arXiv subjects

Daniel Nogradi

Publications and source records attributed to Daniel Nogradi.

At least 19 recordsLinked to original sources

arXiv2026

QFT on flat, compact, orientable manifolds

Motivated by the recent observation that rotating space-times at finite temperature can be described by particular flat, compact, orientable manifolds, which are different from $\mathbb T^4$, we catalogue all such 4-manifolds and their properties. There are in total 26 flat, compact, orientable 4-manifolds, 23 of them spin-manifolds, so fermions and a Dirac operator can also be defined on these. Seven of them are appropriate for finite volume periodic boxes undergoing rotation at finite temperature.

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arXiv2025

QCD on the 16-cell honeycomb

We formulate QCD discretized on the four dimensional 16-cell honeycomb. The advantage is a higher degree of rotational symmetry as compared to a traditional cubic lattice leading to much smaller cut-off effects. We demonstrate in quenched QCD, through both gluonic and fermionic observables, that the scaling properties are indeed superior to the cubic lattice and much larger lattice spacings are sufficient for controlled continuum extrapolations. Chiral and topological properties also show remarkable improvement.

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arXiv2025

QFT on rotating boxes at finite temperature

We formulate thermal quantum field theory on a finite spatial periodic volume incorporating finite rotations. Traditional compactifications at finite temperature without rotations typically involve ${\mathbb T}^4$ as the space-time manifold within a path integral formulation and also moving frames can be accommodated by shifted boundary conditions on the same space. We show that consistent descriptions of certain finite rotations are possible on space-time manifolds with topology different from ${\mathbb T}^4$ but still flat and without boundary and we classify all possible geometries. The non-trivial topology may be implemented by rotated boundary conditions allowing for a path integral formulation. The purely imaginary angular velocity in temperature units cannot be arbitrary but several discrete values are possible. We also discuss finite volume effects in detail.

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arXiv2025

Center vortices in the novel phase of staggered fermions

The geometry of center vortices is studied in the novel lattice-artefact phase that appears with staggered fermions to elucidate any insight provided by the center-vortex degrees of freedom. For various numbers of fermion flavors, the single-site shift symmetry of the staggered-fermion action is broken in a finite region of the $(\beta, m)$ phase space. Simulations are performed with six degenerate fermion flavors and a range of $\beta$ values that span the phase boundary. Center vortices are demonstrated to capture the broken shift symmetry that manifests in the unphysical phase. This persists at the level of each individual plaquette orientation, where it is revealed that only the plaquettes that span the broken dimension are affected. Several bulk center-vortex quantities, including the vortex and branching point densities, are considered to highlight other aspects of vortex geometry sensitive to the unphysical phase. A slight preference for the plaquettes affected by the broken shift symmetry to be pierced by a vortex is observed. This translates also to a greater branching point density in three-dimensional slices that span the broken dimension. Combined, these findings provide a novel characterization of the unphysical phase in terms of the fundamental center degrees of freedom.

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arXiv2023

Mesonic decay constant and mass ratios and the conformal window

Two particular ratios related to mesons are proposed for the study of the conformal window in $SU(3)$ gauge theory and fundamental fermions. Lattice and other studies indicate that the lower end, $N_f^*$, is at around 7 - 13 flavors which is a wide range without a clear consensus. Here we propose the decay constant to mass ratios of mesons, $f_{PS,V} / m_V$, as a proxy since below the conformal window lattice studies have shown that they are largely $N_f$-independent while at the upper end of the conformal window they are vanishing. The drop from the non-zero constant value to zero at $N_f = 16.5$ might be indicative of $N_f^*$. We compute $f_V / m_V$ to N$^3$LO and $f_{PS} / m_V$ to NNLO order in (p)NRQCD. The results are unambiguously reliable just below $N_f = 16.5$, hence the results are expanded á la Banks-Zaks in $\varepsilon = 16.5 - N_f$. The convergence properties of the series and matching with the non-perturbative infinite volume, continuum and chiral extrapolated lattice results at $N_f = 10$ suggest that the perturbative results might be reliable down to $N_f = 12$. A sudden drop is observed at $N_f = 12$ and $N_f = 13$ in $f_V / m_V$ and $f_{PS} / m_V$, respectively.

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arXiv2023

The $f_\varrho / m_\varrho$ and $f_π/ m_\varrho$ ratios and the conformal window

The $f_\varrho / m_\varrho$ ratio is calculated at N$^3$LO order within perturbative (p)NRQCD with $N_f$ flavors of mass degenerate fermions. The massless limit of the ratio is expanded á la Banks-Zaks in $ε= 16.5 - N_f$ leading to reliable predictions close to the upper end of the conformal window. The comparison of the NNLO and N$^3$LO results indicate that the Banks-Zaks expansion may be reliable down to twelve flavors. Previous lattice calculations combined with the KSRF relations provide us with the same ratio for the range $2 \leq N_f \leq 10$. Assuming a monotonous dependence on $N_f$ leads to an estimate for the lower end of the conformal window, $N_f^* \simeq 12$, by matching the non-perturbative and our perturbative results. In any case an abrupt change is observed in $f_\varrho / m_\varrho$ at twelve flavors. As a cross-check we also consider the $f_π/ m_\varrho$ ratio for which lattice results are also available. The perturbative calculation at present is only at the NNLO level which is insufficient for a reliable and robust matching between the low $N_f$ and high $N_f$ regions. Nonetheless, using the relative size of the N$^3$LO correction of $f_\varrho / m_\varrho$ for estimating the same for $f_π/ m_\varrho$ leads to the estimate $N_f^* \simeq 13$.

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arXiv2022

Dilaton in scalar QFT: a no-go theorem in $4-\varepsilon$ and $3-\varepsilon$ dimensions

Spontaneous scale invariance breaking and the associated Goldstone boson, the dilaton, is investigated in renormalizable, unitary, interacting non-supersymmetric scalar field theories in $4-\varepsilon$ dimensions. At leading order it is possible to construct models which give rise to spontaneous scale invariance breaking classically and indeed a massless dilaton can be identified. Beyond leading order, in order to have no anomalous scale symmetry breaking in QFT, the models need to be defined at a Wilson-Fisher fixed point with exact conformal symmetry. It is shown that this requirement on the couplings is incompatible with having the type of flat direction which would be necessary for an exactly massless dilaton. As a result spontaneous scale symmetry breaking and an exactly massless dilaton can not occur in renormalizable, unitary $4-\varepsilon$ dimensional scalar QFT. The arguments apply to $ϕ^6$ theory in $3-\varepsilon$ dimensions as well.

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arXiv2022

Radius of convergence in lattice QCD at finite $μ_B$ with rooted staggered fermions

In typical statistical mechanical systems the grand canonical partition function at finite volume is proportional to a polynomial of the fugacity $e^{μ/T}$. The zero of this Lee-Yang polynomial closest to the origin determines the radius of convergence of the Taylor expansion of the pressure around $μ=0$. The computationally cheapest formulation of lattice QCD, rooted staggered fermions, with the usual definition of the rooted determinant, does not admit such a Lee-Yang polynomial. We argue that the radius of convergence is then bounded by the spectral gap of the reduced matrix of the unrooted staggered operator. This is a cutoff effect that potentially affects all estimates of the radius of convergence with the standard staggered rooting. We suggest a new definition of the rooted staggered determinant at finite chemical potential that allows for a definition of a Lee-Yang polynomial, and, therefore of the numerical study of Lee-Yang zeros. We also describe an algorithm to determine the Lee-Yang zeros and apply it to configurations generated with the 2-stout improved staggered action at $N_t = 4$. We perform a finite-volume scaling study of the leading Lee-Yang zeros and estimate the radius of convergence of the Taylor expansion extrapolated to an infinite volume. We show that the limiting singularity is not on the real line, thus giving a lower bound on the location of any possible phase transitions at this lattice spacing. In the vicinity of the crossover temperature at zero chemical potential, the radius of convergence turns out to be $μ_B/T \approx 2$ and roughly temperature independent. Our simulations are performed at strange quark chemical potential $μ_s=0$, but the method can be straightforwardly extended to strangeness chemical potential $μ_S=0$ or strangeness neutrality.

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arXiv2022

Lattice simulations of the QCD chiral transition at real $μ_B$

Most lattice studies of hot and dense QCD matter rely on extrapolation from zero or imaginary chemical potentials. The ill-posedness of numerical analytic continuation puts severe limitations on the reliability of such methods. We studied the QCD chiral transition at finite real baryon density with the more direct sign reweighting approach. We simulate up to a baryochemical potential-temperature ratio of $μ_B/T=2.7$, covering the RHIC Beam Energy Scan range, and penetrating the region where methods based on analytic continuation are unpredictive.This opens up a new window to study QCD matter at finite $μ_B$ from first principles.

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arXiv2021

New approach to lattice QCD at finite density: reweighting without an overlap problem

Approaches to finite baryon density lattice QCD usually suffer from uncontrolled systematic uncertainties in addition to the well-known sign problem. We test a method - sign reweighting - that works directly at finite chemical potential and is yet free from any such uncontrolled systematics: with this approach the only problem is the sign problem itself. In practice the approach involves the generation of configurations with the positive fermionic weights given by the absolute value of the real part of the quark determinant, and a reweighting by a sign. There are only two sectors, +1 and -1 and as long as the average $\left\langle \pm \right\rangle \neq 0$ (with respect to the positive weight) this discrete reweighting has no overlap problem - unlike reweighting from $μ=0$ - and the results are reliable. We also present results based on this algorithm on the phase diagram of lattice QCD with two different actions: as a first test, we apply the method to calculate the position of the critical endpoint with unimproved staggered fermions at $N_τ=4$; as a second application, we study the phase diagram with 2stout improved staggered fermions at $N_τ=6$. This second one is already a reasonably fine lattice - relevant for phenomenology. We demonstrate that the method penetrates the region of the phase diagram where the Taylor and imaginary chemical potential methods lose predictive power.

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arXiv2021

Spin-1 fields and RG flows in 4 dimensions

The most general local, classically scale invariant, perturbatively renormalizable, globally $SU(N)$ invariant Lagrangian is constructed for spin-1 fields in 4 dimensions. The total number of independent couplings is 7 and the 1-loop $β$-functions are computed in the MSbar scheme. A number of asymptotically free RG flows are identified corresponding to non-trivial QFTs. None of these are gauge theories. The details of the large-$N$ limit are also worked out and it is shown that the RG phase space is qualitatively similar for all $N>5$ including the $N\to\infty$ limit.

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arXiv2021

Lattice simulations of the QCD chiral transition at real baryon density

State-of-the-art lattice QCD studies of hot and dense strongly interacting matter currently rely on extrapolation from zero or imaginary chemical potentials. The ill-posedness of numerical analytic continuation puts severe limitations on the reliability of such methods. Here we use the more direct sign reweighting method to perform lattice QCD simulation of the QCD chiral transition at finite real baryon density on phenomenologically relevant lattices. This method does not require analytic continuation and avoids the overlap problem associated with generic reweighting schemes, so has only statistical but no uncontrolled systematic uncertainties for a fixed lattice setup. This opens up a new window to study hot and dense strongly interacting matter from first principles. We perform simulations up to a baryochemical potential-temperature ratio of $μ_B/T=2.5$ covering most of the RHIC Beam Energy Scan range in the chemical potential. We also clarify the connection of the approach to the more traditional phase reweighting method.

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arXiv2021

More on the flavor dependence of $m_\varrho / f_π$

In previous work, arXiv:1905.01909, we have calculated the $m_\varrho / f_π$ ratio in the chiral and continuum limit for $SU(3)$ gauge theory coupled to $N_f = 2,3,4,5,6$ fermions in the fundamental representation. The main result was that this ratio displays no statistically significant $N_f$-dependence. In the present work we continue the study of the $N_f$-dependence by extending the simulations to $N_f = 7, 8, 9, 10$. Along the way we also study in detail the $N_f$-dependence of finite volume effects on low energy observables and a particular translational symmetry breaking unphysical, lattice artefact phase specific to staggered fermions.

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arXiv2021

Vector fields, RG flows and emergent gauge symmetry

We consider the most general perturbatively renormalizable theory of vector fields in four dimensions with a global SU(N) symmetry and massless couplings. The Lagrangian contains 1 quadratic, 2 cubic and 4 quartic couplings. The RG flow among this set of 7 couplings is computed to 1-loop and a rich phase diagram is mapped out; in particular it is shown that a finite number of asymptotically free RG-flows exist corresponding to non-trivial fixed points for the ratios of the couplings. None of these are gauge theories, i.e. possess only global SU(N) invariance but not a local one. We also include the most general ghost couplings, still with global SU(N) invariance, and compute the RG flow to 1-loop for all 9 resulting couplings. Again asymptotically free RG flows exist with non-trivial fixed points for the ratios of couplings. It is shown that Yang-Mills theory emerges at a particular fixed point. The theories at the other fixed points are marginally relevant gauge symmetry violating perturbations of Yang-Mills theory. The large-N limit is also investigated in detail.

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arXiv2020

New approach to lattice QCD at finite density; results for the critical end point on coarse lattices

All approaches currently used to study finite baryon density lattice QCD suffer from uncontrolled systematic uncertainties in addition to the well-known sign problem. We formulate and test an algorithm, sign reweighting, that works directly at finite $μ= μ_B/3$ and is yet free from any such uncontrolled systematics. With this algorithm the {\em only} problem is the sign problem itself. This approach involves the generation of configurations with the positive fermionic weight $|{\rm Re\; det} D(μ)|$ where $D(μ)$ is the Dirac matrix and the signs ${\rm sign} \; ( {\rm Re\; det} D(μ) ) = \pm 1$ are handled by a discrete reweighting. Hence there are only two sectors, $+1$ and $-1$ and as long as the average $\langle\pm 1\rangle \neq 0$ (with respect to the positive weight) this discrete reweighting by the signs carries no overlap problem and the results are reliable. The approach is tested on $N_t = 4$ lattices with $2+1$ flavors and physical quark masses using the unimproved staggered discretization. By measuring the Fisher (sometimes also called Lee-Yang) zeros in the bare coupling on spatial lattices $L/a = 8, 10, 12$ we conclude that the cross-over present at $μ= 0$ becomes stronger at $μ> 0$ and is consistent with a true phase transition at around $μ_B/T \sim 2.4$.

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arXiv2020

Towards a reliable lower bound on the location of the critical endpoint

We perform the first direct determination of the position of the leading singularity of the pressure in the complex chemical potential $μ_B$ plane in lattice QCD using numerical simulations with 2-stout improved rooted staggered fermions. This provides a direct determination of the radius of convergence of the Taylor expansion of the pressure that does not rely on a finite-order truncation of the expansion. The analyticity issues in the complex $μ_B$ plane of the grand canonical partition function of QCD with rooted staggered fermions are solved with a careful redefinition of the fermion determinant that makes it a polynomial in the fugacity on any finite lattice, without changing the continuum limit of the observables. By performing a finite volume scaling study at a single coarse lattice spacing, we show that the limiting singularity is not on the real line in the thermodynamic limit, thus showing that the radius of convergence of the Taylor expansion gives a lower bound on the location of a possible phase transition. In the vicinity of the crossover temperature at zero chemical potential, the radius of convergence turns out to be $μ_B/T \approx 2$ and roughly temperature independent.

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arXiv2020

The semi-classical approximation at high temperature revisited

We revisit the semi-classical calculation of the size distribution of instantons at finite temperature in non-abelian gauge theories in four dimensions. The relevant functional determinants were first calculated in the seminal work of Gross, Pisarski and Yaffe and the results were used for a wide variety of applications including axions most recently. In this work we show that the uncertainty on the numerical evaluations and semi-analytical expressions are two orders of magnitude larger than claimed. As a result various quantities computed from the size distribution need to be reevaluated, for instance the resulting relative error on the topological susceptibility at arbitrarily high temperatures is about 5% for QCD and about 10% for $SU(3)$ Yang-Mills theory. With higher rank gauge groups this discrepancy is even higher. We also provide a simple semi-analytical formula for the size distribution with absolute error $2\cdot10^{-4}$. In addition we also correct the over-all constant of the instanton size distribution in the MSbar scheme which was widely used incorrectly in the literature if non-trivial fermion content is present.

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arXiv2020

The effect of stout smearing on the phase diagram from multiparameter reweigthing in lattice QCD

The phase diagram and the location of the critical endpoint (CEP) of lattice QCD with unimproved staggered fermions on a $N_t=4$ lattice was determined fifteen years ago with the multiparameter reweighting method by studying Fisher zeros. We first reproduce the old result with an exact algorithm (not known at the time) and with statistics larger by an order of magnitude. As an extension of the old analysis we introduce stout smearing in the fermion action in order to reduce the finite lattice spacing effects. First we show that increasing the smearing parameter $ρ$ the crossover at $μ= 0$ gets weaker, i.e., the leading Fisher zero gets farther away from the real axis. Furthermore as the chemical potential is increased the overlap problem gets severe sooner than in the unimproved case, therefore shrinking the range of applicability of the method. Nevertheless certain qualitative features remain, even after introducing the smearing. Namely, at small chemical potentials the Fisher zeros first get farther away from the real axis and later at around $aμ_q = 0.1 - 0.15$ they start to get closer, i.e., the crossover first gets weaker and later stronger as a function of $μ$. However, because of the more severe overlap problem the CEP is out of reach with the smeared action.

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