We study the transverse momentum ( $p_T$ ) differential anisotropic flow and flow fluctuation in Pb+Pb collisions at $\sqrt{s_{_{NN}}}$ =5.02 TeV at the LHC. A (3+1)-dimensional CLVisc hydrodynamics framework with fluctuating TRENTO (or AMPT) initial conditions is utilized to simulate the space-time evolution of the quark-gluon plasma (QGP) medium. The effects of shear viscosity and the sub-nucleon structure on anisotropic flow and flow fluctuation are analyzed. Our result shows that shear viscosity tends to suppress both flow coefficients ( ${v_2\{2}\}$ , ${v_2\{4\}}$ , and ${\langle v_2\rangle}$ ) and flow fluctuation ( ${\sigma_{v_2}}$ ) owing to its smearing effect on local density fluctuation. The flow coefficients appear to be insensitive to the sub-nucleon structure, whereas the flow fluctuation ${\sigma_{v_2}}$ tends to be suppressed by the sub-nucleon structure in central collisions but enhanced in peripheral collisions. After taking into account the sub-nucleon structure effect, our numerical result can qualitatively describe the relative flow fluctuations ( ${v_2\{4\}/v_2\{2\}}$ , $F({v_2})$ ) measured by the ALICE Collaboration at the LHC. We further investigate the effects of shear viscosity, sub-nucleon structure, and initial condition model on the flow angle and flow magnitude decorrelations ( ${A_2^f}$ , ${M_2^f}$ ) using the four-particle correlation method. We find that the flow decorrelation effect is typically stronger in central collisions than in peripheral collisions. The flow angle decorrelation is found to be insensitive to the shear viscosity and sub-nucleon structure, whereas the flow magnitude decorrelation shows quite different behaviors when using the TRENTO and AMPT initial condition models. Our study sheds light on the anisotropic flow, transport properties, and initial structure of the QGP created in high-energy nuclear collisions.

China

Germany

Jie Zhu

Canada

Xiang-Yu Wu

Guang-You Qin

Anisotropic flow, flow fluctuation, and flow decorrelation in relativistic heavy-ion collisions: the roles of sub-nucleon structure and shear viscosity * Supported in part by the Natural Science Foundation of China (12225503, 11890710, 11890711, 11935007). Zhu Jie is supported in part by the China Scholarship Council (202306770009). Wu Xiang-Yu is supported in part by the National Science Foundation within the framework of the JETSCAPE collaboration (OAC-2004571) and in part by the Natural Sciences and Engineering Research Council of Canada. Some of the calculations were performed in the Nuclear Science Computing Center at Central China Normal University (NSC$^{3}$), Wuhan, Hubei, China.

We compute the overlap Dirac spectrum on three gauge ensembles generated using <math><mn>2</mn><mo>+</mo><mn>1</mn></math>-flavor domain wall fermions. The three ensembles have different lattice spacings, and two of them have quark masses tuned to the physical point. The spectral density is determined up to <math><mi>λ</mi><mo>∼</mo><mn>100</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math> with subpercentage statistical uncertainty. We find that the density is close to a constant below <math><mi>λ</mi><mo>∼</mo><mn>20</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math> as predicted by chiral perturbative theory (<math><mi>χ</mi><mi>PT</mi></math>) and then increases linearly due to the strange quark mass. By fitting to the next-to-leading order <math><mi>χ</mi><mi>PT</mi></math> form and using the nonperturbative renormalization using the regularization independent momentum subtraction scheme, the SU(2) (keeping the strange quark mass at the physical point) and SU(3) chiral condensates at <math><mrow><mover><mrow><mi>MS</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow></math> 2 GeV are determined to be <math><mi>Σ</mi><mo>=</mo><mo>(</mo><mn>265.4</mn><mo>(</mo><mn>0.5</mn><mo>)</mo><mo>(</mo><mn>4.2</mn><mo>)</mo><mtext> </mtext><mtext> </mtext><mi>MeV</mi><msup><mo>)</mo><mn>3</mn></msup></math> and <math><msub><mi>Σ</mi><mn>0</mn></msub><mo>=</mo><mo>(</mo><mn>234.3</mn><mo>(</mo><mn>0.5</mn><mo>)</mo><mo>(</mo><mn>25.8</mn><mo>)</mo><mtext> </mtext><mtext> </mtext><mi>MeV</mi><msup><mo>)</mo><mn>3</mn></msup></math>, respectively. The pion decay constants are also determined to be <math><mi>F</mi><mo>=</mo><mn>84.1</mn><mo>(</mo><mn>1.9</mn><mo>)</mo><mo>(</mo><mn>8.0</mn><mo>)</mo></math> and <math><msub><mi>F</mi><mn>0</mn></msub><mo>=</mo><mn>58.6</mn><mo>(</mo><mn>0.5</mn><mo>)</mo><mo>(</mo><mn>10.0</mn><mo>)</mo><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>. The systematic errors are carefully estimated including the effects of fitting ranges and the uncertainty of low-energy constant <math><msub><mi>L</mi><mn>6</mn></msub></math>. We also show that one can resolve the sea flavor content of the sea quarks and constrain their masses with <math><mrow><mo>∼</mo><mn>10</mn><mo>%</mo><mi>–</mi><mn>20</mn><mo>%</mo></mrow></math> statistical uncertainties using the Dirac spectral density.

United States

Jian Liang

Andrei Alexandru

Yu-Jiang Bi

Terrence Draper

Keh-Fei Liu

Yi-Bo Yang

Detecting the flavor content of the vacuum using the Dirac operator spectrum

General exotic bi-gravity, obtained in Ozkan et al. (Phys Rev Lett 123(3):031303, 2019), is a unitary parity-preserving model which describes two interacting spin-two fields in three-dimensional spacetime. Adopting a symplectic viewpoint, we investigate the dynamical structure of general exotic bi-gravity theory. In particular, by exploiting the properties of the corresponding pre-symplectic matrix and its associated zero-modes, we explicitly derive all constraints of the theory, including the integrability conditions and scalar relationships between all the parameters and fields defining the model. Then, as an application, these scalar relationships are used for studying the anti-de Sitter background. After that, we derive the gauge transformations for the dynamical variables from the structure of the remaining zero-modes, meaning that such zero-modes are indeed the generators of the gauge symmetry of the theory. Finally, by switching off one of the four coupling constants  $$\beta _{n}$$  <math> <msub> <mi>β</mi> <mi>n</mi> </msub> </math>   and assuming the invertibility of some of the dreibeins, we find that the general exotic bi-gravity theory has two physical degrees of freedom.

Mexico

Omar Rodríguez-Tzompantzi

Faddeev–Jackiw Hamiltonian formulation for general exotic bi-gravity

We compute the first twenty moments of three convergent quartic bi-tracial 2-matrix ensembles in the large N limit. These ensembles are toy models for Euclidean quantum gravity originally proposed by John Barrett and collaborators. A perturbative solution is found for the first twenty moments using the Schwinger-Dyson equations and properties of certain bi-colored unstable maps associated to the model. We then apply a result of Guionnet et al. to show that the perturbative and convergent solution coincide for a small neighbourhood of the coupling constants. For each model we compute an explicit expression for the free energy, critical points, and critical exponents in the large N limit. In particular, the string susceptibility is found to be γ = 1/2, hinting that the associated universality class of the model is the continuous random tree.

Masoud Khalkhali

Nathan Pagliaroli

Coloured combinatorial maps and quartic bi-tracial 2-matrix ensembles from noncommutative geometry

We formulate a version of the double copy for classical fields in curved spacetimes. We provide a correspondence between perturbative solutions to the bi-adjoint scalar equations and those of the Yang-Mills equations in position space. At the linear level, we show that there exists a map between these solutions for maximally symmetric spacetime backgrounds, that provides every Yang-Mills solution by the action of an appropriate differential operator on a bi-adjoint scalar solution. Given the existence of a linearized map, we show that it is possible to cast the solutions of the Yang-Mills equations at arbitrary perturbation order in terms of the corresponding bi-adjoint scalar solutions. This all-order map is reminiscent of the flat space BCJ double copy, and works for any curved spacetime where the perturbative expansion holds. We show that these results have the right flat space limit, and that the correspondence is agnostic to the choice of gauge.

India

Siddharth Prabhu

The classical double copy in curved spacetimes: perturbative Yang-Mills from the bi-adjoint scalar

Continuing the previous initiatives [1, 2], we pursue the exploration of operator growth and Krylov complexity in dissipative open quantum systems. In this paper, we resort to the bi-Lanczos algorithm generating two bi-orthogonal Krylov spaces, which individually generate non-orthogonal subspaces. Unlike the previously studied Arnoldi iteration, this algorithm renders the Lindbladian into a purely tridiagonal form, thus opening up a possibility to study a wide class of dissipative integrable and non-integrable systems by computing Krylov complexity at late times. Our study relies on two specific systems, the dissipative transverse-field Ising model (TFIM) and the dissipative interacting XXZ chain. We find that, for the weak coupling, initial Lanczos coefficients can efficiently distinguish integrable and chaotic evolution before the dissipative effect sets in, which results in more fluctuations in higher Lanczos coefficients. This results in the equal saturation of late-time complexity for both integrable and chaotic cases, making the notion of late-time chaos dubious.

Poland

Aranya Bhattacharya

Japan

Pratik Nandy

Pingal Nath

Himanshu Sahu

On Krylov complexity in open systems: an approach via bi-Lanczos algorithm

We study integrable deformations of two-dimensional non-linear σ-models and present a new class of classical solutions to critical bi-Yang-Baxter models for general groups. For the simplest example, namely the SL(2, ℝ) bi-Yang-Baxter model, we show that our solutions can be mapped to the known complex uniton solutions of the SU(2) bi-Yang-Baxter model. In general, our solutions are constructed from so-called Sl(2)-orbits that play a central role in the study of asymptotic Hodge theory. This provides further evidence for a close relation between integrable non-linear σ-models and the mathematical principles underlying Hodge theory. We have also included a basic introduction to the relevant aspects of asymptotic Hodge theory and have provided some simple examples.

Netherlands

Thomas Grimm

Jeroen Monnee

Bi-Yang-Baxter models and Sl(2)-orbits

In this paper, we construct a charged soliton with a finite energy and no delta function source in a pure Abelian gauge theory. Specifically, we first consider the three-dimensional Abelian gauge theory, with a Maxwell term and a level <math><mi>N</mi></math> CS term. We find a static solution that carries charge <math><mi>N</mi></math>, angular momentum <math><mfrac><mi>N</mi><mn>2</mn></mfrac></math> and whose radius is <math><mi>N</mi></math> independent. However, this solution has a divergent energy. In analogy to the replacement of the four-dimensional Maxwell action with the BI action, which renders the classical energy of a point charge finite, for the three-dimensional theory which includes a CS term such a replacement leads to a finite energy for the solution of above. We refer to this soliton as a CSBIon solution, representing a finite energy version of the fundamental (sourced) charged electron of Maxwell theory in four dimensions. In three dimensions the <math><mrow><mi>BI</mi><mo>+</mo><mi>CS</mi></mrow></math> action has a static charged solution with finite energy and no source, hence a soliton solution. The CSBIon, similar to its Maxwellian predecessor, has a charge <math><mi>N</mi></math>, angular momentum proportional to <math><mi>N</mi></math> and an <math><mi>N</mi></math>-independent radius. We also present other nonlinear modifications of Maxwell theory that admit similar solitons. The CSBIon may be relevant in various holographic scenarios. In particular, it may describe a D6-brane wrapping an <math><msup><mi>S</mi><mn>4</mn></msup></math> in a compactified D4-brane background. We believe that the CSBIon may play a role in condensed matter systems in <math><mrow><mn>2</mn><mo>+</mo><mn>1</mn></mrow></math> dimensions like graphene sheets.

Brazil

Horatiu Nastase

Israel

Jacob Sonnenschein

Charged soliton of the three-dimensional <math><mrow><mi>CS</mi><mo>+</mo><mi>BI</mi></mrow></math> Abelian gauge theory

Integrable string sigma models on AdS3 backgrounds with 16 supersymmetries have the distinguishing feature that their superisometry group is a direct product. As a result the deformation theory of these models is particularly rich since the two supergroups in the product can be deformed independently. We construct bi-η and bi-λ deformations of two classes of ℤ 4 permutation supercoset sigma models, which describe sectors of the Green-Schwarz and pure-spinor string worldsheet theories on type II AdS3 backgrounds with pure R-R flux. We discuss an important limit of these models when one supergroup is undeformed. The associated deformed supergravity background should preserve 8 supersymmetries and is expected to have better properties than the full bi-deformation. As a step towards investigating the quantum properties of these models, we study the two-loop RG flow of the bosonic truncation of the bi-λ deformation.

United Kingdom

Ben Hoare

France

Nat Levine

Fiona Seibold

Bi-η and bi-λ deformations of ℤ 4 permutation supercosets

We present the vector, scalar, and tensor renormalization constants (RCs) using overlap fermions with either regularization independent momentum subtraction (<math><mrow><mi>RI</mi><mo>/</mo><mi>MOM</mi></mrow></math>) or symmetric momentum subtraction (<math><mrow><mi>RI</mi><mo>/</mo><mi>SMOM</mi></mrow></math>) as the intermediate scheme on the lattice with lattice spacings <math><mi>a</mi></math> from 0.04 fm to 0.12 fm. Our gauge field configurations from the MILC and RBC/UKQCD collaborations include sea quarks using either the domain wall or the HISQ action, respectively. The results show that <math><mrow><mi>RI</mi><mo>/</mo><mi>MOM</mi></mrow></math> and <math><mrow><mi>RI</mi><mo>/</mo><mi>SMOM</mi></mrow></math> can provide consistent renormalization constants to the <math><mover><mi>MS</mi><mo>¯</mo></mover></math> scheme, after proper <math><msup><mi>a</mi><mn>2</mn></msup><msup><mi>p</mi><mn>2</mn></msup></math> extrapolations. But at <math><mi>p</mi><mo>∼</mo><mn>2</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>, both <math><mrow><mi>RI</mi><mo>/</mo><mi>MOM</mi></mrow></math> and <math><mrow><mi>RI</mi><mo>/</mo><mi>SMOM</mi></mrow></math> suffer from nonperturbative effects which cannot be removed by the perturbative matching. The comparison between the results with different sea actions also suggests that the renormalization constant is discernibly sensitive to the lattice spacing but not to the bare gauge coupling in the gauge action.

Fangcheng He

Zhaofeng Liu

<math><mrow><mi>RI</mi><mo>/</mo><mi>MOM</mi></mrow></math> and <math><mrow><mi>RI</mi><mo>/</mo><mi>SMOM</mi></mrow></math> renormalization of quark bilinear operators using overlap fermions