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.

Timetable of department common room.


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.

  • 20 February 2024, Gyorgy Baranka (Eotvos) slides

    Localization of Dirac modes in the SU(2)-Higgs model at finite temperature

    The low-lying Dirac modes become localized at the finite-temperature transition in QCD and in other gauge theories, suggesting a general connection between their localization and deconfinement. This connection can be understood in terms of the "sea/islands'' picture of localization: in the deconfined phase, modes get "trapped" on "islands'' of Polyakov-loop fluctuations, and other gauge field fluctuations that decrease correlations in the temporal direction, within the "sea'' of ordered Polyakov loops.

    As a test of the universality of the "sea/islands" mechanism, one can investigate whether a change in the localization properties of low modes takes place across other thermal transitions where the Polyakov loop gets ordered, besides the usual deconfinement transition. Additionally, one can investigate this phenomenon by changing the type of dynamical matter from fermionic to scalar. A model allowing one to carry out both these tests at once is the lattice fixed-length SU(2)-Higgs model. After mapping out the phase diagram of the model at finite temperature, we study the localization properties of the low-lying modes of the staggered Dirac operator, and how these properties change across the various transitions. We find localized low modes in the deconfined and in the Higgs phase, where the Polyakov loop is strongly ordered, but in both cases they disappear as one crosses over to the confined phase. Our findings confirm the general expectations of the "sea/islands" picture.

  • 5 March 2024, Timea Vitos (Uppsala) slides

    Precision Standard Model tools: electroweak Sudakovs and multi-jet processes

    It is evident that the present state of particle physics requires some additional extension to the current Standard Model in order to capture phenomena which are not covered by this theory. For this task, two very important ingredients are needed, on both the theory and experiment side: on the one hand, developing new models and on the other hand, discriminating in a precise way from the Standard Model background. In this phenomenology-based seminar, I will target the latter aspect in two topics. Firstly, I will present the combination of the leading Sudakov effects in the one-loop electroweak corrections and QCD parton showers, implemented in the widely-used matrix-element generator MadGraph5_aMC@NLO. Secondly, I will discuss a project which aims to improve the simulation of multi-jet events (more than 5-6 QCD jets in the final state) in particle collisions. These processes are present in almost any new physics searches at hadron colliders and hence their efficient simulation is crucial for the possible detection of any signals beyond our current established model.

  • 12 March 2024, Ramon Miravitllas Mas (Wigner) slides

    Trans-series from condensates

    Perturbation theory fails to describe the low-energy phenomenology of QCD, like confinement, the mass gap, and the masses of hadrons. Invoking the Wilson's operator expansion, one can extend perturbative expansions to trans-series, which contain some non-perturbative information encoded in the vacuum condensates. Motivated by this, we will discuss the Gross--Neveu model, a toy QFT of N fermions in 1+1 dimensions which shares some of the non-perturbative properties of QCD. This toy model is amenable to some exact results when the number of fermions N is large. In particular, the two-point function of the fermions can be computed exactly at the first non-trivial order in 1/N. We then compare this result with a direct computation of the first coefficients of the Wilson's operator expansion, also at large N, and find a perfect match. This provides a precise test for the validity of the operator expansion and the methods used to compute its coefficients.

  • 19 March 2024, Maria Vittoria Garzelli (DESY) slides

    Prompt neutrinos in the atmosphere vs. LHC: where do we stand?

    We describe the main mechanisms of production of prompt neutrinos in the atmosphere, where they are a background for the detection of astronomical neutrinos from far sources, and at the Large Hadron Collider. These involve the production and decay of heavy-flavoured hadrons in hadronic collisions. We show the differences in the kinematics relevant for the two cases, also depending on the detail of the experiments capable of detecting these neutrinos. We stress the importance of reducing the present large uncertainties, coming from different sources, ranging from the still too low accuracy of calculation of the partonic cross-sections for charm production, to the quite uncertain charm pole mass value and parton distribution functions of protons and nuclei, to the still quite debated ultra-high-energy cosmic-ray mass composition.

  • 26 March 2024, Claudio Bonati (INFN Pisa) -- cancelled

    Some peculiar transitions in Abelian gauge systems

    In this talk we will introduce some problematics related to the so called "beyond the Landau-Ginzburg-Wilson" critical phenomena, i.e. those critical phenomena which requires gauge fields to be explicitly used in their effective description. In particular we will analyze the case of some three dimensional scalar Abelian lattice systems: the phase diagrams of these models present several lines of phase transitions, whose critical properties are described by the continuum Abelian Higgs model or by more standard universality classes.

  • 9 April 2024, Dennis le Plat (Wigner) slides

    Integrability for higher-point functions in N=4 SYM

    Higher-point functions in N=4 super Yang-Mills theory became accessible by methods from integrability through the introduction of hexagon form factor. Originally proposed for three-point functions, it can also be used to calculate more general higher-point functions. In this talk, I will give an overview of the formalism and present recent results about its application to higher-rank sectors, importing only a minimum of information from the nested Bethe ansatz. Further, I will introduce the Lagrangian insertion technique in this framework, allowing to calculate perturbative corrections without having to resort to the gluing prescription.

  • 16 April 2024, Matteo Giordano (Eotvos) slides

    Constraints on the Dirac spectrum from chiral symmetry restoration in high-temperature QCD

    The nature of the symmetry-restoring transition in finite-temperature QCD in the chiral limit is still an open question, in particular for what concerns the fate of the anomalous U(1)_A symmetry. In this talk I discuss this problem from the point of view of the Dirac spectrum, focussing on the case of two massless fermion flavours. Using only general properties of correlation functions of scalar and pseudoscalar fermion bilinears, I prove that in the limit of vanishing quark mass m all the corresponding susceptibilities must be power series in m^2 with finite coefficients. This is then used to derive constraints on the Dirac spectrum in the chirally symmetric phase. Exploiting these constraints, I then show that for the anomalous U(1)_A symmetry to remain effectively broken in the symmetric phase (i) the spectral density must develop a singular peak near the origin as m goes to zero; (ii) the two-point eigenvalue correlator of near-zero modes must also be singular, and near-zero modes cannot be localised; (iii) the topological charge distribution must be indistinguishable from that of a free gas of instantons and anti-instantons of vanishing density.

  • 23 April 2024, Sam van Thurenhout (Wigner) slides

    Renormalization of composite operators in QCD

    We give an overview of the computation and renormalization of operator matrix elements in QCD. This allows one to extract the corresponding operator anomalous dimensions, which determine the scale dependence of non-perturbative parton distributions. The latter provide important information about hadronic structure and are accessible experimentally in hard scattering processes such as deep-inelastic scattering and deeply-virtual Compton scattering. The extraction of the anomalous dimensions from the renormalization process is non-trivial for exclusive processes because of mixing with total-derivative operators. During the talk we discuss how one can nevertheless reconstruct the functional form of the anomalous dimensions. Particular emphasis will be put on a recently developed method that exploits a consistency relation for the anomalous dimensions which follows from the renormalization structure of the operators.

  • 30 April 2024, David Pesznyak (Eotvos) slides

    Continuum extrapolated high-order baryon fluctuations

    Cumulants of conserved charges of QCD (i.e. baryon number, electric charge and strangeness) play a key role in the study of QCD phases both theoretically and experimentally. Lattice QCD is a valuable tool to calculate them, but going to higher orders remains challenging. During my seminar talk, I will introduce the methodology of computing such cumulants on the lattice at vanishing strangeness chemical potential, and on the so-called strangeness neutral line, relevant for phenomenological studies. Up to the fourth order in baryochemical potential, continuum results are available since 2015. I will present the first continuum results for sixth order baryon fluctuations for temperatures between T = 130-200 MeV, and eighth order at T = 145 MeV in a fixed volume. Our results are in sharp contrast with well known results in the literature obtained at finite lattice spacing. I will also discuss to what extent fluctuations can be used to constraint the position of the coveted critical endpoint of QCD using Pade resummation.

  • 7 May 2024, Gergely Fejos (Eotvos) slides

    Order of the chiral phase transition for N_f flavors

    Based on the epsilon expansion of the renormalization group flows of the Ginzburg-Landau potential for the chiral phase transition of QCD, it has been widely accepted that it is of first order in the zero quark mass limit for N_f > 2, with the possibility of a second order transition for N_f = 2, given the axial anomaly remains strong enough at the critical point. Recently, several lattice QCD studies hint that the transition can be of second order in the whole range of flavor numbers, after all. In this talk, I reanalyze the renormalization group flows of the Ginzburg-Landau potential using the functional renormalization group technique. Instead of employing the epsilon expansion around d = 4, with the inclusion of all (perturbatively) relevant and marginal interactions directly in d = 3, the method predicts that there exist new fixed points in the whole flavor number range potentially belonging to conformal systems going through a finite-temperature chiral transition. The results indicate that the chiral transition can be of second order for N_f >= 5, while its nature depends on the strength of the U_A(1) anomaly for N_f = 2,3,4.

  • 14 May 2024, Claudio Bonanno (IFT Madrid) slides

    Aspects of topology and confinement in large-N gauge theories

    Although the strong interaction observed in Nature is described within the Standard Model by an SU(3) gauge theory, where N=3 is the number of quark "colors", studying the behavior of Yang-Mills theories in the ideal limit N -> infinity provides a unique tool to gain a deeper understanding of the non-perturbative properties of gauge theories, and their connecton with phenomenological aspects of the Standard Model and Beyond.

    In this talk, I will review some of the main predictions obtained for SU(N) gauge theories in the large-N limit using very general theoretical arguments, highlighting the tight connection among topological features of gauge theories and confinement, and discussing several recent novel non-perturbative results confirming the predicted large-N scenario.

  • 21 May 2024, Tamas Kovacs (Eotvos) slides

    The fate of chiral symmetry in the quark-gluon plasma

    I present a new way of understanding how chiral symmetry is realized in the high temperature phase of QCD. I show that a simple instanton-based random matrix model provides an excellent description of the lowest part of the spectrum of the Dirac operator, the part that dominates physical quantities related to chiral symmetry. Remarkably in a strongly interacting theory, this part of the spectrum can be understood in terms of a gas of non-interacting instantons, even in the chiral limit. The model I present does not only provide an intuitive physical picture of how light quarks interact with gluons at high temperature, but also has nontrivial quantitative predictions. In particular it indicates a possible resolution of the long-standing debate about the fate of the anomalous U(1)_A symmetry above the critical temperature.

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

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


Zoltan Tulipant


2020 PhD - University of Debrecen, Hungary

2020 - postdoc - Eotvos University, Hungary




David Pesznyak

PhD student

2021- Eotvos University, Hungary


Gyorgy Baranka

PhD student

2021- Eotvos University, Hungary


Former members

Kornel Kapas

PhD student

2023- postdoc, Technical University, Hungary

2018-2023 Eotvos University, Hungary

Lorinc Szikszai

PhD student

2016 - 2023 Eotvos University, Hungary

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: