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We propose the stringy description of the system consisting of two heavy and four light quarks in the case of two light flavors of equal mass. As an application, we consider the three low-lying Born-Oppenheimer potentials as a function of the heavy quark separation. Our analysis shows that the ground state potential is described in terms of both hadro-quarkonia and hadronic molecules. A connected string configuration makes the dominant contribution to the potential of an excited state at small separations, and for separations larger than $0.1\,\text{fm}$, it exhibits the diquark-diquark-diquark structure $[Qq][Qq][qq]$. For better understanding the quark organization inside the system, we introduce several critical separations related to the processes of string reconnection, breaking and junction annihilation. We also discuss the simplest string configurations including the five-string junctions and their implications for the system, in particular the emergence of composite quark objects different from diquarks and the process of junction fusion., Comment: 35 pages, many figures. arXiv admin note: text overlap with arXiv:2306.08581; v2: minor corrections; v3: clarifications and reference added

This is the second of two companion papers in which we continue to develop the construction of the doubly heavy pentaquark systems using the gauge/string duality. In this paper, we propose a stringy description of the $Q\bar Qqqq$ system in the case of two light flavors. Our goal is to explore the lower-lying Born-Oppenheimer potentials as a function of the separation distance between the heavy quark-antiquark pair. The analysis shows that the ground state Born-Oppenheimer potential is described in terms of both hadro-quarkonia and hadronic molecules. Meanwhile a standard pentaquark configuration, which describes a genuine five-quark interaction, makes the dominant contribution to a higher lying potential. This configuration has an antiquark-diquark-diquark structure $\bar Q[qq][Qq]$ for separations larger than $0.1\,\text{fm}$. The latter enables us to establish a relation among the masses of hadrons in the heavy quark limit. To describe the structure of the potentials more clear, we define some critical separations that are related to the processes of string reconnection, breaking and junction annihilation. Additionally, we consider the generalized baryon vertices, where more than three strings can meet, and explore their implications for the pentaquark systems., Comment: 29 pages, many figures. arXiv admin note: text overlap with arXiv:2211.12305; v2: minor corrections; v3: clarifications and references added; v4: misprint corrected

For the case of two light flavors we propose the stringy description of the system consisting of two heavy and three light quarks, with the aim of exploring the quark organization inside the system and its low-lying Born-Oppenheimer potentials as a function of the heavy quark separation. Our analysis reveals several critical separations related to the processes of string reconnection, breaking and junction annihilation. We find that a compact pentaquark configuration makes the dominant contribution to the potential of the first excited state at small separations, and for separations larger than $0.1\,\text{fm}$, the antiquark-diquark-diquark structure emerges. Moreover, it turns out that the length scale of string junction annihilation is the same as that for the $QQ\bar q\bar q$ system. We also discuss the relation to the potential of the $QQq$ system and some relations among the masses of hadrons in the heavy quark limit., Comment: 26 pages, many figures. arXiv admin note: text overlap with arXiv:2205.12119; v2: minor corrections; v3: clarification added, typos fixed, to appear in PRD

For the case of two light flavors we propose the stringy description of the system made of one heavy and one light quark-antiquark pair, with the aim of exploring the two lower-lying Born-Oppenheimer potentials as a function of a separation of the heavy quark-antiquark pair. Our analysis reveals three critical separations related to the processes of string reconnection, breaking and junction annihilation. In particular, for the ground state potential only the process of string reconnection matters. We find that a tetraquark state makes the dominant contribution to the potential of the first excited state at small separations, and this is the big difference with the $QQ\bar q\bar q$-quark system where it does so to the ground state potential. Another big difference is the emergence of the full diquark picture $[Qq][\bar Q\bar q]$ rather than the partial picture $QQ[\bar q\bar q]$ for the tetraquark state. On the other hand, the scales of string junction annihilation, below which the systems can be thought of mainly as the compact tetraquarks, are very close for both cases and become almost the same if the phenomenological rule $E_{QQ}=\frac{1}{2} E_{Q\bar Q}$ holds. The same is also true for the screening lengths whose values are in agreement with lattice QCD., Comment: 22 pages, many figures; v2: typos corrected; v3: improved discussion, references added; v4: typo corrected; v5: the sign in (3.23) corrected

We propose a string theory construction for the system of two heavy quarks and two light antiquarks. The potential of the system is a function of separation between the quarks. We define a critical separation distance below which the system can be thought of mainly as a compact tetraquark. The results show the universality of the string tension and factorization at small separations expected from heavy quark-diquark symmetry. Our estimate of the screening length is in the range of lattice QCD. We also make a comparison with the potential of the $QQq$ system. The potentials look very similar at small quark separations but at larger separations they differ. The reason for this is that the flattening of the potentials happens at two well-separated scales as follows from the two different mechanisms: string breaking by light quarks for $QQq$ and string junction annihilation for $QQ\bar q\bar q$. Moreover, a similar construction can also be applied to the $\bar Q\bar Q qq$ system., Comment: 20 pages, 12 Figures; v2: reference added; v3: typos corrected, reference and comments added

Using the gauge/string duality, we model a heavy quark-antiquark pair in a color singlet state moving through a cold medium and explore the consequences of temperature and velocity on string breaking. We show that the string breaking distance slowly varies with temperature and velocity away from the critical line but could fall near it., Comment: 13 pages, 8 figures; v2. minor corrections, references added, Nucl.Phys.B version

Making use of the gauge/string duality, it is possible to study some aspects of the string breaking phenomenon in the three quark system. Our results point out that the string breaking distance is not universal and depends on quark geometry. The estimates of the ratio of the string breaking distance in the three quark system to that in the quark-antiquark system would range approximately from $\frac{2}{3}$ to $1$. In addition, it is shown that there are special geometries which allow more than one breaking distance., Comment: v2: 30 pages, 19 figures, 1 table, discussion improved, title modified, references added, accepted version for PRD; v3: references updated

We propose a string theory construction which allows us to study properties of the potential of two heavy quarks coupled to a light quark. In such a case, the potential is a function of separation between the heavy quarks. The results show the universality of the string tension and factorization at small separations expected from heavy quark-diquark symmetry. In addition, we make an estimate of the string breaking distance. With the parameter values we use, this distance is found to be almost the same as that for the heavy quark-antiquark potential. We also discuss the heavy quark-quark potential and its relation to Lipkin rule., Comment: 22 pages, 13 figures; v2: typos fixed; v3: discussion improved, results unchanged, reference added; v4: sect.V rewritten, references added, accepted for publication in JHEP

The string breaking phenomenon in QCD can be studied using the gauge/string duality. In this approach, one can make estimates of some of the string breaking distances at non-zero temperature and baryon chemical potential. These point towards the enhancement of baryon production in strong decays of heavy mesons in dense baryonic medium., Comment: 20 pages, 7 figures, extended version of arXiv:1909.12771; v2: minor corrections; v3: matches published version

We consider the string breaking phenomenon within effective string models which purport to mimic QCD with two light flavors, with a special attention to baryon modes. We make some estimates of the string breaking distances at zero and non-zero baryon chemical potentials. Our estimates point towards the enhancement of baryon production in strong decays of heavy mesons in dense baryonic matter. We also suggest that the enhanced production of $\Lambda_c^+$ baryons in PbPb collisions is mainly due to larger values of chemical potential., Comment: 6 pages, 3 figures; v2: typos corrected; v3: modification in title, comments and references added, journal version

We use gauge/string duality to model a heavy quark-antiquark pair in a color singlet moving through a thermal plasma. In particular, we explore the effect of velocity on the string tension and Debye screening mass. Then we apply the results to the analysis of heavy quarkonium bound states. With some assumptions, we estimate the characteristic size of quarkonium and its dissociation temperature., Comment: 17 pages, 8 figures; v2: improved presentation and discussion, typos corrected, references added

We use gauge/string duality to model a doubly heavy diquark in a color antitriplet moving in a thermal plasma at temperatures near the critical. With the assumption that there is no relative motion between the constituents, we calculate the drag force on the diquark. At high enough speed we find that diquark string configurations develop a cusp. In addition, we estimate the spatial string tension at non-zero baryon chemical potential, and also briefly discuss an extension to a triply heavy triquark in a color triplet., Comment: 22 pages, many figures; v2: typos corrected; v3: minor improvements and corrections made

Heavy quark transport coefficients in a strongly coupled Quark-Gluon Plasma can be evaluated using a gauge/string duality and lattice QCD. Via this duality, one can argue that for low momenta the drag coefficient for heavy quarks is proportional to the spatial string tension. Such a tension is well studied on the lattice that allows one to straightforwardly make non-perturbative estimates of the heavy quark diffusion coefficients near the critical point. The obtained results are consistent with those in the literature., Comment: 4 pages, 3 figures; v2. figure added, presentation improved; v3. reference added, minor corrections

We consider a multi-string configuration that provides a new way to compute the expectation value of the Polyakov loop in a five-dimensional framework known as AdS/QCD. The obtained results are in reasonably good agreement with those obtained by lattice simulations for pure SU(3) gauge theory and also by the usual single string configuration., Comment: 11 pages, 7 figures; v2: comments and references added, published version

We use gauge/string duality to estimate the Debye screening mass at non-zero temperature and baryon chemical potential. We interpret this mass as the smallest one in the open string channel. Comparisons are made with the results from holography and lattice QCD., Comment: 26 pages, many figures; v2: presentation improved, typos corrected

We analytically evaluate the expectation value of a baryonic Wilson loop in a holographic model of an SU(3) pure gauge theory. We then discuss three aspects of a static three-quark potential: an aspect of universality which concerns properties independent of a geometric configuration of quarks; a heavy diquark structure; and a relation between the three and two-quark potentials., Comment: 35 pages, many figures; v2: appendix and two figures added, minor improvements in presentation; v3: improved presentation, some points clarified, reference added; v4: typo corrected

We use gauge-string duality to model the $N$-quark potential in pure Yang-Mills theories. For $SU(3)$, the result agrees remarkably well with lattice simulations. The model smoothly interpolates between almost the $\Delta$-law at small distances and the Y-law at large distances., Comment: 5 pages, 4 figures; v2: improved discussion, references added; v3: presentation improved

We use gauge/string duality to model some hybrid pseudo-potentials in a pure SU(N) gauge theory. The pseudo-potentials under consideration can't be described by a single Nambu-Goto string. This is why we call them "exotic". A comparison with the calculation of the pseudo-potential shows the universality of the spatial string tension., Comment: 12 pages, 5 figures; v2: presentation improved, one plot added; v3: final version to appear in PRD. arXiv admin note: substantial text overlap with arXiv:1207.1892

We use gauge/string duality to model some hybrid heavy-quark potentials. The potentials under consideration can't be described by a single Nambu-Goto string. This is why we call them "exotic". For $\Sigma_u^-$, the result is in quite good agreement with lattice simulations., Comment: 14 pages, 5 figures; v2: typos corrected

Three subjects are considered here: the relativistic hydrodynamics equations for a boost-invariant expanding fluid; the fuzzy bag model for the pressure which recently appeared in QCD phenomenology; and the early space-time evolution of the QCD matter, drawn from model studies, which can also be expected to arise in realistic fluid dynamics relevant to heavy ion collisions at LHC., Comment: 10 pages, 5 figures; v3: additional discussion of lattice data, minor clarifications, references added

Using a duality approach we give an example of modeling nonlocal and mixed condensates whose behavior mimics that of QCD. Quantitatively, the estimated value of the condensate parameter $m_0^2$ is approximately $0.6-0.7 GeV^2$., Comment: 10 pages, 3 figures

We use gauge/string duality to analytically evaluate correlation lengths of the renormalized field strength correlators in pure Yang-Mills theories at zero and finite temperature., Comment: 9 pages, 2 figures; v2: new prediction added, discussion improved, to appear in Phys.Lett.B

We make an estimate of the quadratic correction in the pressure of cold quark matter using gauge/string duality., Comment: 7 pages; v.2: reference added; v.3: reference and comments added, version to appear in PRD; v4. final version to appear in PRD; v.5: key reference added

We use gauge/string duality to analytically evaluate the renormalized Polyakov loop in pure Yang-Mills theories. For SU(3), the result is in a quite good agreement with lattice simulations for a broad temperature range., Comment: 4 pages, 2 figures

We give examples of modeling the string free energy whose behavior mimics that of QCD: a power-law at high temperature and an exponential decrease at low temperature. Although the effective description is in terms of strings, no limiting temperature exists, as expected for a crossover., Comment: 7 pages; v3: discussion improved in section 2, figure and references added

The static three-quark potential and pseudo-potential of a pure SU(3) gauge theory are studied in a five-dimensional framework known as AdS/QCD. The results support the Y-ansatz for the baryonic area law. A comparison with the quark-antiquark calculations shows the universality of the string tension as well as the spatial string tension. We also discuss extensions to SU(N) gauge theories., Comment: 18 pages, 7 figures; v2: a few sentences added and typos corrected

The spatial string tension of a SU(N) gauge theory without quarks is calculated using gauge/string duality for 1.2T_c

The thermodynamic properties of a SU(3) gauge theory without quarks are calculated using a string formulation for 1.2T_c < T < 3T_c. The results are in good agreement with the lattice data. We also comment on SU(N) gauge theories., Comment: 10 pages, 5 figures

We test gauge/string duality by evaluating expectation values of small Wilson loops in pure Yang-Mills theories. On the gauge-theory side, there exists rich phenomenology. The dual formulation provides with a universal language to evaluate the gluon condensate and quadratic correction in terms of the metric in the fifth coordinate. Quantitatively, the estimated value of the gluon condensate is approximately 0.010 GeV^4., Comment: 4 pages; v4: minor corrections

In this paper we explore some of the features of a heavy quark-antiquark pair at finite temperature using a five-dimensional framework nowadays known as AdS/QCD. We shall show that the resulting behavior is consistent with our qualitative expectations of thermal gauge theory. Some of the results are in good agreement with the lattice data that provides additional evidence for the validity of the proposed model., Comment: 15 pages, 10 figures; v2: comments added, misprints corrected

We present results of modeling the temperature dependence of the spatial string tension and thermal phase transition in a five-dimensional framework nowadays known as AdS/QCD. For temperatures close to the critical one we find a behaviour remarkably consistent with the lattice results., Comment: 8 pages, 4 figures

We give an example of modeling phenomenological heavy-quark potentials in a five-dimensional framework nowadays known as AdS/QCD. In particular we emphasize the absence of infrared renormalons., Comment: 10 pages, 3 figures; v3: some corrections, to appear in PRD

We make an estimate of the quadratic correction based on gauge/string duality. Like in QCD, it proves to be negative and proportional to the string tension., Comment: 6 pages

We explore the possibilities for scaling violation in gauge theories that have string duals. Like in perturbative QCD, short-distance behaviour yields logarithms that violate the scaling., Comment: 11 pages, 4 figures; v3: typos corrected, minor changes, to appear in PRD

We propose stringy hadronic amplitudes that combine some of the features of sister trajectories and running tension. By summing over string amplitudes with varying Regge trajectories that have integer tension and converging intercept, we obtain parton hard-scattering and Regge soft-scattering behaviors, while preserving discrete poles in both momentum and angular momentum., Comment: 17 pages; a new section and references added

We propose a possible scheme for getting the known QCD scaling laws within string theory. In particular, we consider amplitudes for exclusive scattering of hadrons at large momentum transfer, hadronic form factors and distribution functions., Comment: 13 pages, 2 figures, a comment and a reference added, a final version to appear in Physical Review D