A remarkable double copy relation of Einstein gravity to QCD in Regge asymptotics is $Γ^{μν}= \frac12C^μC^ν- \frac12N^μN^ν$, where $Γ^{μν}$ is the gravitational Lipatov vertex in the $2\to 3$ graviton scattering amplitude, $C^μ$ its Yang-Mills counterpart, and $N^μ$ the QED bremssstrahlung vertex. In QCD, the Lipatov vertex is a fundamental building block of the BFKL equation describing $2\to N$ scattering of gluons at high energies. Likewise, the gravitational Lipatov vertex is a key ingredient in a 2-D effective field theory framework describing trans-Planckian $2\to N$ graviton scattering. We construct a quantitative correspondence between a semi-classical Yang-Mills framework for radiation in gluon shockwave collisions and its counterpart in general relativity. In particular, we demonstrate the Lipatov double copy in a dilute-dilute approximation corresponding to $R_{S,L}$, $R_{S,H}$ $ \ll b$, with $R_{S,L}$, $R_{S,H}$ the respective emergent Schwarzchild radii generated in shockwave collisions and $b$ is the impact parameter. We outline extensions of the correspondence developed here to the dilute-dense computation of gravitational wave radiation in close vicinity of one of the black holes, the construction of graviton propagators in the shockwave background, and a renormalization group approach to compute $2\rightarrow N$ amplitudes that incorporates graviton reggeization and coherent graviton multiple scattering.
Collisions of asymmetric planar shocks in maximally supersymmetric Yang-Mills theory are studied via their dual gravitational formulation in asymptotically anti-de Sitter spacetime. The post-collision hydrodynamic flow is found to be very well described by appropriate means of the results of symmetric shock collisions. This study extends, to asymmetric collisions, previous work of Chesler, Kilbertus, and van der Schee examining the special case of symmetric collisions. Given the universal description of hydrodynamic flow produced by asymmetric planar collisions one can model, quantitatively, n…
We reanalyze high energy QCD scattering regimes from scattering in cut-off AdS via gravity-gauge dualities (a la Polchinski-Strassler). We look at 't Hooft scattering, Regge behaviour and black hole creation in AdS. Black hole creation in the gravity dual is analyzed via gravitational shockwave collisions. We prove the saturation of the QCD Froissart unitarity bound, corresponding to the creation of black holes of AdS size, as suggested by Giddings.
In a previous paper, we have analyzed high energy QCD from AdS-CFT and proved the saturation of the Froissart bound (a purely QCD proof of which is still lacking). In this paper we describe the calculation in more physical terms and map it to QCD language. We find a remarkable agreement with the 1952 Heisenberg description of the saturation (pre-QCD!) in terms of shockwave collisions of pion field distributions. It provides a direct map between gauge theory physics and the gravitational physics on the IR brane of the Randall-Sundrum model. Saturation occurs through black hole production on the…
We analyze the high energy scattering of hadrons in QCD in an effective theory model inspired from a gravity dual description. The nucleons are skyrmion-like solutions of a DBI action, and boosted nucleons give pions field shockwaves necessary for the saturation of the Froissart bound. Nuclei are analogs of BIon crystals, with the DBI skyrmions forming a fluid with a fixed inter-nucleon distance. In shockwave collisions one creates scalar (pion field) ``fireballs'' with horizons of nonzero temperature, whose scaling with mass we calculated. They are analogous to the hydrodynamic ``dumb holes,'…
Exploiting the universality between the QCD critical point and the three dimensional Ising model, closed form expressions derived (arXiv:1506.00645 ) for non-equilibrium critical cumulants on the crossover side of the critical point reveal that they can differ both in magnitude and sign from equilibrium expectations. We demonstrate here that key elements of the Kibble-Zurek framework of non-equilibrium phase transitions can be employed to describe the dynamics of these critical cumulants. Our results suggest that observables sensitive to critical dynamics in heavy-ion collisions should be expr…
The flavor dependence of the QCD phase diagram presents universal properties in the heavy quark limit. For the wide class of models where the quarks are treated at the one-loop level, we show, for arbitrary chemical potential, that the flavor dependence of the critical quark masses-for which the confinement-deconfinement transition is second order-is insensitive to the details of the (confining) gluon dynamics and that the critical temperature is constant along the corresponding critical line. We illustrate this with explicit results in various such one-loop models studied in the literature: e…
We study the universal properties of the phase diagram of QCD near the critical point using the exact renormalization group. For two-flavour QCD and zero quark masses we derive the universal equation of state in the vicinity of the tricritical point. For non-zero quark masses we explain how the universal equation of state of the Ising universality class can be used in order to describe the physical behaviour near the line of critical points. The effective exponents that parametrize the growth of physical quantities, such as the correlation length, are given by combinations of the critical expo…
In these lectures I review some basic examples of how the concepts of universality and scaling can be used to study aspects of the chiral and the deconfinement transition, if not in QCD directly but in QCD-like theories. As an example for flavor dynamics I discuss a quark-hadron model to describe the phase diagram of two-color QCD with the functional renormalization group. Universal aspects of deconfinement are illustrated mainly in the 2+1 dimensional SU(N) gauge theories with second order transition where many exact results from spin models can be exploited.
Estimates of the light hadron masses, decay constants and couplings in AdS/QCD models are generally more accurate than should have been expected. Certain predictions based on the AdS/CFT correspondence, such as the ratio of the equilibrium viscosity to entropy density, are universal and therefore provide firm experimental tests of these models. Other observables, while not completely universal, may be relatively insensitive to model details. We calculate the dependence of a number of low-energy hadronic observables on details of the hard-wall AdS/QCD model. In particular, we vary the infrared …
Using non-trivial mathematical properties of a class of nonlinear evolution equations, we obtain the universal terms in the asymptotic expansion in rapidity of the saturation scale and of the unintegrated gluon density from the Balitsky-Kovchegov equation. These terms are independent of the initial conditions and of the details of the equation. The last subasymptotic terms are new results and complete the list of all possible universal contributions. Universality is interpreted in a general qualitative picture of high energy scattering, in which a scattering process corresponds to a tree struc…
Using recent lattice data on the thermodynamics of QCD in the presence of a background magnetic field, we show that the ratio of transverse to longitudinal pressure exhibits, to good accuracy, a simple scaling behavior over a wide range of temperature and magnetic field, essentially depending only on the ratio $T/\sqrt B$. We compare this QCD response to the corresponding magnetoresponse in maximally supersymmetric Yang Mills theory. Given suitable calibrations defining the comparison, we find excellent agreement. This may be viewed as a further test of the applicability of holographic models …
With proposing a unified description of the fields variation at the level of generating functional, we obtain a new identity for the quark-gluon interaction vertex based on gauge symmetry, which is similar to the Slavnov-Taylor Identities(STIs) based on the Becchi-Rouet-Stora-Tyutin transformation. With these identities, we find that in Landau gauge, the dressing function of the ghost propagator approaches to a constant as its momentum goes to zero, which provides a strong constraint on the infrared behaviour of ghost propagator.
Based on random matrix theory in the unitary ensemble, we derive the double-microscopic massive spectral correlators corresponding to the Dirac operator of QCD_3 with an even number of fermions N_f. We prove that these spectral correlators are universal, and demonstrate that they satisfy exact massive spectral sum rules of QCD_3 in a phase where flavor symmetries are spontaneously broken according to U(N_f) -> U(N_f/2) x U(N_f/2).
We introduce a new non-Hermitian random matrix model for QCD with a baryon chemical potential. This model is a direct chiral extension of a previously studied model that interpolates between the Wigner-Dyson and Ginibre ensembles. We present exact results for all eigenvalue correlations for any number of quark flavors using the orthogonal polynomial method. We also find that the parameters of the model can be scaled to remove the effects of the chemical potential from all thermodynamic quantities until the finite density phase transition is reached. This makes the model and its extensions well…
In this lecture we discuss correlations of the QCD Dirac eigenvalues. We find that below a scale of $E_c\sim Λ/L^2$ they are given by chiral Random Matrix Theory. This follows from analytical arguments based on partially quenched Chiral Perturbation Theory and is substantiated by lattice QCD and instanton liquid simulations.
We consider the class of effective supergravity theories from the weakly coupled heterotic string in which local supersymmetry is broken by gaugino condensation in a hidden sector, with dilaton stabilization achieved through corrections to the classical dilaton Kähler potential. If there is a single hidden condensing (simple) gauge group, the axion is massless (up to contributions from higher dimension operators) above the QCD condensation scale. We show how the standard relation between the axion mass and its Planck scale coupling constant is modified in this class of models due to a contribu…
We review recent results on the phase structure of QCD and bulk QCD thermodynamics. In particular we discuss how universal critical scaling related to spontaneous breaking of the chiral symmetry manifests itself in recent lattice QCD simulations and how the knowledge on non-universal scaling parameter can be utilized in the exploration of the QCD phase diagram. We also show how various (generalized) susceptibilities can be employed to characterize properties of QCD matter at low and hight temperatures, related to deconfining aspects of the QCD transition. Finally, we address the input these la…
We derive an exact unified formula for all condensates (quark and monopole) in the hybrid r vacua in N=2 supersymmetric QCD slightly deformed by a μA^2 term. The gauge group is assumed to be U(N) and the number of the quark flavors N_f subject to the condition N< N_f < 2N. In the r vacua r quarks and N-r-1 monopoles from non-overlapping subgroups of U(N) develop vacuum expectation values (r<N). We then briefly review possible dynamical regimes (confinement, screening, and "instead of confinement") in the hybrid r vacua in μ-deformed N=2 SQCD (the small-μlimit).
We present the general form of a universal soft-collinear distribution operator to compute the soft-virtual cross-section to next-to-next-to-next-to-next-to-leading order (N$^4$LO) in QCD for a process with any number of final state colorless particles in hadron colliders. By acting this universal operator on the pure virtual corrections, which need to be computed explicitly for a process, the soft-virtual cross-section can be obtained. The operator is constructed by exploiting the factorization and renormalization group evolution of amplitudes in QCD, and the universality of soft gluon contri…
Universal Features of Chiral Symmetry Breaking in Large-$N$ QCD
Instituto de Física Teórica UAM-CSIC（UAM-CSIC理论物理研究所）；Universidad Autónoma de Madrid（马德里自治大学）；Hiroshima University（广岛大学）；University of Turin（都灵大学）；INFN（意大利国家核物理研究所）
In these lectures we review recent results on universal fluctuations of QCD Dirac spectra and applications of Random Matrix Theory (RMT) to QCD. We review general properties of Dirac spectra and discuss the relation between chiral symmetry breaking and correlations of Dirac eigenvalues. In particular, we will focus on the microscopic spectral density density, i.e. the spectral density near zero virtuality on the scale of a typical level spacing. The relation with Leutwyler-Smilga sum-rules will be discussed. The success of applications of RMT to spectra of 'complex' systems leads us to the int…
We elaborate on the radiative behaviour of tree-level scattering amplitudes in the soft regime. We show that the sub-leading soft term in single-gluon emission of quark-gluon amplitudes in QCD is controlled by differential operators, whose universal form can be derived from both on-shell recursion relation and gauge invariance, as it was shown to hold for graviton- and gluon-scattering.
We derive an exact formula for the stochastic evolution of the characteristic determinant of a class of deformed Wishart matrices following from a chiral random matrix model of QCD at finite chemical potential. In the WKB approximation, the characteristic determinant describes a sharp droplet of eigenvalues that deforms and expands at large stochastic times. Beyond the WKB limit, the edges of the droplet are fuzzy and described by universal edge functions. At the chiral point, the characteristic determinant in the microscopic limit is universal. Remarkably, the physical chiral condensate at fi…
In these two lectures given at the 1997 Zakopane workshop on "New Developments in Quantum Field Theory" we review recent results on universal fluctuations in QCD Dirac spectra. We start the first lecture with a review of some general properties of Dirac spectra. It will be argued that there is an intimate relation between chiral symmetry breaking and correlations of Dirac eigenvalues. In particular, we will focus on the microscopic spectral density density, i.e. the spectral density near zero virtuality on the scale of a typical level spacing. The relation with Leutwyler-Smilga sum-rules will …
In the $\varepsilon$-regime of chiral perturbation theory the spectral correlations of the Euclidean QCD Dirac operator close to the origin can be computed using random matrix theory. To incorporate the effect of temperature, a random matrix ensemble has been proposed, where a constant, deterministic matrix is added to the Dirac operator. Its eigenvalue correlation functions can be written as the determinant of a kernel that depends on temperature. Due to recent progress in this specific class of random matrix ensembles, featuring a deterministic, additive shift, we can determine the limiting …
We construct a random matrix model that, in the large $N$ limit, reduces to the low energy limit of the QCD partition function put forward by Leutwyler and Smilga. This equivalence holds for an arbitrary number of flavors and any value of the QCD vacuum angle. In this model, moments of the inverse squares of the eigenvalues of the Dirac operator obey sum rules, which we conjecture to be universal. In other words, the validity of the sum rules depends only on the symmetries of the theory but not on its details. To illustrate this point we show that the sum rules hold for an interacting liquid o…
