Mr
Giuseppe Gagliardi
(Bielefeld University)

7/25/18, 2:00 PM

Theoretical Developments

Lattice QCD in a color singlet representation has been studied since decades in the limit $\beta\to 0$. In this limiting case it is possible to integrate out analytically the partition function at finite density which is then written in terms of dual, integer, degrees of freedom representing mesons and baryons. The partition function can be then sampled by means of Worm algorithms. It turned...

Dr
Sreeraj T P
(The Institute of Mathematical Sciences, Chennai, India)

7/25/18, 2:20 PM

Theoretical Developments

Dual description of SU(2) lattice gauge theory in 2+1 dimensions is shown to be the theory of interacting gauge invariant ‘abelian like’ electric loops. The Gauss law is solved exactly to construct the Hilbert space of the gauge invariant theory using the Schwinger boson representation. This is achieved by envisaging what is called the ‘splitting of a point'. Such a 'point split' lattice...

Mr
Daniel Goeschl
(University of Graz)

7/25/18, 2:40 PM

Theoretical Developments

We investigate the phase structure of the 2-d U(1) gauge-Higgs model at non-vanishing topological angle $\theta$. The sign problem arising from the topological term is avoided by invoking a dual representation of the gauge-Higgs model. This allows us to observe a 1st order transition in the topological charge at the symmetrical point $\theta=\pi$. By using the Villain action to discretize the...

Jesse Stryker
(University of Washington)

7/25/18, 3:00 PM

Theoretical Developments

Quantum computers have the potential to solve certain problems in lattice gauge theory that are thought to be exponentially hard for classical computers. The proposed starting point for such computations has been the Kogut-Susskind Hamiltonian supplemented by the Gauss law constraint, with a cutoff on electric field values. There are several disadvantages to this approach, including having to...

Judah Unmuth-Yockey
(Syracuse University)

7/25/18, 3:20 PM

Theoretical Developments

Starting with the 2D Abelian Higgs model with the quartic self-coupling taken infinitely large we study the finite-size scaling of the Polyakov loop. We find an exponential decay for large temporal extents which is dictated by the energy gap between the ground states of a system with the Polyakov loop inserted, and one without. We study this system using the tensor renormalization group, and...

Prof.
C.-J. David Lin
(National Chiao-Tung University)

7/26/18, 8:30 AM

Theoretical Developments

We present results from our study of the 1+1 dimensional Thirring model employing the techniques of Matrix Product States. As the first step of a research programme for examining this model with the Hamiltonian formalism on the lattice, we determine the phase structure of the theory. In particular, we confirm the existence of the critical phase in the Thirring model in two dimensions. This...

Dr
Stefan Kuehn
(Perimeter Institute for Theoretical Physics)

7/26/18, 8:50 AM

Theoretical Developments

Gaussian states, meaning states whose density matrix can be expressed as a Gaussian function in the creation and annihilation operators, are widely used in various areas to describe fermionic as well as bosonic systems. However, in cases where both bosons and fermions are present, they cannot describe any correlations between the two species beyond mean-field. This renders them at first glance...

Yannick Meurice
(U. of Iowa)

7/26/18, 9:10 AM

Theoretical Developments

In most lattice simulations, the variables of integration are compact and character expansion (for instance Fourier analysis for $U(1)$ models) can be used
to rewrite the partition function and average observables as discrete sums of contracted tensors. This reformulations have been used for RG blocking but they are also suitable for quantum computing. We discuss FAQ about tensorial...

Mr
Ryo Sakai
(Kanazawa University)

7/26/18, 9:30 AM

Theoretical Developments

The tensor renormalization group attracts great attention as a new numerical method because it is free of the sign problem. In addition to this striking feature, it has also an attractive aspect as a coarse-graining of space-time; that is to say, the computational cost scales logarithmically with the space-time volume. This fact allows us to aggressively approach the thermodynamic limit. While...

Yusuke Yoshimura
(CCS, University of Tsukuba)

7/26/18, 9:50 AM

Theoretical Developments

Tensor renormalization group is a new type of numerical method which does not suffer from the sign problem.
We have developed the tensor renormalization group for 3-dimensional $Z_2$ gauge theory.
We apply it to finite temperature $Z_2$ gauge thery in (2+1) dimensions and
compare the results with those obtained by a previous Monte Carlo study.

Roman Sverdlov
(University of New Mexico)

7/26/18, 10:10 AM

Theoretical Developments

Causal set theory, originally introduced by Rafael Sorkin, is a model of spacetime as a partially ordered set: an element of a set corresponds to a point in spacetime, while partial ordering corresponds to lightcone causal relation. There is no coordinate system: all of the geometry is to be deduced from partial ordering alone. Consequently, one has to rewrite Lagrangians in quantum field...

Dr
Alan Horowitz
(IUP)

7/26/18, 11:00 AM

Theoretical Developments

I will show that naive and staggered fermions on simplicial lattices and their dual lattices in any dimension can be formulated about as simply as on hypercubic lattices. Point, chiral and discrete symmetry properties are however more subtle. Despite the absence of an exact chiral symmetry, there is no additive mass renormalization. There is an interesting duality between vector and axial...

Prof.
Richard C. Brower
(Boston University)

7/26/18, 11:20 AM

Theoretical Developments

Conformal or near conformal QFTs would benefit from
a rigorous non-perturbative lattice formulation beyond the flat
Euclidean space, $\mathbb R^d.\;$ Although all UV complete QFT are
known to be also perturbatively renormalizable on any smooth Riemann
manifold, non-perturbative realization on simplicial lattices (triangulations) encounter difficulties as the UV cut-off...

Dr
Matthias Puhr
(University of Regensburg)

7/26/18, 11:40 AM

Theoretical Developments

In general, perturbative expansions of observables in quantum field
theories are divergent (asymptotic) series. It is often possible to
apply resummation techniques to assign a unique finite value to the
asymptotic series, but a particular pattern of divergence, the
so-called renormalon, gives rise to non-perturbative ambiguities. The
framework of numerical stochastic perturbation theory...

Prof.
Francesco Di Renzo
(University of Parma and INFN)

7/26/18, 12:00 PM

Theoretical Developments

Numerical Stochastic Perturbation Theory (NSPT) enables very high order computations in Lattice Gauge Theories. We report on the determination of the gluon condensate from lattice QCD measurements of the basic plaquette. This is a long standing problem, which was eventually solved a few years ago in pure gauge. In this context NSPT is crucial: it is actually the only tool enabling the...

Prof.
Joel Giedt
(Rensselaer Polytechnic Institute)

7/26/18, 12:20 PM

Theoretical Developments

We explain our recent formulation of this theory on the lattice, and also discuss other formulations. Issues related to tuning and decoupling of auxiliary sectors are examined. The continuum limit is explored.

Jacek Wosiek
(Jagiellonian University)

7/27/18, 2:00 PM

Theoretical Developments

Finding positive representations of complex weights still attracts a fair amount of interest. Extension of probabilistic Langevin dynamics into a complex domain works in some cases and fails in the others. For that reason some attempts were made to directly construct pairs of corresponding distributions, without invoking stochastic processes. One of such schemes, and its new theoretical and...

Mr
Blazej Ruba
(Jagiellonian University)

7/27/18, 2:20 PM

Theoretical Developments

Many research programs aiming to deal with the sign problem were proposed since the advent of lattice field theory. Several of these try to achieve this by exploiting properties of analytic functions. This is also the case for one of the approaches we're developing. There auxillary complex variables are introduced and desired weight is obtained after integrating them out. In this talk I will...

Prof.
Wayne Polyzou
(University of Iowa)

7/27/18, 2:40 PM

Theoretical Developments

Scattering theory can be formulated given a representation of the
quantum mechanical Hilbert space and a set of self-adjoint Poincar\'e
generators satisfying cluster properties. These are both provided by
the Osterwalder-Schrader reconstruction theorem, where the input is a
collection of Euclidean-covariant reflection-positive distributions.
In this representation both Hilbert space...

Carlotta Marchis
(University of Graz)

7/27/18, 3:00 PM

Theoretical Developments

We explore new representations for lattice gauge theories with fermions, where the space time lattice is divided into dynamically fluctuating regions, inside which different types of degres of freedom are used in the path integral. The first kind of regions is a union of so-called bags, in which the dynamics is described by the free propagation of composite degrees of freedom of the original...

Ms
Casey Berger
(University of North Carolina at Chapel Hill)

7/27/18, 3:20 PM

Theoretical Developments

Quantum field theories with a complex action suffer from a sign problem in stochastic non-perturbative treatments, making many systems of great interest - such as polarized or mass-imbalanced fermions and QCD at finite baryon density - extremely challenging to treat numerically. Another such system is that of bosons at finite angular momentum; experimentalists have successfully achieved vortex...

Mr
Samuel Foreman
(University of Iowa)

7/27/18, 3:40 PM

Theoretical Developments

We illustrate how principal component analysis of simulation data represented as images generated from the worm algorithm, a method to sample the strong coupling contributions, can be used to identify the critical temperature Tc in the Ising model. It is shown that the eigenvalue corresponding to the first principal component of the covariance matrix obtained from pixel ensembles scales...

Mr
Eduardo Ibanez Bribian
(Instituto de Fisica Teorica UAM-CSIC)

7/27/18, 4:30 PM

Theoretical Developments

We report on our computation of the perturbative running of the 't Hooft coupling in a pure gauge SU(N) theory with twisted boundary conditions. The computation was performed using gradient flow methods in four dimensions, in the continuum, and using dimensional regularisation. The coupling is defined in terms of the energy density of the flow fields at a scale given by a particular...

Prof.
Anna Hasenfratz
(university of colorado boulder)

7/27/18, 4:50 PM

Theoretical Developments

We discuss a continuous real space renormalization group transformation based on gradient flow, allowing for a numerical study of renormalization without the need for costly ensemble matching. Applying the technique in a pilot study of SU$(3)$ gauge theory with $N_f = 12$ fermions in the fundamental representation, we find the mass anomalous dimension to be $\gamma_m = 0.23(6)$, consistent...

Andrea Carosso
(University of Colorado, Boulder)

7/27/18, 5:10 PM

Theoretical Developments

Gradient flow has proved useful in the definition and measurement of renormalized quantities on the lattice. Recently, the fact that it suppresses high-modes of the field has been used to construct new, continuous RG transformations on the lattice, distinct from the usual blocking techniques in spin models and gauge theories. In this talk, we discuss two approaches to define an RG...

Mr
Rudrajit Banerjee
(Department of Physics and Astronomy, University of Pittsburgh)

7/27/18, 5:30 PM

Theoretical Developments

A lattice version of the widely used
Functional Renormalization Group (FRG)
for the Legendre effective action is
solved (exactly) in terms of a linked
cluster expansion. The graph rules
invoke only one-line irreducible and
a new type of labeled tree graphs.
Conversely, the FRG induces nonlinear
flow equations governing suitable
resummations of the graph expansion....

Dr
Daisuke Kadoh
(Keio University)

7/27/18, 5:50 PM

Theoretical Developments

In this talk, we show that the gradient flow equation is defined in ${\small\cal N} = 1$ SYM in a way that is consistent with supersymmetry in the Wess-Zumino gauge. Using the perturbation theory, we find that two-point function of flowed gauge multiplet is UV-finite at the one-loop level when four dimensional SYM is renormalized.

Prof.
Gennady Kozlov
(JINR)

7/27/18, 6:10 PM

Theoretical Developments

Parallel

The critical phenomena of strongly interacting matter are studied in the random fluctuation walk model at finite temperature. The phase transitions are considered in systems where the Critical Point (CP) is a distinct singular one existence of which is dictated by the dynamics of conformal symmetry breaking.
The physical approach to the effective CP is predicted through the influence...