Abstract The open N = 2 string theory is defined on the 4D space-time with the split signature (+, +, −, −). The string field theory action of the open N = 2 string theory is described by the 4D Wess–Zumino–Witten (WZW$_{4}$) model. The equation of motion of the WZW$_{4}$ model is the Yang equation, which is equivalent to the anti-self-dual Yang–Mills equation. In this paper, we study soliton-type classical solutions of the WZW$_{4}$ model in the split signature by calculating the action density of the WZW$_{4}$ model. We find that the action density of the one-soliton solutions is localized on a 3D hyperplane. This shows that there would be codimension-one-solitonic objects, or equivalently some kind of three-branes in the open N = 2 string theory. We also prove that, in the asymptotic region of the space-time, the action density of the n-soliton solutions is a “non-linear superposition” of n one-solitons. This suggests the existence of n intersecting three-branes in the N = 2 strings. Finally we make a reduction to a (1 + 2)D real space-time to calculate the energy densities of the soliton solutions. We can successfully evaluate the energy distribution for the two-soliton solutions and find that there is no singularity in the interacting region. This implies the existence of smooth intersecting codimension-one branes in the whole region. Soliton solutions in the Euclidean signature are also discussed.

Japan

Masashi Hamanaka

Shan-Chi Huang

Hiroaki Kanno

Solitons in open = 2 String Theory Kahler-Chen-Simons theory A tour through N=2 strings On soliton solutions of the anti-self-dual Yang-Mills equations from the perspective of integrable systems Soliton solutions in an integrable chiral model in 2+1 dimensions On the space-time monopole equation A review on tachyon condensation in open string field theories Soliton equations as dynamical systems on infinite dimensional Grassmann manifold

In this study, we investigate the impact of jet quenching on the   $ p_{T} $   dispersion (  $ p_{T} $  ) of inclusive jets (  $ p_{T} $  ) in central Pb+Pb (0%–10%) collisions at   $ p_{T} $   TeV. The partonic spectrum in the initial hard scattering of elementary collisions is obtained by an event generator POWHEG+PYTHIA, which matches the next-to-leading order (NLO) matrix elements with parton showering, and the energy loss of a fast parton traversing through hot/dense QCD medium is calculated using Monte Carlo simulation within the Higher-Twist formalism of jet quenching in heavy-ion collisions. We present model calculations of the normalized   $ p_{T} $   distributions of inclusive jets in p+p and central Pb+Pb collisions at   $ p_{T} $   TeV, which offer good descriptions of ALICE measurements. It is shown that the   $ p_{T} $   distributions of inclusive jets in central Pb+Pb collisions shift significantly to a higher   $ p_{T} $   region relative to those in p+p collisions. Thus, the nuclear modification ratio of the   $ p_{T} $   distributions of inclusive jets is smaller than unity in the small   $ p_{T} $   region and larger than one in the large   $ p_{T} $   region. This behavior is caused by a more uneven   $ p_{T} $   distribution for jet constituents as well as the fraction alteration of quark/gluon initiated jets in heavy-ion collisions. The difference in   $ p_{T} $   distribution between groomed and ungroomed jets in Pb+Pb collisions is also discussed.

China

Shi-Yong Chen

Jun Yan

Wei Dai

Ben-Wei Zhang

En-Ke Wang

  Dispersion of Inclusive Jets in High-energy Nuclear Collisions  

Motivated by the problem of expanding the single-trace tree-level amplitude of Einstein-Yang-Mills theory to the BCJ basis of Yang-Mills amplitudes, we present an alternative expansion formula in gauge invariant vector space. Starting from a generic vector space consisting of polynomials of momenta and polarization vectors, we define a new sub-space as a gauge invariant vector space by imposing constraints on the gauge invariant conditions. To characterize this sub-space, we compute its dimension and construct an explicit gauge invariant basis from it. We propose an expansion formula in this gauge invariant basis with expansion coefficients being linear combinations of the Yang-Mills amplitude, manifesting the gauge invariance of both the expansion basis and coefficients. With the help of quivers, we compute the expansion coefficients via differential operators and demonstrate the general expansion algorithm using several examples.

Bo Feng

Xiao-Di Li

Rijun Huang

Expansion of EYM amplitudes in gauge invariant vector space B.F. is supported by Qiu-Shi Funding and the National Natural Science Foundation of China (NSFC) (11935013, 11575156); R.H. is supported by the National Natural Science Foundation of China (NSFC) (11805102), Natural Science Foundation of Jiangsu Province (BK20180724) and ShuangChuang Talent Program of Jiangsu Province

We present the first theoretical study of medium modifications of the global geometrical pattern, i.e., transverse sphericity ( $$S_{\perp }$$  <math> <msub> <mi>S</mi> <mo>⊥</mo> </msub> </math>  ) distribution of jet events with parton energy loss in relativistic heavy-ion collisions. In our investigation, POWHEG + PYTHIA is employed to make an accurate description of transverse sphericity in the p + p baseline, which combines the next-to-leading order (NLO) pQCD calculations with the matched parton shower (PS). The Linear Boltzmann Transport (LBT) model of the parton energy loss is implemented to simulate the in-medium evolution of jets. We calculate the event normalized transverse sphericity distribution in central Pb + Pb collisions at the LHC, and give its medium modifications. An enhancement of transverse sphericity distribution at small  $$S_{\perp }$$  <math> <msub> <mi>S</mi> <mo>⊥</mo> </msub> </math>   region but a suppression at large  $$S_{\perp }$$  <math> <msub> <mi>S</mi> <mo>⊥</mo> </msub> </math>   region are observed in A + A collisions as compared to their p + p references, which indicates that in overall the geometry of jet events in Pb + Pb becomes more pencil-like. We demonstrate that for events with 2 jets in the final-state of heavy-ion collisions, the jet quenching makes the geometry more sphere-like with medium-induced gluon radiation. However, for events with  $$\ge 3$$  <math> <mrow> <mo>≥</mo> <mn>3</mn> </mrow> </math>   jets, parton energy loss in the QCD medium leads to the events more pencil-like due to jet number reduction, where less energetic jets may lose their energies and then fall off the jet selection kinematic cut. These two effects offset each other and in the end result in more jetty events in heavy-ion collisions relative to that in p + p.

Shan-Liang Zhang

Qing Zhang

The global geometrical property of jet events in high-energy nuclear collisions

The averaged jet charge characterizes the electric charge of the initiating parton and provides a powerful tool to distinguish quark jets from gluon jets. We predict, for the first time, the medium modification of the averaged jet charge in the heavy-ion collisions at the LHC, where jet productions in p+p collisions are simulated by PYTHIA6, and the parton energy loss in QGP is calculated with two Monte Carlo models of jet quenching: PYQUEN and JEWEL. We found that the distribution of averaged jet charge is significantly suppressed by initial state isospin effects due to the participation of neutrons with zero electric charge during nuclear collisions. The considerable enhancement of the averaged jet charge in central Pb+Pb collisions is observed relative to peripheral collisions, since the jet quenching effect is more pronounced in central collisions. The distinct feature of the averaged jet charge between quark and gluon jets, along with the sensitivity of medium modifications on the jet charge to flavor dependence of the parton energy loss, could be very useful to discriminate the energy loss pattern between quark and gluon jets in heavy-ion collisions.

Enke Wang

Jet charge in high-energy nuclear collisions This research is supported in part by the NSFC of China with Project Nos. 11935007 and 11435004

In the present paper, the exact solutions of spherically symmetrical Einstein field equations describing wormholes supported by phantom energy that violates the null energy condition from Shan–Chen background fluid are obtained. We have considered the important case of the model parameter ψ≈1 , which corresponds to the “saturation effect”, and this regime corresponds to an effective form of “asymptotic freedom” for the fluids, but occurring at cosmological rather than subnuclear scales. Then we investigate the allowed range for the values of the model parameters g and ω when the spacetime metrics describe wormholes and discuss the possible singularities of the solutions, finding that the obtained spacetimes are geodesically complete. Furthermore, we construct two traversable wormholes through matching our obtained interior solutions to the exterior Schwarzschild solutions and analyze the traversablities of the wormholes. Finally, we consider the case of anisotropic pressure and discover that the transverse pressure also crosses the phantom divide -1 with the growth of the wormhole dimension, and it tends to be the same as the radial pressure with the growth of the wormhole radius.

Deng Wang

Xin-He Meng

Wormholes supported by phantom energy from Shan–Chen cosmological fluids