# The 35th International Symposium on Lattice Field Theory

18-24 June 2017
Palacio de Congresos
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# Theoretical Developments

## Place

Location: Palacio de Congresos
Date: from 21 Jun 09:00 to 23 Jun 19:10

## Conveners

• 21 Jun 09:00 - 11:00
• catterall, simon (syracuse university)
• 21 Jun 11:30 - 13:30
• Prof. Chandrasekharan, Shailesh (Duke University)
• 22 Jun 15:00 - 16:40
• Dr. Dalla Brida, Mattia (Universita' di Milano-Bicocca & INFN)
• 22 Jun 17:10 - 19:10
• Prof. Onogi, Tetsuya (Osaka University)
• 23 Jun 15:00 - 16:40
• Prof. Gattringer, Christof (University of Graz, Austria)
• 23 Jun 17:10 - 19:10
• Dr. CIchy, Krzysztof (Goethe University Frankfurt)

## Timetable | Contribution List

Displaying 34 contributions out of 34
Type: Parallel Session: Theoretical Developments
Track: Theoretical Developments
The gradient flow and its small flow-time expansion provide a very versatile method to represent renormalized composite operators in a regularization-independent manner. This technique has been utilized to construct typical Noether currents such as the energy-momentum tensor and the axial-vector current in lattice gauge theory. In this paper, we apply the same technique to the supercurrent in the ... More
Presented by Ms. Aya KASAI on 21/6/2017 at 10:00
Type: Parallel Session: Theoretical Developments
Track: Theoretical Developments
The Abelian Color Cycle (ACC) technique is a method to dualize non-abelian lattice field theories. The crucial step of this approach is to decompose the action into a sum over complex numbers by writing explicitly all the traces, matrix and vector multiplications. This allows for the factorization of the Boltzmann weight into local factors, that are then Taylor expanded. After the analytical inte ... More
Presented by Ms. Carlotta MARCHIS on 21/6/2017 at 11:50
Type: Parallel Session: Theoretical Developments
Track: Theoretical Developments
This is the second talk followed to the first one of general formulation proposing a new type of lattice field theory without lattice chiral fermion problem. It has been formulated by the momentum space by introducing a new continuum momentum on the lattice and has non-local nature in the coordinate space. The recovery of associativity of the non-local product led us to this new formulat ... More
Presented by Prof. Noboru KAWAMOTO on 21/6/2017 at 8:40
Type: Parallel Session: Theoretical Developments
Track: Theoretical Developments
We propose an unconventional formulation of lattice field theories which is quite general, although originally motivated by the quest of exact lattice supersymmetry. Two long standing problems have a solution in this context: 1) Each degree of freedom on the lattice corresponds to 2^d degrees of freedom in the continuum, but all these doublers have(in the case of fermions) the same chirality and ... More
Presented by Mr. Alessandro D'ADDA, Prof. Noboru KAWAMOTO on 21/6/2017 at 8:20
Type: Parallel Session: Theoretical Developments
Track: Theoretical Developments
We study a tensor network formulation of the two dimensional lattice $\mathcal{N}=1$ Wess$\unicode{x2013}$Zumino model with Wilson derivatives for fermions and bosons. The tensor renormalization group allows us to compute the partition function without the sign problem, and basic ideas to obtain a tensor network for both fermion and scalar boson systems were already given in previous works. While ... More
Presented by Mr. Ryo SAKAI on 23/6/2017 at 18:10
Type: Parallel Session: Theoretical Developments
Track: Theoretical Developments
Recently, the Atiyah-Patodi-Singer(APS) index theorem attracts attention for understanding physics on the surface of materials in topological phases. Although it is widely applied to physics, the mathematical setup in original APS index theorem is too abstract and general (allowing non-trivial metric and so on) and also the connection bewteen the APS boundary condition and the physical boundary co ... More
Presented by Prof. Tetsuya ONOGI on 23/6/2017 at 15:40
Type: Parallel Session: Theoretical Developments
Track: Theoretical Developments
The positivity of the Boltzmann weight, needed for its probabilistic interpretation and for the application of the Monte Carlo method is absent for theories with complex actions. We propose avoiding the latter problem substituting Monte Carlo simulations by computations with convergent 'non-perturbative' expansions. We discuss constructions of such expansions and first numerical results on the exa ... More
Presented by Dr. Vasily SAZONOV on 22/6/2017 at 18:10
Type: Parallel Session: Theoretical Developments
Track: Theoretical Developments
We have developed Grassmann higher order tensor renormalization group (GHOTRG) to analyze higher dimensional fermionic systems. We first apply it to three-dimensional free Wilson fermions as a benchmark to check its effectiveness. The results of the free energy and the fermion Green functions are presented in comparison with the exact values. We also briefly discuss to what extent the results are ... More
Presented by Mr. Yusuke YOSHIMURA on 21/6/2017 at 12:50
Type: Parallel Session: Theoretical Developments
Track: Theoretical Developments
Various approaches to construction of dual formulations of non abelian lattice gauge theories are reviewed. In the case of U(N) LGT we use a theory of the Weingarten functions to construct a dual formulation. In particular, the dual representations are constructed 1) for pure gauge models in all dimensions, 2) in the strong coupling limit for the models with arbitrary number of flavours and 3) for ... More
Presented by Dr. Oleg BORISENKO on 21/6/2017 at 13:10
Type: Parallel Session: Theoretical Developments
Track: Theoretical Developments
Flavor-twisted boundary conditions can be used for exponential reduction of finite volume artifacts in flavor-averaged observables in lattice QCD calculations with SU(Nf) light quark flavor symmetry. Finite volume artifact reduction arises from destructive interference effects in a manner closely related to the phase averaging which leads to large Nc volume independence. With a particular choice o ... More
Presented by Mr. Aleksey CHERMAN on 22/6/2017 at 15:00
Type: Parallel Session: Theoretical Developments
Track: Theoretical Developments
The three-particle quantization condition is derived, using the particle-dimer picture in the non-relativistic effective field theory. The procedure for the extraction of various observables in the three-particle sector (the particle-dimer scattering amplitudes, breakup amplitudes, etc.) from the finite-volume lattice spectrum is discussed in detail. As an illustration of the general formalism, th ... More
Presented by Dr. Akaki RUSETSKY on 22/6/2017 at 16:00
Type: Parallel Session: Theoretical Developments
Track: Theoretical Developments
We argue that it is possible to uniquely define function support that preserves elementary properties of the function domain. This leads, among other things, to rigorous and general definition of the localization property.
Presented by Prof. Ivan HORVATH on 22/6/2017 at 18:50
Type: Parallel Session: Theoretical Developments
Track: Theoretical Developments
Using the example of a two dimensional four-fermion lattice field theory, we show that Feynman diagrams can generate a mass gap in a theory with massless fermions that interact via a marginally relevant coupling. We show this by introducing an infrared cutoff that makes the perturbation series for the partition function convergent. One can then use a Monte Carlo approach to sample sufficiently h ... More
Presented by Prof. Shailesh CHANDRASEKHARAN on 23/6/2017 at 15:20
Type: Parallel Session: Theoretical Developments
Track: Theoretical Developments
We investigate the possibility of using numerical stochastic perturbation theory (NSPT) to probe high orders in the perturbative expansion of lattice gauge theories with massless Wilson fermions. Twisted boundary conditions are used to regularise the gauge zero-mode; the extension of these boundary conditions to include fermions in the fundamental representation requires to introduce a smell degre ... More
Presented by Mr. Gianluca FILACI on 22/6/2017 at 15:40
Type: Parallel Session: Theoretical Developments
Track: Theoretical Developments
Through the development of many-body methodology and algorithms, it has become possible to describe quantum systems composed of a large number of particles with great accuracy. Essential to all these methods is the application of auxiliary fields via the Hubbard-Stratonovich transformation. This transformation effectively reduces two-body interactions to interactions of one particle with the auxil ... More
Presented by Mr. Christopher KOERBER on 22/6/2017 at 16:20
Type: Parallel Session: Theoretical Developments
Track: Theoretical Developments
We derive a full Kramers-Wannier dualization of the SU(2) principal chiral model. In a first step the trace and color multiplications in the action are written explicitly, such that only commuting numbers ("Abelian Color Fluxes") remain. The individual Boltzmann factors are then expanded and the original degrees of freedom are integrated out explicitly. The expansion indices become the new variabl ... More
Presented by Prof. Christof GATTRINGER on 21/6/2017 at 12:10
Type: Parallel Session: Theoretical Developments
Track: Theoretical Developments
Through a careful study of smooth Wilson loop operators on the lattice, we are able to obtain very accurate confirmation of the $1/N^2$ scaling predicted by `t Hooft for the pure $\mathrm{SU}(N)$ gauge theory. We present our results for Wilson loops smoothed with the Yang-Mills gradient flow and matched through the scale $t_0$. This allows us to have renormalizable operators and test the $1/N^2$ ... More
Presented by Mr. Miguel Francisco GARCÍA VERA on 23/6/2017 at 15:00
Type: Parallel Session: Theoretical Developments
Track: Theoretical Developments
While the sign problem of the Dirac fermion is conditioned by the positivity of a determinant, that of the Majorana fermion is conditioned by the positivity of a Pfaffian. We introduce one sufficient condition for the positivity of a Pfaffian. Based on the positivity condition, we study an effective model of the Majorana edge states in condensed matter physics. We also present the application t ... More
Presented by Arata YAMAMOTO on 21/6/2017 at 9:00
Type: Parallel Session: Theoretical Developments
Track: Theoretical Developments
Many correlators in lattice QCD show an exponential degradation of the signal-to-noise ratio with distance. This problem can be addressed by performing *multilevel* Monte Carlo sampling. However, to date, multilevel techniques have been limited to bosonic theories. To overcome this limitation, we developed a factorization into independent spacetime domains of the Wilson fermions determinant con ... More
Presented by Dr. Marco CÈ on 22/6/2017 at 15:20
Type: Parallel Session: Theoretical Developments
Track: Theoretical Developments
In principle the loop equation provides a complete formulation of a gauge theory purely in terms of Wilson loops. In the case of lattice gauge theories the loop equation is a well defined equation for a discrete set of quantities and can be easily solved at strong coupling either numerically or by series expansion. At weak coupling, however, we argue that the equations are not well defined unless ... More
Presented by Prof. Martin KRUCZENSKI on 21/6/2017 at 9:40
Type: Parallel Session: Theoretical Developments
Track: Theoretical Developments
We analyze the CP(1) model using the Loop optimization for Tensor network renormalization (Loop-TNR). This method makes it possible to completely remove short-range entanglement at each coarse-graining step which can not be removed by the Tensor renormalization group. We compare the results of these methods in the presence of the theta term.
Presented by Mr. Hikaru KAWAUCHI on 23/6/2017 at 17:30
Type: Parallel Session: Theoretical Developments
Track: Theoretical Developments
The problem of finding a positive distribution, which corresponds to a given complex density in complex Langevin approach, is studied. By the requirement that the moments of the positive distribution and of the complex density are equal, one can reduce the problem to solving the matching conditions. After imposing the positivity of the distribution, these conditions become a set of quadratic equat ... More
Presented by Mr. Adam WYRZYKOWSKI on 22/6/2017 at 18:30
Type: Parallel Session: Theoretical Developments
Track: Theoretical Developments
The QCD at finite density is not well understood yet, where standard Monte-Carlo simulation suffers from sign problem. In order to overcome the sign problem, the method of Lefschetz thimble has been explored. Basically, the original sign problem can be less severe in a complexified theory due to the constancy of the imaginary part of an action on each thimble. However, so-called global sign proble ... More
Presented by Shoichiro TSUTSUI on 22/6/2017 at 17:30
Type: Parallel Session: Theoretical Developments
Track: Theoretical Developments
We study the one-loop effective action defined by the chiral overlap operator in the 4-dimensional lattice formulation of chiral gauge theories by Grabowska and Kaplan. In the tree-level continuum limit, the left-handed component of the fermion is coupled only to the original gauge field~$A$, while the right-handed one is coupled only to~$A_\star$, which is given by the gradient flow of~$A$ with i ... More
Presented by Mr. Okuto MORIKAWA on 23/6/2017 at 16:00
Type: Parallel Session: Theoretical Developments
Track: Theoretical Developments
Classical real-time lattice simulations play an important role in understanding non-equilibrium phenomena in gauge theories and are used in particular to model the prethermal evolution of heavy- ion collisions. Above the Debye scale the classical Yang-Mills (CYM) theory can be matched smoothly to kinetic theory. First we study the limits of the quasiparticle picture of the CYM fields by determini ... More
Presented by Mr. Jarkko PEURON on 23/6/2017 at 17:10
Type: Parallel Session: Theoretical Developments
Track: Theoretical Developments
A positive representation for a sample of complex densities is constructed. In particular, complex measures on a direct product of $U(1)$ groups are studied. After identifying general conditions which such representations should satisfy, several concrete realisations are proposed. Their performance is illustrated in few concrete examples representing problems in abelian lattice gauge th ... More
Presented by Jacek WOSIEK on 22/6/2017 at 17:10
Type: Parallel Session: Theoretical Developments
Track: Theoretical Developments
It is an old idea to replace averages of observables with respect to complex weight by an average of its analytic continuation to complexified space with respect to some probabilistic measure. This is precisely what one would like to get from complex Langevin simulations. Unfortunately, these fail in many cases of physical interest. In my talk I will describe method of deriving positive representa ... More
Presented by Mr. Błażej RUBA on 22/6/2017 at 17:50
Type: Parallel Session: Theoretical Developments
Track: Theoretical Developments
Machine learning has been a fast growing field of research in several areas dealing with large datasets. We report recent progress on using RG ideas in the context of machine learning. We discuss the correspondence between principal components analysis (PCA) and RG flows across the transition for worm configurations of the 2D Ising model. More generally, we discuss the relationship between ... More
Presented by Prof. Yannick MEURICE on 23/6/2017 at 18:30
Type: Parallel Session: Theoretical Developments
Track: Theoretical Developments
Quantum Finite Element (QFE) seeks to generalize lattice field theory to any smooth Euclidean Riemann manifold by adapting the Finite Elements Method (FEM) in the classical limit and the geometrical characterization of Regge Calculus, supplemented by counter terms required to cancel the local scheme due to ultraviolet divergences at simplicial cut-off. High precision numerical test are presented ... More
Presented by Prof. Richard BROWER on 21/6/2017 at 12:30
Type: Parallel Session: Theoretical Developments
Track: Theoretical Developments
Tensor Network methods have been established over the last decade as a powerful technique for the simulation of strongly-correlated systems in low dimensions. Employing the formalism of Matrix Product States, we investigate the phase diagram of the massive Thirring model. Several distinct sectors of the total fermion number are observed. We discuss the interpretation of these sectors in the dual s ... More
Presented by Mr. David Tao-Lin TAN on 23/6/2017 at 17:50
Type: Parallel Session: Theoretical Developments
Track: Theoretical Developments
I discuss a method to define a theta-angle in 1+1D gauge theories with matter in a way which allows for a dual description without the sign problem. The method begins with non-compact gauge theory with a continuous R-valued center symmetry. By gauging the center symmetry down to U(1), a natural theta-term can be introduced through the gauge field for the center symmetry. The theory in this formula ... More
Presented by Dr. Tin SULEJMANPASIC on 23/6/2017 at 16:50
Type: Parallel Session: Theoretical Developments
Track: Theoretical Developments
We study the impact of the Gradient Flow on the topology in various models. The topological susceptibility is measured directly, and by the "slab method", which is based on the topological content of sub-volumes ("slabs"). The results obtained by both methods are consistent, but the impact of the Gradient Flow on the characteristic quantity of the slab method is different in 2-flavor Q ... More
Presented by Mr. Hector MEJIA-DIAZ on 23/6/2017 at 16:20
Type: Parallel Session: Theoretical Developments
Track: Theoretical Developments
We describe our studies of truncation of the twisted formulation of four-dimensional lattice N=4 super Yang-Mills from U(N) gauge theory to SU(N) gauge theory. One approach involves imposing the constraint that the complexified bosonic link matrices are elements of the group SL(N,C). We describe how this is consistent with SU(N) lattice gauge invariance. The second approach achieves this objective ... More
Presented by Prof. Joel GIEDT on 21/6/2017 at 9:20
Type: Parallel Session: Theoretical Developments
Track: Theoretical Developments
A continuum Lagrangian can be rewritten as an equivalent lattice action of discretely labelled variables. When the discrete variables come from wavelets, new possible criteria for acceptable actions open up.
Presented by Prof. Herbert NEUBERGER on 21/6/2017 at 11:30
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