $\vartheta$…
The large N reduction is an equivalence between large N gauge theories and matrix models discovered by Eguchi and Kawai in the early 80s. In particular the continuum version of the quenched Eguchi-Kawai model may be useful in studying supersymmetric and/or chiral gauge theories nonperturbatively. We apply this idea to matrix quantum mechanics, which is relevant, for instance, to nonperturbative studies of the BFSS Matrix Theory, a conjectured nonperturbative definition of M-theory. In the bosonic case we present Monte Carlo results confirming the equivalence directly, and discuss a possible ex…
We study the suppression of non-planar diagrams in a scalar QCD model of a meson system in $3+1$ space-time dimensions due to the inclusion of the color degrees of freedom. As a prototype of the color-singlet meson, we consider a flavor-nonsinglet system consisting of a scalar-quark and a scalar-antiquark with equal masses exchanging a scalar-gluon of a different mass, which is investigated within the framework of the homogeneous Bethe-Salpeter equation. The equation is solved by using the Nakanishi representation for the manifestly covariant bound-state amplitude and its light-front projectio…
We study stability of noncommutative spaces in matrix models and discuss the continuum limit which leads to noncommutative Yang-Mills theories (NCYM). It turns out that most of noncommutative spaces in bosonic models are unstable. This indicates perturbative instability of fuzzy R^D pointed out by Van Raamsdonk and Armoni et al. persists to nonperturbative level in these cases. In this sense, these bosonic NCYM are not well-defined, or at least their matrix model formulations studied in this paper do not work. We also show that noncommutative backgrounds are stable in a supersymmetric matrix m…
We present a class of solvable SO(D) symmetric matrix models with D bosonic matrices coupled to chiral fermions. The SO(D) symmetry is spontaneously broken due to the phase of the fermion integral. This demonstrates the conjectured mechanism for the dynamical generation of four-dimensional space-time in the IIB matrix model, which was proposed as a nonperturbative definition of type IIB superstring theory in ten dimensions.
The IIB matrix model is one of the candidates for nonperturbative formulation of string theory, and it is believed that the model contains gravitational degrees of freedom in some manner. In some preceding works, it was proposed that the matrix model describes the curved space where the matrices represent differential operators that are defined on a principal bundle. In this paper, we study the dynamics of the model in this interpretation, and point out the necessity of the principal bundle from the viewpoint of the stability and diffeomorphism invariance. We also compute the one-loop correcti…
In string bit models, the superstring emerges as a very long chain of "bits", in which s fermionic degrees of freedom contribute positively to the ground state energy in a way to exactly cancel the destabilizing negative contributions of d=s bosonic degrees of freedom. We propose that the physics of string formation be studied nonperturbatively in the class of string bit models in which s>d, so that a long chain is stable, in contrast to the marginally stable (s=d=8) superstring chain. We focus on the simplest of these models with s=1 and d=0, in which the string bits live in zero space dimens…
This thesis is devoted to the development of a nonperturbative quantum field theoretical approach to flavour physics, with special attention to cosmological applications. Neutrino flavour oscillation is nowadays a fairly well-established experimental fact. However, the formulation of flavour oscillations in a relativistic field theoretical framework presents non-trivial difficulties. A nonperturbative approach for building flavour states has been proposed by Blasone, Vitiello and coworkers. The formalism implies a non-trivial physical vacuum (called "flavour vacuum"), which might act as a sour…
The emergence of (3+1)-dimensional expanding space-time in the Lorentzian type IIB matrix model is an intriguing phenomenon which was observed in Monte Carlo studies of this model. In particular, this may be taken as a support to the conjecture that the model is a nonperturbative formulation of superstring theory in (9+1) dimensions. In this paper we investigate the space-time structure of the matrices generated by simulating this model and its simplified versions, and find that the expanding part of the space is described essentially by the Pauli matrices. We argue that this is due to an appr…
The emergence of (3+1)-dimensional expanding spacetime from complex Langevin simulations of the Lorentzian type IIB matrix model with deformations
National Technical University of Athens（雅典国立技术大学）；Setsunan University（摂南大学）；Università degli Studi di Milano-Bicocca（米兰比可卡大学）；Istituto Nazionale di Fisica Nucleare (INFN)（意大利国家核物理研究所）；High Energy Accelerator Research Organization（高能加速器研究机构）；SOKENDAI（日本综合研究大学院大学）；Shizuoka University（静冈大学）
