<p>We compute the coefficients <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">(</mo><mi>T</mi><mo>,</mo><mi>B</mi><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>c</mi><mn>4</mn></msub><mo stretchy="false">(</mo><mi>T</mi><mo>,</mo><mi>B</mi><mo stretchy="false">)</mo></math> of the Taylor expansion for the pressure in powers of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>μ</mi><mi>B</mi></msub><mo>/</mo><mi>T</mi></math> in the presence of a large magnetic field within perturbative quantum chromodynamics (QCD) at finite temperature and baryon density up to two-loops for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>f</mi></msub><mo>=</mo><mn>3</mn></math> flavors with physical quark masses. We also present results for the excess of pressure, baryon density, and baryon number susceptibility as functions of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>μ</mi><mi>B</mi></msub></math>, as well as susceptibilities as functions of the temperature in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">{</mo><msub><mi>μ</mi><mi>B</mi></msub><mo>,</mo><msub><mi>μ</mi><mi>Q</mi></msub><mo>,</mo><msub><mi>μ</mi><mi>S</mi></msub><mo stretchy="false">}</mo></math> basis. Our results can be directly compared to recent lattice QCD data. Even though current lattice results do not overlap with its region of validity, perturbative results seem to be compatible with those obtained on the lattice for large temperatures.</p>

Brazil

Eduardo S. Fraga

Letícia F. Palhares

United States

Tulio E. Restrepo

Susceptibilities and Taylor coefficients of magnetic QCD from perturbation theory

<p>In this paper we develop a systematic analysis of the properties of entanglement entropy in curved backgrounds using the replica approach. We explore the analytic (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>q</mi><mo>−</mo><mn>1</mn></mrow></math>) expansion of Rényi entropy <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>S</mi><mi>q</mi></msub></math> and its variations; our setup applies to generic variations, from symmetry transformations to variations of the background metric or entangling region. Our methodology elegantly reproduces and generalizes results from the literature on entanglement entropy in different dimensions, backgrounds and states. We use our analytic expansions to explore the behavior of entanglement entropy in static black hole backgrounds under specific scaling transformations, and we explain why this behavior is key to determining whether there are islands of entanglement.</p>

United Kingdom

Arvind Shekar

Marika Taylor

Replica analysis of entanglement properties

In this paper we systematically develop the flat/CFT holographic dictionary, building on AdS/CFT holography. After analysing the behaviour of scalar field modes on hyperbolic slices of Minkowski and performing the holographic renormalisation for the associated onshell action, we obtain a holography dictionary between the bulk theory and the corresponding dual theory on the celestial sphere. We propose that a single scalar field in the bulk is dual to two series of operators on the celestial sphere; the scaling dimension of these operators takes values on the principal series. The real time features of the bulk theory, such as the dynamical and the casual structure, are encoded in the construction of correlation functions on the boundary via the coefficients of the bulk modes. Moreover, we will see that the two series of operators can be interpreted as ingoing and outgoing waves in the bulk. We illustrate our dictionary with the example of a single shock wave. Our results lay foundations for further computation within the flat/celestial CFT correspondence.

Zezhuang Hao

Flat holography and celestial shockwaves

Exponential resummation of the QCD finite-density Taylor series has been recently introduced as an alternative way of resumming the finite-density lattice QCD Taylor series. Unfortunately the usual exponential resummation formula suffers from stochastic bias which must be subtracted before identifying genuine higher-order contributions. In this paper, we present a new way of subtracting the stochastic bias at the level of each individual gauge configuration, up to a certain order of either the Taylor series or the cumulant expansion, by modifying the argument of the exponential. Retaining the exponential form of the resummation allows us to also calculate the phase factor of the fermion determinant on each gauge configuration. We present our results for the excess pressure, number density, and the average phase factor and show that the new results contain less stochastic bias and are in better agreement with the QCD Taylor series compared to the previous exponential resummation.

India

Sabarnya Mitra

Prasad Hegde

QCD equation of state at finite chemical potential from an unbiased exponential resummation of the lattice QCD Taylor series

We discuss the definition of conserved quantities in asymptotically locally de Sitter spacetimes. One may define an analog of holographic charges at future and past infinity and at other Cauchy surfaces <math><msub><mi>I</mi><mi>t</mi></msub></math> as integrals over the intersection of timelike surfaces <math><mi>C</mi></math> and the Cauchy surface <math><msub><mi>I</mi><mi>t</mi></msub></math>. In general, the charges <math><msup><mi>Q</mi><mi>t</mi></msup></math> defined on the Cauchy surface <math><msub><mi>I</mi><mi>t</mi></msub></math> depend on <math><mi>C</mi></math>, but if gravitational flux is absent the charges are independent of <math><mi>C</mi></math>. On the other hand, if there is a net gravitational flux entering or leaving the spacetime region bounded by <math><mrow><msub><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></math>, <math><mrow><msub><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math> and two Cauchy surfaces then <math><mi>Δ</mi><msup><mi>Q</mi><mi>t</mi></msup><mo>(</mo><msub><mi>C</mi><mn>1</mn></msub><mo>,</mo><msub><mi>C</mi><mn>2</mn></msub><mo>)</mo><mo>=</mo><msup><mi>Q</mi><mi>t</mi></msup><mo>(</mo><msub><mi>C</mi><mn>1</mn></msub><mo>)</mo><mo>−</mo><msup><mi>Q</mi><mi>t</mi></msup><mo>(</mo><msub><mi>C</mi><mn>2</mn></msub><mo>)</mo></math> changes by the same amount.

Aaron Poole

Kostas Skenderis

Charges, conserved quantities, and fluxes in de Sitter spacetime

Taylor expansion of the thermodynamic potential in powers of the (baryo)chemical potential <math><msub><mi>μ</mi><mi>B</mi></msub></math> is a well-known method to bypass the sign problem of lattice QCD. Due to the difficulty in calculating the higher order Taylor coefficients, various alternative expansion schemes as well as resummation techniques have been suggested to extend the Taylor series to larger values of <math><msub><mi>μ</mi><mi>B</mi></msub></math>. Recently, a way to resum the contribution of the first <math><mi>N</mi></math> charge density correlation functions <math><msub><mi>D</mi><mn>1</mn></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mi>D</mi><mi>N</mi></msub></math> to the Taylor series to all orders in <math><msub><mi>μ</mi><mi>B</mi></msub></math> was proposed in [Phys. Rev. Lett. 128, 022001 (2022)]. The resummation takes the form of an exponential factor. Since the correlation functions are calculated stochastically, the exponential factor contains a bias which can be significant for large <math><mi>N</mi></math> and <math><msub><mi>μ</mi><mi>B</mi></msub></math>. In this paper, we present a new method to calculate the QCD equation of state based on the well-known cumulant expansion from statistics. By truncating the expansion at a maximum order <math><mi>M</mi></math>, we end up with only finite products of the correlation functions which can be evaluated in an unbiased manner. Although our formalism is also applicable for <math><msub><mi>μ</mi><mi>B</mi></msub><mo>≠</mo><mn>0</mn></math>, here we present it for the simpler case of a finite isospin chemical potential <math><msub><mi>μ</mi><mi>I</mi></msub></math> for which there is no sign problem. We present and compare results for the pressure and the isospin density obtained using Taylor expansion, exponential resummation and cumulant expansion, and provide evidence that the absence of bias in the latter actually improves the convergence.

Germany

Christian Schmidt

New way to resum the lattice QCD Taylor series equation of state at finite chemical potential

Using high statistics datasets generated in (<math><mrow><mn>2</mn><mo>+</mo><mn>1</mn></mrow></math>)-flavor QCD calculations at finite temperature, we present results for low-order cumulants of net-baryon-number fluctuations at nonzero values of the baryon chemical potential. We calculate Taylor expansions for the pressure (zeroth-order cumulant), the net-baryon-number density (first-order cumulant), and the variance of the distribution on net-baryon-number fluctuations (second-order cumulant). We obtain series expansions from an eighth-order expansion of the pressure and compare these to diagonal Padé approximants. This allows us to estimate the range of values for the baryon chemical potential in which these expansions are reliable. We find <math><mrow><msub><mrow><mi>μ</mi></mrow><mrow><mi>B</mi></mrow></msub><mo>/</mo><mi>T</mi><mo>≤</mo><mn>2.5</mn></mrow></math>, 2.0, and 1.5 for the zeroth-, first-, and second-order cumulants, respectively. We, furthermore, construct estimators for the radius of convergence of the Taylor series of the pressure. In the vicinity of the pseudocritical temperature <math><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi>p</mi><mi>c</mi></mrow></msub><mo>≃</mo><mn>156.5</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></mrow></math>, we find <math><mrow><msub><mrow><mi>μ</mi></mrow><mrow><mi>B</mi></mrow></msub><mo>/</mo><mi>T</mi><mo>≳</mo><mn>2.9</mn></mrow></math> at vanishing strangeness chemical potential and somewhat larger values for strangeness neutral matter. These estimates are temperature dependent and range from <math><mrow><msub><mrow><mi>μ</mi></mrow><mrow><mi>B</mi></mrow></msub><mo>/</mo><mi>T</mi><mo>≳</mo><mn>2.2</mn></mrow></math> at <math><mrow><mi>T</mi><mo>=</mo><mn>135</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></mrow></math> to <math><mrow><msub><mrow><mi>μ</mi></mrow><mrow><mi>B</mi></mrow></msub><mo>/</mo><mi>T</mi><mo>≳</mo><mn>3.2</mn></mrow></math> at <math><mi>T</mi><mo>=</mo><mn>165</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>. The estimated radius of convergences is the same for any higher-order cumulant.

D. Bollweg

J. Goswami

O. Kaczmarek

F. Karsch

Swagato Mukherjee

P. Petreczky

C. Schmidt

P. Scior

Taylor expansions and Padé approximants for cumulants of conserved charge fluctuations at nonvanishing chemical potentials

Taylor expansion in powers of baryon chemical potential (<math><mrow><msub><mrow><mi>μ</mi></mrow><mrow><mi>B</mi></mrow></msub></mrow></math>) is an oft-used method in lattice QCD to compute QCD thermodynamics for <math><mrow><msub><mrow><mi>μ</mi></mrow><mrow><mi>B</mi></mrow></msub><mo>&gt;</mo><mn>0</mn></mrow></math>. Based only upon the few known lowest order Taylor coefficients, it is difficult to discern the range of <math><msub><mi>μ</mi><mi>B</mi></msub></math> where such an expansion around <math><msub><mi>μ</mi><mi>B</mi></msub><mo>=</mo><mn>0</mn></math> can be trusted. We introduce a resummation scheme for the Taylor expansion of the QCD equation of state in <math><msub><mi>μ</mi><mi>B</mi></msub></math> that is based on the <math><mi>n</mi></math>-point correlation functions of the conserved current (<math><msub><mi>D</mi><mi>n</mi></msub></math>). The method resums the contributions of the first <math><mi>N</mi></math> correlation function <math><mrow><msub><mrow><mi>D</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>D</mi></mrow><mrow><mi>N</mi></mrow></msub></mrow></math> to the Taylor expansion of the QCD partition function to all orders in <math><msub><mi>μ</mi><mi>B</mi></msub></math>. We show that the resummed partition function is an approximation to the reweighted partition function at <math><msub><mi>μ</mi><mi>B</mi></msub><mo>≠</mo><mn>0</mn></math>. We apply the proposed approach to high-statistics lattice QCD calculations using <math><mrow><mn>2</mn><mo>+</mo><mn>1</mn></mrow></math> flavors of Highly Improved Staggered Quarks with physical quark masses on <math><mrow><msup><mrow><mn>32</mn></mrow><mrow><mn>3</mn></mrow></msup><mo>×</mo><mn>8</mn></mrow></math> lattices and for temperatures <math><mrow><mi>T</mi><mo>≈</mo><mn>145</mn><mi>–</mi><mn>176</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></mrow></math>. We demonstrate that, as opposed to the Taylor expansion, the resummed version not only leads to improved convergence but also reflects the zeros of the resummed partition function and severity of the sign problem, leading to its eventual breakdown. We also provide a generalization of scheme to include resummation of powers of temperature and quark masses in addition to <math><msub><mi>μ</mi><mi>B</mi></msub></math>, and show that the alternative expansion scheme of [S. Borsányi et al., Phys. Rev. Lett. 126, 232001 (2021).] is a special case of this generalized resummation.

Sourav Mondal

Lattice QCD Equation of State for Nonvanishing Chemical Potential by Resumming Taylor Expansions

We extend earlier studies of transverse Ward-Fradkin-Green-Takahashi identities in QED, their usefulness to constrain the transverse fermion-boson vertex and their importance for multiplicative renormalizability, to the equivalent gauge identities in QCD. To this end, we consider transverse Slavnov-Taylor identities that constrain the transverse quark-gluon vertex and derive its eight associated scalar form factors. The complete vertex can be expressed in terms of the quark’s mass and wave-renormalization functions, the ghost-dressing function, the quark-ghost scattering amplitude and a set of eight form factors. The latter parametrize the hitherto unknown nonlocal tensor structure in the transverse Slavnov-Taylor identity which arises from the Fourier transform of a four-point function involving a Wilson line in coordinate space. We determine the functional form of these eight form factors with the constraints provided by the Bashir-Bermudez vertex and study the effects of this novel vertex on the quark in the Dyson-Schwinger equation using lattice QCD input for the gluon and ghost propagators. We observe significant dynamical chiral symmetry breaking and a mass gap that leads to a constituent mass of the order of 500 MeV for the light quarks. The flavor dependence of the mass and wave-renormalization functions as well as their analytic behavior on the complex momentum plane is studied and as an application we calculate the quark condensate and the pion’s weak decay constant in the chiral limit. Both are in very good agreement with their reference values.

Luis Albino

Mexico

Adnan Bashir

Bruno El-Bennich

Colombia

Eduardo Rojas

Fernando Serna

Roberto Silveira

The impact of transverse Slavnov-Taylor identities on dynamical chiral symmetry breaking

Thimble regularization is a possible solution to the sign problem, which is evaded by formulating quantum field theories on manifolds where the imaginary part of the action stays constant (Lefschetz thimbles). A major obstacle is due to the fact that one in general needs to collect contributions coming from more than one thimble. Here we explore the idea of performing Taylor expansions on Lefschetz thimbles. We show that in some cases we can compute expansions in regions where only the dominant thimble contributes to the result in such a way that these (different, disjoint) regions can be bridged. This can most effectively be done via Padé approximants. In this way multi-thimble simulations can be circumvented. The approach can be trusted provided we can show that the analytic continuation we are performing is a legitimate one, which thing we can indeed show. We briefly discuss two prototypal computations, for which we obtained a very good control on the analytical structure (and singularities) of the results. All in all, the main strategy that we adopt is supposed to be valuable not only in the thimble approach, which thing we finally discuss.