Conveners
Theoretical Developments
- Daniel Nogradi
Theoretical Developments
- Karl Jansen (DESY)
Theoretical Developments
- Michele Pepe (INFN - National Institute for Nuclear Physics)
Theoretical Developments
- SHINJI TAKEDA (Kanazawa university)
Theoretical Developments
- George Fleming (Yale University)
Theoretical Developments
- Tetsuya Onogi (Osaka University)
Theoretical Developments
- Richard Brower (Boston University)
Anomalous dimensions of composite operators like the scalar, tensor, or baryon are important
to determine energy dependent renormalization constants. Until now only perturbative predictions were available.
The recent proposal [PRL 121 (2018) 201601] provides a non-perturbative determination of anomalous dimensions in conformal systems
by defining a continuous real-space renormalization group...
We analyse the leading logarithmic corrections to the $a^2$ scaling of lattice artefacts in QCD, following the seminal work of Balog, Niedermayer and Weisz in the O(n) non-linear sigma model. Limiting to contributions from the action, the leading logarithmic corrections can be determined by the anomalous dimensions of a minimal on-shell basis of mass-dimension 6 operators. We present results...
We construct a gradient flow equation in N=1 SQCD. The flow is supersymmetric in a sense that the flow time and the supersymmetry transformation commute with each other up to a gauge transformation. We also discuss the UV property of flowed correlators.
We report some preliminary results of our ongoing non-perturbative computation of the twisted 't Hooft running coupling in a particular set-up, using the gradient flow to define the coupling and step scaling techniques to compute it. For the computation we considered a pure gauge SU(3) theory in four dimensions, defined on the lattice on an asymmetrical torus endowed with twisted boundary...
A renormalization group transformation defined as a simple stochastic process is proposed, and its relation to functional RG is described. The transformation leads to a new instantiation of Monte Carlo Renormalization Group that is amenable to lattice simulation by performing a Langevin equation integration on top of the ensemble of bare fields generated by traditional MCMC methods. The...
Critical behavior of 4-dimensional Ising model has been attracting the interest of particle physicists for a long time in the context of the triviality of the φ^4 theory. The perturbative renormalization group analysis predicts logarithmic corrections to the mean-field type of scaling properties for this model. Although a lot of numerical work have been carried out to make a nonperturbative...
We study the complex $\phi^{4}$ theory with finite chemical potential. To closely understand nontrivial effects such as the Silver Blaze phenomenon, experimental studies on the lattice will give some knowledge; however, on account of the finite chemical potential, there is a sign problem in Monte Carlo simulations. In this study, to overcome the problem, the tensor renormalization group...
In the talk, I will discuss how to obtain a tensor network representation for real-time path integral. As an example, I deal with 1+1 dimensional lattice scalar field theory with the Minkowski metric. I show some numerical results to assess the validity of the formulation.
In this talk, we present concluding results from our study of phase structure of the lattice version of the massive Thirring model in 1+1 dimensions. Employing the method of matrix product state (MPS), several quantities have been investigated, leading to firm numerical evidence of a Kosterlitz-Thouless phase transition. In particular, we examine two correlators and determine the relevant...
Spin-flavor symmetries in hadronic physics have been thought to follow from large-N. However, lattice data suggests an SU(16) spin-flavor symmetry for baryons in the SU(3) limit that does not have a large-N explanation. We discuss how the enhanced symmetry corresponds to suppressed entanglement in scattering processes, and conjecture that the strong interactions may be dynamically...
In O(N) models, the multi-cluster algorithm generates spins
clusters, which are usually considered as purely algorithmic
objects. We show that the histograms of their sizes scale
towards a continuum limit, with a fractal dimension D, which
suggests that these clusters do have a physical meaning.
We demonstrate this property for the quantum rotor in separate
topological sectors (where D=1), for...
The $2-d$ $O\left(3\right)$ model shares many features with $4-d$ non-Abelian gauge theories, including asymptotic freedom, a nonperturbatively generated mass gap and a nontrivial topological charge $Q$. By an analytic rewriting of the partition function, we identify merons (a particular type of Wolff clusters with $Q=\pm1/2$) as the relevant topological charge carriers.
In contrast to...
Motivated by recent studies on the resurgence structure of quantum field theories, we numerically study the nonperturbative phenomena of the SU(3) gauge theory in a weak coupling regime. We find that topological objects with a fractional charge emerge if the theory is regularized by an infrared (IR) cutoff via the twisted boundary conditions. Some configurations with nonzero instanton number...
We here focus on CP^{N-1} models on R x S^1 with the Z_N twisted boundary conditions, whose importance has recently been increasing in terms of resurgence theory, volume independence and its relation to 4D gauge theory. We have performed lattice simulations for the models with N=3-20 on several lattice sizes (e.g. 40 x 8, 200 x 8, 400 x 12), with emphasis on Polyakov loop, Casimir energy and...
Dipolar molecular platforms provide a possibility of realizing analog quantum simulators for quantum field theories such as quantum link models, a discrete version of lattice field theories in terms of the degrees of freedom for each link variable. We apply the method of effective Hamiltonians to a system of dipolar molecules with electric dipole-dipole interactions with tunable parameters to...
Lattice gauge theory calculations exponentially hard on today's machines could become a reality with the advent of quantum computation. To get there, the choice of variables optimal for exploiting the quantum advantage will likely be quite different than what we are accustomed to. We give a construction of a non-Abelian gauge theory with quark matter using a loop-string formulation that has...
It is well known that the action for General Relativity (GR) can be rewritten in terms of a tetrad field $e_\mu$ and a spin connection $\omega_\mu$ where the former
is loosely a square root of the metric and the latter is a gauge field
needed to ensure local Lorentz invariance. It is less well known that these
two can be combined into a single gauge field associated with local (anti)de...
We construct a qubit formulation of the lattice $O(N)$ non-linear sigma model in $d+1$ dimensions. For the $O(3)$ model, our construction uses two qubits per lattice site. We show that this Hamiltonian in two spatial dimensions has a quantum critical point where the well known scale invariant physics of the Wilson-Fisher fixed point is reproduced. Free massive bosons arise in three spatial...
We formulate the many-body system of non-relativistic fermions (Hubbard model) in the canonical formulation using transfer matrices in fixed fermion number sectors. By analytically integrating out the auxiliary Hubbard-Stratanovich field due to the four-fermion interaction, we express the system in terms of discrete, local fermion occupation numbers which are the only remaining degrees of...
In recent years several lattice field theories were exactly rewritten in terms of so-called dual variables which are worldlines for matter fields and worldsheets for the gauge degrees of freedom. I discuss recent developments within this approach with a focus on topological terms and non-abelian symmetry groups.
Abelian lattice gauge theories can be reformulated exactly in terms of dual variables which are discretized worldsheets. An interesting question is how the topological terms can be incorporated in such a dual theory. We analyze the general structure of such terms and discuss some examples.
Cardy (1985) pointed out that radial quantization may provide a useful numerical approach to study CFTs compared to traditional finite size scaling techniques. The problem that the cylindrical manifold $R \times S^{d-1}$ is curved for $d > 2$ has been ameliorated -- and perhaps solved -- for renormalizable QFTs by the development of the quantum finite element (QFE) method in recent years. ...
A long ago, Callan and Harvey showed a view of gauge anomaly as
a missing current into an extra-dimension, and the total contribution,
including the Chern-Simons current in the bulk, is conserved.
But in their computation, the edge and bulk contributions are separately
evaluated and their cross correlations, which should be relevant
at boundary, are simply ignored. In this talk, we revisit...
Rough gauge fields are an obstacle in large-scale dynamical fermion simulations with Wilson quarks when the pion mass is lowered and the gap of the lattice Dirac operator shrinks. In this talk, a reformulation of the O(a) improved Wilson-Dirac operator is given which is largely protected from numerical instabilities during the molecular dynamics evolution. First results are very promising as...
The Atiyah-Patodi-Singer index theorem describes the bulk-edge correspondence of symmetry protected topological insulators. In 2017, we showed that the same integer as the APS index can be obtained from the eta-invariant of the domain-wall Dirac operator. In this work, we invite three mathematicians to our group and prove that this correspondence is not a coincidence but generally true.
Atiyah-Singer index theorem on a lattice without boundary is well understood owing to the seminal work by Hasenfratz.
But its extension to the system with boundary ( the so-called Atiyah-Patodi-Singer index theorem), which surprisingly plays a crucial role in T-anomaly cancellation between bulk- and edge-modes in 3+1 dimensional topological matters, is known only in the continuum theory and...
The Elitzur theorem does not rule out the breaking of a global subgroup of a gauge group in some gauge, either spontaneously or dynamically. But it is known that such breaking occurs at different couplings in different gauges, and is not necessarily associated with a thermodynamic transition. In this talk I will outline a gauge invariant distinction between the unbroken and Higgs regions of a...
Topological insulators in odd dimensions are characterized by topological numbers. We prove the well-known relation between the topological number given by the Chern character of the Berry curvature and the Chern-Simons level of the low energy effective action for a general class of Hamiltonians bilinear in the fermion with general U(1) gauge interactions including non-minimal couplings by an...
We will present recent results of the application of spectral analysis
in the setting of the Monte Carlo approach to Quantum Gravity known as
Causal Dynamical Triangulations (CDT), discussing the behaviour of the
lowest lying eigenvalues of the Laplace-Beltrami operator computed on
spatial slices. We will show that such a kind of analysis can provide
information about running scales of the...
We present results for meson masses in the continuum limit
for pure Yang-Mills theory in the large N limit. The results are
obtained with both Wilson fermions and twisted mass. Some preliminary
results for meson masses in large N gauge theories with dynamical
fermions are also given.
It is believed that the two-dimensional massless $\mathcal{N}=2$ Wess--Zumino model becomes the $\mathcal{N}=2$ superconformal field theory (SCFT) in the IR limit. We examine this theoretical conjecture of the Landau--Ginzburg (LG) description of the $\mathcal{N}=2$ SCFT by numerical simulations on the basis of a supersymmetric-invariant momentum-cutoff regularization. We study one or two...
Computing the entanglement entropy in lattice gauge theories is often accompanied by ambiguities. In this talk I argue that compactifying the theory on a small circle $\mathbb S^1$ evades these difficulties. In particular, I study Yang-Mills theory on $\mathbb R^3\times \mathbb S^1$ with double-trace deformations or adjoint fermions and hold it at temperatures near the deconfinement...
