The curvature of the chiral pseudocritical line from LQCD: analytic continuation and Taylor expansion compared

We present a determination of the curvature $\kappa$ of the chiral pseudocritical line from $N_f=2+1$ lattice QCD at the physical point obtained by adopting the Taylor expansion approach. Numerical simulations performed at three lattice spacings lead to a continuum extrapolated curvature $\kappa = 0.0145(25)$, a value that is in excellent agreement with continuum limit estimates obtained via analytic continuation within the same discretization scheme, $\kappa = 0.0135(20)$. The agreement between the two calculations is a solid consistency check for both methods.Comment: Quark Matter 201

Between Anthropology and Literature: Liminality in William Shakespeare's "Troilus and Cressida"

openA partire dalle considerazioni di Clifford Geertz sul rapporto interdipendente, benché spesso contestato, tra letteratura e antropologia, e dalle osservazioni di Victor Turner circa l’importanza della narrazione e della performance in ambito socio-culturale, il presente elaborato si pone come obiettivo l’indagine del concetto antropologico del Limite tramite il filtro di un’opera letteraria, cercando, nelle similitudini e analogie che accomunano i due ambiti disciplinari, una comune dimensione di analisi, dibattito e riflessione. Per la sua struttura, le sue tematiche, la sua storia derivativa e la difficoltà d’inquadramento in un contesto di genere, Troilus e Cressida di William Shakespeare appare come caso di studio appropriato. Si traccerà, a sostegno dell’analisi, un excursus storico e letterario delle variazioni e reinterpretazioni della Guerra di Troia, da cui deriva il soggetto primario dell’opera. Parallelamente, si andranno a presentare gli studi di Arnold Van Gennep e Victor Turner sul concetto di limite e liminalità nel più ampio contesto culturale, evidenziando l’importanza che essi rivestono tutt’ora, in particolare nelle società a carattere urbano-industriale. Unendo dunque le osservazioni tratte in questi ambiti apparentemente divergenti e affiancandole ad un appropriato apparato critico e teorico, si cercherà di dare una lettura di Troilus e Cressida, evidenziando l’emergenza del limite nelle sue macro e micro strutture narrative: dalle circostanze all’ambientazione, dalla pervasiva incertezza della guerra al senso identitaria dei personaggi, dalla dissoluzione del senso dell’eroismo all’ansia performativa. Oltre a offrire l’occasione di considerare le opere letterarie come validi casi di studio etnografico, l’elaborato mira a sottolineare le potenzialità multidisciplinari dell’approccio qui adottato, idealmente applicabili in contesti didattici per incoraggiare la ricezione critica e la rielaborazione dinamica di concetti altresì consolidati. A tale scopo, il lavoro troverà la sua conclusione in osservazioni personali sull’indagine, sul metodo adottato e su possibili sviluppi futuri.Drawing from Clifford Geertz's considerations on the interwoven, yet often contested relationship between literature and anthropology, ad from Victor Turner's observations regarding the importance of narration and performance in socio-cultural contexts, this paper aims to investigate the anthropological concept of Liminality through the lens of a literary work, seeking, in the shared facets of these seemingly distinct disciplines, a common ground for analysis, debate, and reflection. William Shakespeare's 'Troilus and Cressida' emerges as a fitting case study owing to its structure, thematic depth, historical derivation, and its resistance to genre classification. The analysis will present a historical and literary survey of the variations fo the Trojan War narrative, from which derived the primary subject of the play; conversely, it will provide a theoretical framework of reference by discussing the studies on limits and liminality conducted by Arnold Van Gennep and Victor Turner, highlighting the enduring relevance of these concepts within the broader cultural landscape, particularly in modern urban-industrial societies. Combining observations drawn from these apparently disparate scope and integrating them with a robust critical and theoretical framework, the dissertation will then provide an attempt of critical and interpretative reading of Troilus and Cressida, emphasizing the emergence of the liminal element in its macro and micro narrative structures: from the circumstances of war to the setting, from the pervasive uncertainty of the conflict to the characters’ sense of identity, from the dissolution of heroism to performative anxiety. Beyond serving as an opportunity to consider literary works as valid cases for ethnographic inquiries, this thesis seeks to highlight the potential of the multidisciplinary approach adopted herein, which appears ideally suited for educational purposes to encourage critical reception and dynamic reinterpretations of established concepts. To this end, the work will conclude with personal observations on the investigation, the methodologies employed, and prospects for potential future developments

Solution of the Thirring model in thimble regularization

Thimble regularization of lattice field theories has been proposed as a solution to the infamous sign problem. It is conceptually very clean and powerful, but it is in practice limited by a potentially very serious issue: in general many thimbles can contribute to the computation of the functional integrals. Semiclassical arguments would suggest that the fundamental thimble could be sufficient to get the correct answer, but this hypothesis has been proven not to hold true in general. A first example of this failure has been put forward in the context of the Thirring model: the dominant thimble approximation is valid only in given regions of the parameter space of the theory. Since then a complete solution of this (simple) model in thimble regularization has been missing. In this paper we show that a full solution (taking the continuum limit) is indeed possible. It is possible thanks to a method we recently proposed which de facto evades the need to simulate on many thimbles

On the Lefschetz thimbles structure of the Thirring model

The complexification of field variables is an elegant approach to attack the sign problem. In one approach one integrates on Lefschetz thimbles: over them, the imaginary part of the action stays constant and can be factored out of the integrals so that on each thimble the sign problem disappears. However, for systems in which more than one thimble contribute one is faced with the challenging task of collecting contributions coming from multiple thimbles. The Thirring model is a nice playground to test multi-thimble integration techniques; even in a low dimensional theory, the thimble structure can be rich. It has been shown since a few years that collecting the contribution of the dominant thimble is not enough to capture the full content of the theory. We report preliminary results on reconstructing the complete results from multiple thimble simulations.Comment: 7 pages, 5 figures, Proceedings of the 37th Annual International Symposium on Lattice Field Theory, 16-22 June 2019, Wuhan, Chin

Taylor expansions and Padé approximations for Lefschetz thimbles and beyond

Deforming the domain of integration after complexification of the field variables is an intriguing idea to tackle the sign problem. In thimble regularization the domain of integration is deformed into an union of manifolds called Lefschetz thimbles. On each thimble the imaginary part of the action stays constant and the sign problem disappears. A long standing issue of this approach is how to determine the relative weight to assign to each thimble contribution in the (multi)-thimble decomposition. Yet this is an issue one has to face, as previous work has shown that different theories exist for which the contributions coming from thimbles other than the dominant one cannot be neglected. Historically, one of the first examples of such theories is the one-dimensional Thirring model. Here we discuss how Taylor expansions can be used to by-pass the need for multi-thimble simulations. If multiple, disjoint regions can be found in the parameters space of the theory where only one thimble gives a relevant contribution, multiple Taylor expansions can be carried out in those regions to reach other regions by single thimble simulations. Better yet, these Taylor expansions can be bridged by Padé interpolants. Not only does this improve the convergence properties of the series, but it also gives access to information about the analytical structure of the observables. The true singularities of the observables can be recovered. We show that this program can be applied to the one-dimensional Thirring model and to a (simple) version of HDQCD. But the general idea behind our strategy can be helpful beyond thimble regularization itself, i.e. it could be valuable in studying the singularities of QCD in the complex µB plane. Indeed this is a program that is currently being carried out by the Bielefeld-Parma collaboration

Taylor expansions and Padé approximations for Lefschetz thimbles and beyond

Deforming the domain of integration after complexification of the field variables is an intriguing idea to tackle the sign problem. In thimble regularization the domain of integration is deformed into an union of manifolds called Lefschetz thimbles. On each thimble the imaginary part of the action stays constant and the sign problem disappears. A long standing issue of this approach is how to determine the relative weight to assign to each thimble contribution in the (multi)-thimble decomposition. Yet this is an issue one has to face, as previous work has shown that different theories exist for which the contributions coming from thimbles other than the dominant one cannot be neglected. Historically, one of the first examples of such theories is the one-dimensional Thirring model. Here we discuss how Taylor expansions can be used to by-pass the need for multi-thimble simulations. If multiple, disjoint regions can be found in the parameters space of the theory where only one thimble gives a relevant contribution, multiple Taylor expansions can be carried out in those regions to reach other regions by single thimble simulations. Better yet, these Taylor expansions can be bridged by Padé interpolants. Not only does this improve the convergence properties of the series, but it also gives access to information about the analytical structure of the observables. The true singularities of the observables can be recovered. We show that this program can be applied to the one-dimensional Thirring model and to a (simple) version of HDQCD. But the general idea behind our strategy can be helpful beyond thimble regularization itself, i.e. it could be valuable in studying the singularities of QCD in the complex µB plane. Indeed this is a program that is currently being carried out by the Bielefeld-Parma collaboration

One-thimble regularisation of lattice field theories: is it only a dream?

Lefschetz thimbles regularisation of (lattice) field theories was put forward as a possible solution to the sign problem. Despite elegant and conceptually simple, it has many subtleties, a major one boiling down to a plain question: how many thimbles should we take into account? In the original formulation, a single thimble dominance hypothesis was put forward: in the thermodynamic limit, universality arguments could support a scenario in which the dominant thimble (associated to the global minimum of the action) captures the physical content of the field theory. We know by now many counterexamples and we have been pursuing multi-thimble simulations ourselves. Still, a single thimble regularisation would be the real breakthrough. We report on ongoing work aiming at a single thimble formulation of lattice field theories, in particular putting forward the proposal of performing Taylor expansions on the dominant thimble.Comment: 7 pages, 1 figure, Proceedings of the 37th Annual International Symposium on Lattice Field Theory, 16-22 June 2019, Wuhan, Chin

One-thimble regularisation of lattice field theories: Is it only a dream?

Lefschetz thimbles regularisation of (lattice) field theories was put forward as a possible solution to the sign problem. Despite elegant and conceptually simple, it has many subtleties, a major one boiling down to a plain question: how many thimbles should we take into account? In the original formulation, a single thimble dominance hypothesis was put forward: in the thermodynamic limit, universality arguments could support a scenario in which the dominant thimble (associated to the global minimum of the action) captures the physical content of the field theory. We know by now many counterexamples and we have been pursuing multi-thimble simulations ourselves. Still, a single thimble regularisation would be the real breakthrough. We report on ongoing work aiming at a single thimble formulation of lattice field theories, in particular putting forward the proposal of performing Taylor expansions on the dominant thimble