Lattice Gauge Theory group

GPU Research Center We are the lattice gauge theory group at the Eotvos University in Budapest, part of the Department of Theoretical Physics at the Faculty of Science.

Currently there are nine members and we are seeking new ones. Positions are available for PhD students and postdocs for 2 - 4 years appointments. If you are interested please email Sandor Katz at or Daniel Nogradi at

Our activities are and were funded by various funding agencies for which we are grateful, these include the Lendulet grant of the Hungarian Academy of Sciences, the OTKA-NF-104034 grant of OTKA and the EU Framework Programme 7 grant (FP7/2007-2013)/ERC No 208740.


Our primary interests are:

  • Chiral symmetry restoration and deconfinement in QCD with Wilson fermions
  • Finite chemical potential
  • QCD hadron spectrum
  • Eigenvalue distributions of the overlap Dirac operator
  • Strongly interacting Higgs sector - strong dynamics
  • Conformal gauge theories


Weekly ELFT seminars at the Department of Theoretical Physics

Location: 2nd floor, 2.54, Novobatzky room, 1117 Budapest, Pazmany Peter setany 1/a

If you'd like to receive seminar email announcements please write to

Time: Tuesdays at 14:15

See the archive for seminars since 2014.

  • 13 September 2022, Gergely Barnafoldi (Wigner) slides

    Estimating elliptic flow coefficient in heavy ion collisions using deep learning

    Machine learning techniques have been employed for the high energy physics community since the early 80s to deal with a broad spectrum of problems. This work explores the prospects of using deep learning techniques to estimate elliptic flow (v2) in heavy-ion collisions at the RHIC and LHC energies. A novel method is developed to process the input observables from particle kinematic information. The proposed deep neural network (DNN) model is trained with Pb-Pb collisions at sNN=5.02 TeV minimum bias events simulated with a multiphase transport model. The predictions from the machine learning technique are compared to both simulation and experiment. The deep learning model seems to preserve the centrality and energy dependence of v2 for the LHC and RHIC energies. The DNN model is also quite successful in predicting the pT dependence of v2. When subjected to event simulation with additional noise, the proposed DNN model still keeps the robustness and prediction accuracy intact up to a reasonable extent.

    N. Mallick et al: Phys.Rev. D105 (2022) 11, 114022

  • 20 September 2022, Gabor Etesi (BME) slides

    The universal von Neumann algebra of smooth four-manifolds

    Making use of its smooth structure only, out of a connected oriented smooth 4-manifold a von Neumann algebra is constructed. As a special four dimensional phenomenon this von Neumann algebra contains algebraic (i.e., formal or coming from a metric) curvature tensors of the underlying 4-manifold and the von Neumann algebra itself is a hyperfinite factor of type II_1 hence is unique up to abstract isomorphisms of von Neumann algebras. Over a fixed 4-manifold this universal von Neumann algebra admits a particular representation on a Hilbert space such that its unitary equivalence class is preserved by orientation-preserving diffeomorphisms consequently the Murray--von Neumann coupling constant of this representation is well-defined and gives rise to a new and computable real-valued smooth 4-manifold invariant. Its link with Jones' subfactor theory is noticed as well as computations in the simply connected closed case are carried out.

    Application to the cosmological constant problem is also discussed. Namely, the aforementioned mathematical construction allows to reformulate the classical vacuum Einstein equation with cosmological constant over a 4-manifold as an operator equation over its tracial universal von Neumann algebra such that the trace of a solution is naturally identified with the cosmological constant. This framework permits to use the observed magnitude of the cosmological constant to estimate by topological means the number of primordial black holes about the Planck era. This number turns out to be negligable which is in agreement with known density estimates based on the Press--Schechter mechanism.

    Based on this preprint.

  • 27 September 2022, Timea Vitos (Lund University) slides

    Improving on accuracy and efficiency of Standard Model theory predictions

    In the process of improving experimental accuracy at the LHC and other colliders, it is essential that theory predictions keep up this pace. Specifically, in the search of theories beyond the Standard Model, it is crucial to have a very precise handle on what this successful model actually predicts. This task consists of using the existing tools for various key observables, and also to improve on the scope and efficiency of the tools. In this talk, three important LHC processes and corresponding spin-related observables at NLO electroweak precision are presented: Z+jet, W+jet (also including NNLO QCD) and top-antitop pair production. In addition, the first steps towards a more efficient approach to handle high-multiplicity jet processes is presented, via the next-to-leading colour approximation of the colour matrix.

  • 4 October 2022, Zoltan Peli (ELTE) slides

    Vacuum stability and scalar masses in the superweak extension of the standard model

    We study the allowed parameter space of the scalar sector in the superweak extension of the standard model (SM). The allowed region is defined by the conditions of (i) stability of the vacuum and (ii) perturbativity up to the Planck scale, (iii) the pole mass of the Higgs boson falls into its experimentally measured range. The method can be generalized in a straightforward way to simpe beyond the standard model scenarios such as the singlet scalar extension. We confront our findings against the measured mass of the W boson and the measured width of the Higgs boson. Preliminary results for collider search constraints are also shown.

  • 11 October 2022, Rachel Houtz (Durham IPPP) slides

    Hamiltonian Truncation Effective Theory

    Hamiltonian truncation is a non-perturbative numerical method for calculating observables of a quantum field theory. In this talk, I will show how to treat Hamiltonian truncation systematically using effective field theory methodology. The starting point for this method is to truncate the interacting Hamiltonian to a finite-dimensional space of states below some energy cutoff Emax. The effective Hamiltonian can be computed by matching a transition amplitude to the full theory, and gives corrections order by order as an expansion in powers of 1/Emax. This method is demonstrated using 2D lambda phi^4 theory, and gives 1/Emax^2 corrections to the effective Hamiltonian. Numerical diagonalization of the effective Hamiltonian then shows residual errors of order 1/Emax^3, as expected by our power counting.

  • 18 October 2022, Miklos Vincze (ELTE) slides

    Modeling atmospheric and ocean dynamics in the lab

    Based on the principle of hydrodynamic similarity many fundamental aspects of Earth's climate system can be modeled using laboratory-scale experimental set-ups. Under laboratory conditions it is possible to control the governing physical parameters and thus to separate different processes that cannot be studied independently in such complex systems as the real atmosphere or oceans. In our research at the von Karman Laboratory for Environmental Fluids of our institute and similar research facilities around the world we have investigated climate dynamics-motivated problems focusing on the transitions between different states of "minimal models" of the mid-latitude atmospheric and ocean circulation, shedding light on the processes that had yielded the formation of permanent ice cover on Antarctica 34 million years ago, the distribution of extreme temperature fluctuations in a changing climate, and various forms of atmospheric fluid dynamic instabilities.

  • 25 October 2022, Andras Laszlo (Wigner) slides

    On generally covariant mathematical formulation of Feynman integral in Lorentz signature

    Feynman integral is one of the most promising methodologies for defining a generally covariant formulation of nonperturbative interacting quantum field theories (QFTs) without a fixed prearranged causal background. Recent literature indicates that in such scenario, one needs to consider the problematics in the original Lorentz signature. Lorentz signature Feynman integrals are known, however, to be mathematically ill-defined. The Feynman integral formulation has, however, a differential reformulation: the master Dyson-Schwinger (MDS) equation for field correlators. In this talk we show that with the right choice of variables, the MDS equation is mathematically well defined: the involved function spaces and operators can be defined and their properties can be established. Therefore, MDS equation can serve as a substitute for the Feynman integral, in a mathematically sound formulation of constructive QFT, in arbitrary signature, without a fixed background causal structure. It is also shown that the Wilsonian regularization of the MDS equation can be canonically defined. Our main result is a necessary and sufficient condition for the regularized MDS solution space to be nonempty, which also provides a convergent iterative approximation for the solution. The talk is based on the paper: Class.Quant.Grav.39(2022)185004.

  • 15 November 2022, Gergely Fejos (ELTE) slides

    Thermal fate of the U_A(1) anomaly from the functional renormalization group

    I will review some recent results regarding the finite temperature behavior of the axial anomaly. Using the functional renormalization group technique, I will show how to effectively resum an infinite class of anomaly breaking operators in the framework of the three flavor meson model. The resulting condensate dependent anomaly coupling shows that mesonic fluctuations actually strengthen the U_A(1) breaking toward the pseudocritical temperature, which are to be compared with the effects of the instantons. Numerics suggest that there is an intermediate region below T_c, where the former can become the dominant factor. If time permits I will also challenge some old results concerning the order of the chiral transition for massless quarks, which, surprisingly, may also be strongly related to the thermal fate of the axial symmetry.

    Based on G. Fejos and A. Patkos, Phys. Rev. D105, 096007 (2022) and G. Fejos, Phys. Rev. D105, L071506 (2022)

  • 29 November 2022, Dimitrios Bachtis (Paris, Ecole normale superieure) slides

    Machine learning and the inverse renormalization group

    Standard renormalization group methods iteratively eliminate degrees of freedom within a system and are therefore applicable for a limited number of steps before the degrees of freedom vanish. In this talk I will present the construction of inverse renormalization group transformations with the use of machine learning. Inverse renormalization group transformations enable the generation of configurations for increasing lattice size in absence of the critical slowing down effect and can, in principle, be applied for an arbitrary number of steps. I will additionally discuss the interpretation of machine learning functions as physical observables to introduce a Hamiltonian-agnostic reweighting approach, and the inclusion of neural networks within Hamiltonians to break or restore the symmetry of a system without any knowledge of the system's order parameter. Applications will be presented based on the phi^4 theory and the Ising model, with an emphasis on the calculation of multiple critical exponents and the critical fixed point.

For students

Our group offers BSc/MSc diploma, PhD and TDK topics in Lattice Field Theory.

Please contact Sandor: or Daniel: in case you are interested.

Current topics include:

  • QCD thermodynamics
  • 2 and 4 dimensional CFT
  • Beyond Standard Model


Matteo Giordano

assistant professor

2009 PhD - University of Pisa, Italy

2010-2010 postdoc - IPhT/CEA-Saclay, France

2010-2012 postdoc - University of Zaragoza, Spain

2012-2015 postdoc - ATOMKI, Debrecen, Hungary

2015-2018 postdoc - Eotvos University, Budapest, Hungary

Kornel Kapas

PhD student

2018- Eotvos University, Hungary









Sandor Katz


2001 PhD - Eotvos University, Hungary

2001-2003 postdoc - DESY, Hamburg, Germany

2003-2005 postdoc - University of Wuppertal, Germany

2006-2012 assistant professor - Eotvos University, Hungary

2012- professor - Eotvos University, Hungary

Tamas Kovacs


1996 PhD - UCLA, USA

1996-1998 postdoc - University of Colorado, Boulder, USA

1998-2000 postdoc - University of Leiden, the Netherlands

2000-2002 postdoc - DESY, Zeuthen, Germany

2002-2011 professor - University of Pecs, Hungary

2011- senior researcher - ATOMKI, Debrecen, Hungary

2020- professor, Eotvos University, Hungary

Daniel Nogradi


2005 PhD - University of Leiden, the Netherlands

2005-2007 postdoc - University of Wuppertal, Germany

2007-2009 postdoc - UCSD, USA

2009-2011 senior research fellow - Eotvos University, Budapest

2012 - 2020 assistant professor - Eotvos University, Budapest

2020- professor - Eotvos University, Budapest

Attila Pasztor


2015 PhD - Eotvos University, Hungary

2016-2018 postdoc - Wuppertal University, Germany

2018- postdoc - Eotvos University, Hungary






Lorinc Szikszai

PhD student

2016- Eotvos University, Hungary






Zoltan Tulipant


2020 PhD - University of Debrecen, Hungary

2020 - postdoc - Eotvos University, Hungary





Former members

Gergely Endrodi

2009 PhD - Eotvos University, Hungary

2010-2015 postdoc - University of Regensburg, Germany

2016- Emmy Noether group leader - University of Frankfurt, Germany

2020- professor - University of Bielefeld, Germany

Santanu Mondal

2013 PhD - University of Calcutta, India

2013-2016 postdoc - Eotvos University, Hungary

2016-2018 postdoc - National Chiao Tung University, Taiwan

2018- postdoc - Los Alamos National Laboratory, USA

Ferenc Pittler

2013 PhD - University of Pecs, Hungary

2013-2016 postdoc - Eotvos University, Budapest

2017- postdoc - Bonn University, Germany

Csaba Torok

2017 PhD - Eotvos University, Hungary

2017- postdoc - Wuppertal University, Germany


Balint Toth

2005-2006 research assistant - University of Wuppertal, Germany

2007 assistant lecturer - University of Pecs, Hungary

2010 PhD - Eotvos University, Hungary

2010- postdoc - University of Wuppertal, Germany



Norbert Trombitas

PhD student

2015 PhD - Eotvos University, Hungary



Zoltan Varga

PhD student

2018- Eotvos University, Hungary




Since it is tricky to locate all papers by a large number of people whose names are not unique on inspire, you can try various search queries:


Our group has access to a number of high performance computer installations in Europe and also maintains several PC and GPU clusters on site in Budapest.

For visitors

Our department is on the Buda side of the Danube very close to the Petofi Bridge, the address is Budapest 1117, Pazmany Peter setany 1/A:

The Department of Theoretical Physics is on the sixth floor opposite the Danube facing side of the building: