We present a microscopic calculation of the electric conductivity and net-particle diffusion coefficients for a viscous and resistive ultra-relativistic plasma. Our results might be of interest for several astrophysical and cosmological problems, but the main physical application we have in mind is the hot deconfined matter produced in relativistic heavy-ion collisions. Accordingly, as charged particles of the medium we take three species (flavors) of light (massless for the sake of simplicity) quarks – $\textit{u}$, $\textit{d}$ and $\textit{s}$ – and antiquarks, entailing the existence of three macroscopic conserved charges: baryon number $$\mathcal{B}$$ , electric charge $\textit{Q}$ and strangeness $\textit{S}$. Our results are valid both in a weakly and in a strongly-magnetized plasma, where the energy stored in the magnetic field is comparable to the one carried by the medium particles. Actually, for a conformal fluid, the behavior of the system only depends on the ratio between the thermal and the magnetic pressure, the so-called plasma beta-parameter, acting as a scaling variable. Our calculation, starting from a relativistic Boltzmann-Vlasov equation, is based on a generalized Chapman–Enskog approach in which space-time gradients and the local electric field are treated as first-order quantities in a perturbative expansion, while terms containing magnetic corrections are considered of zeroth order and hence self-consistently resummed. We find that, also in the strong-field limit, for each conserved charge a generalized Wiedemann-Franz law, connecting charge conductivity and diffusion coefficient, exists. However these transport coefficients acquire a non-trivial tensor structure, reflecting the development of a longitudinal, a transverse and a Hall current as a response to electric fields or density gradients.

Italy

Ferdinando Frascà

Andrea Beraudo

Luca Del Zanna

Electric conductivity and flavor diffusion in a viscous, resistive quark-gluon plasma for weak and strong magnetic fields

Abstract We discuss spontaneous chiral symmetry breaking and the quark bilinear condensate in large-N$_{c}$ quantum chromodynamics (QCD). It is known that the existence of the η′ meson is implied in large-N$_{c}$ QCD, as pointed out by Witten[27] and Veneziano[28]. First, we show that the existence of η′ and the Ward–Takahashi identities implies the existence of Nambu–Goldstone bosons from chiral symmetry breaking SU(N$_{f}$)$_{L}$ × SU(N$_{f}$)$_{R}$ → SU(N$_{f}$)$_{V}$. Second, we show that a QCD inequality implies a non-zero lower bound on the quark bilinear condensate.

Japan

Ryosuke Sato

Chiral symmetry breaking and the quark bilinear condensate in large- Qcd La Rivista del Nuovo Cimento Quarks and strings on a lattice

We study the orientifold projections of the <math><mi>N</mi><mo>=</mo><mn>1</mn></math> superconformal field theories describing D3-branes probing the Pseudo del Pezzo singularities PdP<math><msub><mrow></mrow><mrow><mn>3</mn><mi>b</mi></mrow></msub></math> and PdP<math><msub><mrow></mrow><mrow><mn>3</mn><mi>c</mi></mrow></msub></math>. The PdP<math><msub><mrow></mrow><mrow><mn>3</mn><mi>c</mi></mrow></msub></math> parent theory admits two inequivalent orientifolds. Exploiting a maximization, we find that one of the two has an a-charge smaller than what one would expect from the orientifold projection, which suggests that the theory flows to the fixed point in the infrared. Surprisingly, the value of a coincides with the charge of the unoriented PdP<math><msub><mrow></mrow><mrow><mn>3</mn><mi>b</mi></mrow></msub></math> and we interpret this as the sign of an infrared duality.

Andrea Antinucci

Salvo Mancani

Fabio Riccioni

Infrared duality in unoriented Pseudo del Pezzo

Motivated by understanding M2-branes, we propose to reformulate partition functions of M2-branes by quantum curves. Especially, we focus on the backgrounds of del Pezzo geometries, which enjoy Weyl group symmetries of exceptional algebras. We construct quantum curves explicitly and turn to the analysis of classical phase space areas and quantum mirror maps. We find that the group structure helps in clarifying previous subtleties, such as the shift of the chemical potential in the area and the identification of the overall factor of the spectral operator in the mirror map. We list the multiplicities characterizing the quantum mirror maps and find that the decoupling relation known for the BPS indices works for the mirror maps. As a result, with the group structure we can present explicitly the statement for the correspondence between spectral theories and topological strings on del Pezzo geometries.

Sanefumi Moriyama

Spectral theories and topological strings on del Pezzo geometries

At the earliest times after a heavy-ion collision, the magnetic field created by the spectator nucleons will generate an extremely strong, albeit rapidly decreasing in time, magnetic field. The impact of this magnetic field may have detectable consequences, and is believed to drive anomalous transport effects like the Chiral Magnetic Effect (CME). We detail an exploratory study on the effects of a dynamical magnetic field on the hydrodynamic medium created in the collisions of two ultrarelativistic heavy-ions, using the framework of numerical ideal MagnetoHydroDynamics (MHD) with the ECHO-QGP code. In this study, we consider a magnetic field captured in a conducting medium, where the conductivity can receive contributions from the electromagnetic conductivity $$\sigma $$ <math><mi>σ</mi></math>  and the chiral magnetic conductivity $$\sigma _{\chi }$$ <math><msub><mi>σ</mi><mi>χ</mi></msub></math> . We first study the elliptic flow of pions, which we show is relatively unchanged by the introduction of a magnetic field. However, by increasing the magnitude of the magnetic field, we find evidence for an enhancement of the elliptic flow in peripheral collisions. This effect is stronger at RHIC than the LHC, and it is evident already at intermediate collision centralities. Next, we explore the impact of the chiral magnetic conductivity on electric charges produced at the edges of the fireball. This initial $$\sigma _\chi $$ <math><msub><mi>σ</mi><mi>χ</mi></msub></math>  can be understood as a long-wavelength effective description of chiral fermion production. We then demonstrate that this chiral charge, when transported by the MHD medium, produces a charge dipole perpendicular to the reaction plane which extends a few units in rapidity. Assuming charge conservation at the freeze-out surface, we show that the produced charge imbalance can have measurable effects on some experimental observables, like $$v_1$$ <math><msub><mi>v</mi><mn>1</mn></msub></math>  or $$\langle \sin \phi \rangle $$ <math><mrow><mo>⟨</mo><mo>sin</mo><mi>ϕ</mi><mo>⟩</mo></mrow></math> . This demonstrates the ability of a MHD fluid to transport the signature of the initial chiral magnetic fields to late times. We also comment on the limitations of the ideal MHD approximation and detail how further development of a dissipative-resistive model can provide a more realistic description of the QGP.

Finland

Gabriele Inghirami

Mark Mace

South Korea

Yuji Hirono

United States

Dmitri Kharzeev

Germany

Marcus Bleicher

Magnetic fields in heavy ion collisions: flow and charge transport

We investigate the 
					 invariant mass distribution in the 
					 reaction at a center-of-mass energy of 
					 GeV measured by the BESIII collaboration, which concluded that no significant signals were observed for 
					 because of the low statistics. We show, however, that the 
					 invariant mass distribution is compatible with the existence of the 
					 state, appearing as a peak, and a strong cusp structure at the 
					 threshold, resulting from the molecular nature of the 
					 state, which provides a substantial contribution to the reaction. This is consistent with our previous analysis of the 
					 decay measured by the LHCb collaboration. We strongly suggest further measurements of this process with more statistics to clarify the nature of the 
					 and 
					 resonances.
				

China

En Wang

Ju-Jun Xie

Li-Sheng Geng

Spain

Eulogio Oset

The X(4140) and X(4160) resonances in the 
					 reaction Partly supported by the National Natural Science Foundation of China (11735003, 11522539, 11505158, 11475015, 11647601), supported by the Youth Innovation Promotion Association CAS (2016367), Key Research Projects of Henan Higher Education Institutions (20A140027), and the Academic Improvement Project of Zhengzhou University. This work is also partly supported by the Spanish Ministerio de Economia y Competitividad and European FEDER funds under the contract number FIS2014-57026-REDT, FIS2014-51948-C2-1-P, and FIS2014-51948-C2-2-P, the Generalitat Valenciana in the program Prometeo II2014/068, and the proyecto Severo Ochoa del IFIC, SEV-2014-0398.

We revisit a correspondence between toroidal compactifications of M-theory and del Pezzo surfaces, in which rational curves on the del Pezzo are related to <math><mfrac><mn>1</mn><mn>2</mn></mfrac></math>-BPS branes of the corresponding compactification. We argue that curves of higher genus correspond to nongeometric backgrounds of the M-theory compactifications, which are related to exotic branes. In particular, the number of “special directions” of the exotic brane is equal to the genus of the corresponding curve. In addition to predicting three new nongeometric backgrounds, we discuss a relation between addition of curves in the del Pezzo and the brane polarization effect.

Justin Kaidi

Exotic branes from del Pezzo surfaces

The dilepton invariant mass spectra and integrated branching ratios of the single and double Dalitz decays and (; or ) are predicted by means of a data-driven approach based on the use of rational approximants applied to and transition form factor experimental data in the space-like region.

Rafel Escribano

Sergi Gonzàlez-Solís

A data-driven approach to and single and double Dalitz decaysSupported by the FPI scholarship BES-2012-055371 (S.G-S), the Secretaria d’Universitats i Recerca del Departament d’Economia i Coneixement de la Generalitat de Catalunya under grant 2014 SGR 1450, the Ministerio de Ciencia e Innovación under grant FPA2011-25948, the Ministerio de Economía y Competitividad under grants CICYT-FEDER-FPA 2014-55613-P and SEV-2012-0234, the Spanish Consolider-Ingenio 2010 Program CPAN (CSD2007-00042), and the European Commission under program FP7-INFRASTRUCTURES-2011-1 (283286) S.G-S also Received Support from the CAS President’s International Fellowship Initiative for Young International Scientist (2017PM0031)

We present an explicit expression for the grand potential of the U(N )3 superconformal Chern-Simons theory with the Chern-Simons levels being (k, 0, −k). From the viewpoint of the Newton polygon, it is expected that the grand potential is given by the free energy of the topological string theory on the local D 5 del Pezzo geometry, though the explicit identification was a puzzle for years. We show how the expectation is realized explicitly. As a bonus, we can also study the  <math><msub><mi>ℤ</mi><mn>2</mn></msub></math> $$ {\mathbb{Z}}_2 $$ orbifold of this theory and find the grand potential is now given in terms of the local E 7 del Pezzo geometry.

Tomoki Nosaka

Katsuya Yano

Superconformal Chern-Simons theories from del Pezzo geometries

We present an improved version of the ECHO-QGP numerical code, which self-consistently includes for the first time the effects of electromagnetic fields within the framework of relativistic magneto-hydrodynamics (RMHD). We discuss results of its application in relativistic heavy-ion collisions in the limit of infinite electrical conductivity of the plasma. After reviewing the relevant covariant 3+1 formalisms, we illustrate the implementation of the evolution equations in the code and show the results of several tests aimed at assessing the accuracy and robustness of the implementation. After providing some estimates of the magnetic fields arising in non-central high-energy nuclear collisions, we perform full RMHD simulations of the evolution of the quark–gluon plasma in the presence of electromagnetic fields and discuss the results. In our ideal RMHD setup we find that the magnetic field developing in non-central collisions does not significantly modify the elliptic flow of the final hadrons. However, since there are uncertainties in the description of the pre-equilibrium phase and also in the properties of the medium, a more extensive survey of the possible initial conditions as well as the inclusion of dissipative effects are indeed necessary to validate this preliminary result.

Iran

Mohsen Haddadi Moghaddam

Francesco Becattini

Numerical magneto-hydrodynamics for relativistic nuclear collisions