The high-density region of the QCD phase diagram displays an intricate competition between color superconductivity and the QCD Kondo effect due to color exchange in quark matter containing a single heavy quark impurity. We explore the characteristic impurity-induced superconducting subgap states arising in such systems by generalizing the surrogate model solver, recently considered in the context of condensed matter physics [<a href="http://dx.doi.org/10.1103/PhysRevB.108.L220506">Phys. Rev. B 108, L220506 (2023)</a>]. The method consists of approximating the full superconducting bulk by only a small number of effective levels whose parameters are chosen so as to best reproduce the Matsubara frequency dependence of the impurity-bulk hybridization function. We numerically solve a surrogate QCD Kondo model describing a quantum impurity color exchange coupled to a two-color two-flavor superconducting bulk. The results directly indicate the presence of multiple phase transitions as the coupling of the impurity to the bulk is increased, due to the interplay between various overscreened states. The methods introduced here are straightforward enough to be extended to more realistic QCD scenarios.

Romania

Virgil V. Baran

Denmark

Jens Paaske

Yu-Shiba-Rusinov states in color-superconducting quark matter

We establish a precise correspondence between the giant graviton expansion of the superconformal index of field theories in $\textit{D}$ ≤ 4, and the master volume formalism of Gauntlett, Martelli and Sparks (GMS) which determines the near horizon geometries of certain BPS black holes and black strings in supergravity. We focus on 4d $$ \mathcal{N} $$ = 1 superconformal field theories arising on the world volume of $\textit{N}$ D3 branes placed at the tip of a cone over a toric Sasaki-Einstein manifold SE , the simplest example of which is $\textit{S}$ , corresponding to $$ \mathcal{N} $$ = 4 super-Yang-Mills. The giant graviton expansion realises the superconformal index as the sum of contributions from wrapped D3 branes in the dual AdS × SE . We argue that, for large wrapping numbers, the asymptotics of each such contribution is governed by the $\textit{master volume}$ of a particular metric deformation of SE (suitably fibred over $\textit{S}$ ). In particular, the wrapping numbers of a generic giant graviton configuration are identified with Kähler moduli of the corresponding metric. We further show that at large $\textit{N}$ the entropy function of the relevant AdS × SE BPS rotating black hole is recovered by extremising over these moduli. Our results suggest that the complex Euclidean geometries corresponding to rotating BPS black holes in AdS are determined by a close analogue of GMS volume minimisation, and that conversely, the off-shell geometries considered in such minimisation procedures should be understood as the near-horizon geometries of back-reacted giant gravitons. We present analogous results for 3d $$ \mathcal{N} $$ = 2 theories holographically dual to M-theory on AdS × SE .

Taiwan

Japan

Heng-Yu Chen

United Kingdom

Nick Dorey

Sanefumi Moriyama

Rishi Mouland

Czechia

Canberk Şanlı

Giant gravitons and volume minimisation

We study $ \cos2\phi $ azimuthal asymmetry in doubly longitudinally polarized proton-proton Drell-Yan collisions within the transverse momentum dependent factorization framework. The asymmetry arises from the convolution of the longitudinal transversity distribution $ h_{1L}^{\perp} $ for both protons. Using the Bacchetta-Delcarro-Pisano-Radici-Signori parameterization for the nonperturbative Sudakov form factor and the Wandzura-Wilczek approximation for collinear $ h_{1L}^{\perp} $ , we predict the double spin asymmetry $ A_{LL}^{\cos2\phi} $ at RHIC and NICA kinematics. Our results demonstrate sensitivity to sea quark distributions, with the asymmetry reaching up to 25% for maximal sea quark contributions. These predictions highlight the potential of polarized Drell-Yan measurements to probe sea quark dynamics and advance our understanding of nucleon structures.

China

Hui Li

Ting Hu

Liang-Liang Liu

Xiao-Yu Wang

Zhun Lu

Asymmetry ${{\boldsymbol A}_{\boldsymbol{LL}}^{\bf\cos2\boldsymbol\phi}} $ in the polarized proton-proton Drell-Yan process within TMD factorization * Hui Li is supported by Fundamental Research Program of Shanxi Province (202203021222224) and Natural Science Foundation of Shanxi Normal University (JCYJ2023021). Xiao-Yu Wang is supported by the Natural Science Foundation of Henan Province (242300421377, 232300421140)

The horizon of black hole is surrounded by the photon sphere and an outside observer cannot easily examine the geometry inside the photon sphere. In this note, we propose a way to investigate the region from dual conformal field theory by making use of AdS/CFT correspondence. We first construct gravastar geometry as an asymptotic anti-de Sitter spacetime, where the region inside the photon sphere is replaced by a horizon-less geometry. It is known that bulk-cone singularities in the retarded Green function in dual conformal field theory can encode the bulk null geodesics. We then compute numerically the retarded Green function from the bulk theory and observe bulk-cone singularities corresponding to null geodesics traveling into the interior region. In this way, we show that it is possible to examine the region inside the photon sphere from bulk-cone singularities of dual conformal field theory.

Yasuaki Hikida

Yasutaka Koga

AdS gravastar and bulk-cone singularities

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.

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 determine the complex geometries dual to the semi-classical saddles in three-dimensional gravity with positive or negative cosmological constant. We examine the semi-classical saddles in Liouville field theory and interpret them in terms of gravity theory. For this, we describe the gravity theory by Chern-Simons theory and classify the possible saddles based on the homotopy group argument. We further realize the semi-classical saddles using the mini-superspace model of quantum gravity and explicitly determine the integral contour. In the case of positive cosmological constant, we recovered the geometry used for no-boundary proposal of Hartle and Hawking. In the case of negative cosmological constant, the geometry can be identified with Euclidean anti-de Sitter space attached with imaginary radius spheres. The geometry should be unphysical and several arguments on this issue are provided. Partial results were already presented in our earlier letter, and more detailed derivations and explanations on the results are given along with additional results. In particular, we reproduce the classical Liouville action from the Chern-Simons formulation of dual gravity theory.

Yusuke Taki

Takahiro Uetoko

The semi-classical saddles in three-dimensional gravity via holography and mini-superspace approach

We find out the complex geometries corresponding to the semiclassical saddles of three-dimensional quantum gravity by making use of the known results of dual conformal field theory (CFT), which is effectively given by Liouville field theory. We examine both the cases with positive and negative cosmological constants. We determine the set of semiclassical saddles to choose from the homotopy argument in the Chern-Simons formulation combined with CFT results and provide strong supports from the minisuperspace approach to the quantum gravity. For the case of positive cosmological constant, partial results were already obtained in our previous works, and they are consistent with the current ones. For the case of negative cosmological constant, we identify the geometry corresponding a semiclassical saddle with three-dimensional Euclidean anti–de Sitter space dressed with imaginary radius three-dimensional spheres. The geometry is generically unphysical, but the fact itself should not lead to any problems as derived from consistent dual CFT. We thus find an intriguing example, where the gravity path integral is performed over unphysical geometries.

Semiclassical saddles of three-dimensional gravity via holography

We examine the black hole solutions of <math><mrow><msub><mrow><mi>dS</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></math> gravity by applying the explicit <math><mrow><msub><mrow><mi>dS</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow><mo>/</mo><msub><mrow><mi>CFT</mi></mrow><mn>2</mn></msub></math> correspondence. The gravity theory is described by Chern-Simons theory with complex gauge group <math><mrow><mi>SL</mi><mo>(</mo><mn>2</mn><mo>,</mo><mi>C</mi><mo>)</mo></mrow></math>, and the complexified theory is known to have too many saddle points. We determine the set of “allowable geometry” from dual conformal field theory correlators. Concretely, we classify the possible complex solutions corresponding to <math><mrow><msub><mrow><mi>dS</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></math> black holes from Liouville two-point functions. We extend the analysis to Liouville multipoint functions and among others we study geometry corresponding to two linked Wilson loops on <math><msup><mi>S</mi><mn>3</mn></msup></math> by the monodromy matrix of Liouville four-point function. Some parts of the results were presented in a previous letter but here they are explained in more details and extended in various ways. In particular, we generalize the results to the case with higher-spin gravity by focusing the effects of higher-spin charges.

Complex saddles of Chern-Simons gravity and <math><mrow><msub><mrow><mi>dS</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow><mo>/</mo><msub><mrow><mi>CFT</mi></mrow><mn>2</mn></msub></math> correspondence

We determine complex saddles of three-dimensional gravity with a positive cosmological constant by applying the recently proposed holography. It is sometimes useful to consider a complexified metric to study quantum gravity as in the case of the no-boundary proposal by Hartle and Hawking. However, there would be too many saddles for complexified gravity, and we should determine which saddles to take. We describe the gravity theory by three-dimensional <math><mrow><mi>SL</mi><mo>(</mo><mn>2</mn><mo>,</mo><mi>C</mi><mo>)</mo></mrow></math> Chern-Simons theory. At the leading order in the Newton constant, its holographic dual is given by Liouville theory with a large imaginary central charge. We examine geometry with a conical defect, called a de Sitter black hole, from a Liouville two-point function. We also consider geometry with two conical defects, whose saddles are determined by the monodromy matrix of Liouville four-point function. Utilizing Chern-Simons description, we extend the similar analysis to the case with higher-spin gravity.

Complex saddles of three-dimensional de Sitter gravity via holography

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.

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