A. M. Polyakov
In this article, prepared for the book "The birth of string theory", I recall the sequence of ideas which led to non-critical strings and gauge/strings duality. I also comment on some promising future directions.
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These are my personal impressions of the environment in which string theory was born, and what the important developments affecting my work were during the hadronic string era, 1968-1974. I discuss my motivations and concerns at the time, particularly in my work on loop amplitudes and on closed strings.
In this contribution we go through the developments that in the years 1968 to 1974 led from the Veneziano model to the bosonic string.
Invited contribution to the collective book "The Birth of String Theory"
The tremendous progress achieved through the study of black holes and branes suggests that their time dependent generalizations called Spacelike branes (S-branes) may prove similarly useful. An example of an established approach to S-branes is to include a string boundary interaction and we first summarize evidence for the death of open string degrees of freedom for the homogeneous rolling tachyon on a decaying brane. Then, we review how to extract the flat S-brane worldvolumes describing the homogeneous rolling tachyon and how large deformations correspond to creation of lower dimensional str…
The decay of the string perturbative vacuum, if triggered by a suitable, duality-breaking dilaton potential, can efficiently proceed via the parametric amplification of the Wheeler-De Witt wave function in superspace, and can appropriately describe the birth of our Universe as a quantum process of pair production from the vacuum.
New-born strings are tensionless
本文首次提出无张力弦的物理起源，通过在有限寿命设定下构建弦动力学，揭示无张力弦仅在诞生时刻出现，其全球超局部卡罗尔结构特征被发现。
In a Wheeler-de Witt approach to quantum string cosmology, the present state of the Universe arises from the scattering and reflection of the wave function representing the initial string vacuum in superspace. This scenario is described and compared with the more conventional quantum cosmology picture, in which the birth of the Universe is represented as a process of tunnelling "from nothing" in superspace.
We consider the evolution of an initially FLRW universe after the formation of a long, straight, cosmic string with arbitrary tension and mass per unit length. The birth of the string sources scalar and tensor-type perturbations in the background metric and both density and velocity perturbations in the background fluid, which compensate for the string mass and maintain energy conservation. The former generate the deficit angle within the light cone of the string and a gravitational shock front at the cosmological horizon, whereas the latter are confined within the sound cone. We study the pro…
This is a brief summary of an introductory lecture for students and scholars in general given by the author at Nambu Memorial Symposium which was held at Osaka City University on September 29, 2015. We review the invention of string theory by Professor Yoichiro Nambu following the discovery of the Veneziano amplitude. We also discuss Professor Nambu's proposal on string theory in the Schild gauge in 1976 which is related to the matrix model of Yang-Mills type.
The decay of the string perturbative vacuum into our present cosmological state is associated to the transition from a phase of growing curvature and growing dilaton, to a phase of decreasing curvature and frozen dilaton. The possible approaches to a classical and quantum description of such a transition are introduced and briefly discussed.
We show that a unique, most probable and stable solution for the wavefunction of the universe, with a very small cosmological constant $Λ_1 \simeq (\fracπ{l_p N})^2$, can be predicted from the supersymmetric minisuperspace with $N$ vacua, of the landscape of string theory without reffering to the antropic principle. Due to the nearest neighbor tunneling in moduli space lattice, the $N$-fold degeneracy of vacua is lifted and a discrete spectrum of bound state levels over the whole minisuperspace emerges. $SUSY$ is spontaneously broken by these bound states, with discrete nonzero energy levels $…
We investigate the stability against small deformations of strings dangling into AdS_5-Schwarzschild from a moving heavy quark-anti-quark pair. We speculate that emission of massive string states may be an important part of the evolution of certain unstable configurations.
Using the gauge-string duality, I compute two-point functions of the force acting on an external quark moving through a finite temperature bath of N=4 super-Yang-Mills theory. I comment on the possible relevance of the string theory calculations to heavy quarks propagating through a quark-gluon plasma.
The quark mass dependence of the energy spectrum in the Nambu--Goto string with point--like masses (quarks) at its ends is analyzed. To this end, linearized equations of motion and boundary conditions in this model are considered. It is shown that for sufficiently large quark masses, the first excited state in string spectrum may be arbitrary close to the ground state. Obviously this points to infrared instability in the system under consideration. Possible modifications of string model which could remove this drawback are discussed.
We correct the energy of the static strings in hep-th/0512295, for large quark anti-quark separation. This energy is a smooth function of the quark separation for any position of the infrared brane. The asymptotic behavior of this energy is that of the Cornell potential as stated in the article. However, this identification does not fixes the AdS radius.
Resubmitted as hep-ph/9502316. Removed from hep-th. Incorrigibly inept submitter publicly excoriated.
From a simple moving open string solution dual to a moving heavy quark with constant velocity in the Poincare AdS_3 spacetime, we construct an accerlerating open string solution dual to a heavy quark-antiquark pair accelerated in opposite directions by performing the three mappings such as the SL(2,R)_L x SL(2,R)_R isometry transformation, the special conformal transformation and the conformal SO(2,2) transformation. Using the string sigma model action we construct two open string solutions staying in two different regions whose dividing line is associated with the event horizon appeared on th…
I outline some of the progress over the past few years in applying ideas from string theory to study the quark-gluon plasma, including the computation of the drag force on heavy quarks and estimates of total multiplicity from black hole formation. I also indicate some of the main perils of the string theory approach.
A correction to the Hamiltonian of the quark-antiquark system, arising due to the rigidity term in the gluodynamics string effective action, is obtained. This correction contains additional contributions to the orbital momentum of the system and several higher derivative operators. With the help of the derived Hamiltonian a rigid string-induced term in the Hamiltonian of the relativistic quark model is evaluated for the case of large masses of a quark and antiquark.
This article is based on a talk given at the ``Strings'97'' conference. It discusses the search for the universality class of confining strings. The key ingredients include the loop equations, the zigzag symmetry, the non-linear renormalization group. Some new tests for the equivalence between gauge fields and strings are proposed.
We compute the quark-antiquark potential employing the continuum action for QCD-like random lattice strings proposed by Siegel. The model leads to a potential similar to those obtained from Nambu-Goto string theory but has some modifications which we interpret as velocity dependent contributions. We also propose to add extra terms in the action which lead to physically interesting propagators for partons for the infrared region.
In this paper, we have examined charged strange quark matter attached to the string cloud in the spherical symmetric space-time admitting one-parameter group of conformal motions. For this purpose, we have solved Einstein's field equations for spherical symmetric space-time with strange quark matter attached to the string cloud via conformal motions. Also, we have discussed the features of the obtained solutions.
We describe a way in which spin of quarks can enter a consistent QCD string theory. We show that the spin factor of the 4d massless, spin 1/2 fermions is related to the self-intersection number of a 2d surfaces immersed in the 4d space. We argue that the latter quantity should appear in a consistent description of the QCD string. We also calculate the chiral anomaly and show that the self-intersection number corresponds to the topological charge $F{\tilde F}$ of QCD.
In the world line representation of the fermionic effective action for QCD the interaction between Fermions and the gauge field is contained in the fermionic Wilson loop, namely the Wilson loop for a spin-half particle. It is argued that a string representation of the fermionic Wilson loop can provide a link connecting QCD with a dual description of a meson as a quark and an antiquark connected by a string. This is illustrated by obtaining such a representation in compact U(1) gauge theories. The resulting description contains information about the interaction of the spin of the quark with the…
In this short talk we review basic ideas of string field theory with the emphasis on the recent developments. We show how without too much technicality one can look for analytic solutions to Witten's open string field theory. This is an expanded version of a talk given by the author over the last year at a number of occasions and notably at the conference "Selected Topics in Mathematical and Particle Physics" in honor of Prof. Jiri Niederle's 70th birthday.
A consistent method for calculating the interquark potential generated by the relativistic string with massive ends is proposed. In this approach the interquark potential in the model of the Nambu--Goto string with point--like masses at its ends is calculated. At first the calculation is done in the one--loop approximation and then the variational estimation is performed. The quark mass correction results in decreasing the critical distance (deconfinement radius). When quark mass decreases the critical distance also decreases. For obtaining a finite result under summation over eigenfrequencies…
Following recent work by Lambiase and Nesterenko we study in detail the interquark potential for a Nambu-Goto string with point masses attached to its ends. We obtain exact solutions to the gap equations for the Lagrange multipliers and metric components and determine the potential without simplifying assumptions. We also discuss Lüscher term and argue that it remains universal.
Computing heavy quark-antiquark potentials within the AdS/CFT correspondence often leads to behaviors that differ from what one expects on general physical grounds and field-theory considerations. To isolate the configurations of physical interest, it is of utmost importance to examine the stability of the string solutions dual to the flux tubes between the quark and antiquark. Here, we formulate and prove several general statements concerning the perturbative stability of such string solutions, relevant for static quark-antiquark pairs in a general class of backgrounds, and we apply the resul…
We investigate the behavior of stationary string configurations on a five-dimensional AdS black hole background which correspond to quark-antiquark pairs steadily moving in an N=4 super Yang-Mills thermal bath. There are many branches of solutions, depending on the quark velocity and separation as well as on whether Euclidean or Lorentzian configurations are examined.
In order to study quark and anti-quark interaction, one should consider all effects of the medium in motion of the pair. Because the pair, is not produced at rest in QGP. So the velocity of the pair, has some effects on its interactions that should be taken into account. In this paper we apply some conformal transformations for a rotat- ing string dual to a rotating heavy quark in $AdS_3$ which construct an accelerating string dual to an accelerating quark and anti-quark pair. So, we can have a comparison between when pair has angular velocity or not. Then we can study effects of angular veloc…
Using AdS/CFT, we calculate the energy density of a quark moving through a thermal state of N=4 super-Yang-Mills theory. Relying on previous work for momentum-space representations as well as asymptotic behaviors, we Fourier transform to position space and exhibit a sonic boom at a speed larger than the speed of sound. Nontrivial structure is found at small length scales, confirming earlier analytical work by the authors.
We study some aspects of Maldacena's large $N$ correspondence between N=4 superconformal gauge theory on D3-brane and maximal supergravity on AdS_5xS_5 by introducing macroscopic strings as heavy (anti)-quark probes. The macroscopic strings are semi-infinite Type IIB strings ending on D3-brane world-volume. We first study deformation and fluctuation of D3-brane when a macroscopic BPS string is attached. We find that both dynamics and boundary conditions agree with those for macroscopic string in anti-de Sitter supergravity. As by-product we clarify how Polchinski's Dirichlet / Neumann open str…
We investigate the finite temperature quark anti-quark problem in a compact space $S^{n-1}\times S^1$ by considering static strings in global $AdS_{n+1}$ space with $n\ge 3$. For high temperatures we work in the black hole metric where two possible solutions show up : the big black hole and the small black hole. Using the AdS/CFT correspondence, we calculate the quark anti-quark potential (free energy) as a function of the distance. We show that this potential can be intrepeted as confining for the $AdS$ space and deconfining for the big black hole. We find for the small black hole a confining…
We study baryons in SU(N) gauge theories at finite temperature according to the gauge/string correspondence based on IIB string theory. The baryon is constructed out of D5 brane and $N$ fundamental strings to form a color singlet $N$-quark bound state. At finite temperature and in the deconfining phase, we could find $k(<N)$-quark ``baryons''. Thermal properties of such $k$-quark baryons and also of the $N$-quark baryon are examined. We study the temperature dependence of color screening distance and Debye length of the baryon of $k$-quark and $N$-quark. We also estimate the melting temperatur…
String Theory Bounds on the Cosmological Constant, the Higgs mass, and the Quark and Lepton Masses
本研究基于弦理论亚弦表述的模时空与Born几何概念，结合量子互文性重新阐释宇宙学常数与规范等级问题，并探讨其向夸克、轻子质量及混合矩阵问题的拓展。
I describe Field/String duality as applied to the response of gauge fields to separated quark and antiquark sources. This is a talk contributed to the conference Quark Confinement and the Hadron Spectrum VII, Ponta Delgada, Azores, 2-7 September 2006.
We study baryons in SU(N) gauge theories, according to the gauge/string correspondence based on IIB string theory. The D5 brane, in which $N$ fundamental strings are dissolved as a color singlet, is introduced as the baryon vertex, and its configurations are studied. We find point- and split-type of vertex. In the latter case, two cusps appears and they are connected by a flux composed of dissolved fundamental strings with a definite tension. In both cases, $N$ fundamental quarks are attached on the cusp(s) of the vertex to cancel the surface term. In the confining phase, we find that the quar…
We use the AdS/CFT correspondence to compute the drag force experienced by a heavy quark moving through a maximally supersymmetric SU(N) super Yang-Mills plasma at nonzero temperature and R-charge chemical potential and at large 't Hooft coupling. We resolve a discrepancy in the literature between two earlier studies of such quarks. In addition, we consider small fluctuations of the spinning strings dual to these probe quarks and find no evidence of instabilities. We make some comments about suitable D7-brane boundary conditions for the dual strings.
The equivalence of quantum field theory and string theory as exemplified by the AdS/CFT correspondence is explored from the point of view of lightcone quantization. On the string side we discuss the lightcone version of the static string connecting a heavy external quark source to a heavy external antiquark source, together with small oscillations about the static string configuration. On the field theory side we analyze the weak/strong coupling transition in a ladder diagram model of the quark antiquark system, also from the point of view of the lightcone. Our results are completely consisten…
I discuss a method for producing a quasi-realistic inter-generational quark mass hierarchy in string models. This approach involves non-Abelian singlet states developing intermediate scale vacuum expectation values. I summarize recent investigations into string model realization of this. Talk presented at QCD98, Paris, France, 1-6 June 1998.
We calculate the energy of a static string in an AdS slice between two D3-branes with orbifold condition. The energy for configurations with endpoints on a brane grows linearly for large separation between these points. The derivative of the energy has a discontinuity at some critical separation. Choosing a particular position for one of the branes we find configurations with smooth energy. In the limit where the other brane goes to infinity the energy has a Coulombian behaviour for short separations and can be identified with the Cornell potential for a quark anti-quark pair. This identificat…
General properties of the light and heavy quark propagators have been investigated in the context of string tension interaction. Confinement, chiral symmetry breaking, spectral properties of the propagator are analytically studied and numerically validated. We show that the propagator is analytic in the infrared region even for massless quarks with a non zero radius of convergence. Emergence of more than one mass scale is exemplified. Massless limit of the quark propagator does exhibit critical behaviour.
We construct a consistent action for a massive spinning quark on the end of a QCD string that leads to pure Thomas precession of the quark's spin. The string action is modified by the addition of Grassmann degrees of freedom to the string such that the equations of motion for the quark spin follow from boundary conditions, just as do those for the quark's position.
Using a new type of simulation algorithm for the standard SU(3) lattice gauge theory that yields results with unprecedented precision, we confirm the presence of a $γ/r$ correction to the static quark potential at large distances $r$, with a coefficient $γ$ as predicted by the bosonic string theory. In both three and four dimensions, the transition from perturbative to string behaviour is evident from the data and takes place at surprisingly small distances.
To study drag force on a moving heavy quark through a plasma, we use a deformed AdS space-time, in which deformation parameter $c$ describes non-conformality in AdS/QCD. In this case the quark is mapped to a probe string in the AdS space. Considering probable contribution of deformation parameter in the probe string, we apply a general form of c-dependent string ansatz in the drag force computation. Then we find the acceptable value of this parameter as it satisfies QCD calculations. Using this result, we also discuss diffusion constant which is in agreement with phenomenological result for no…
A static string in an AdS Schwarzschild space is dual to a heavy quark anti-quark pair in a gauge theory at high temperature. This space is non confining in the sense that the energy is finite for infinite quark anti-quark separation. We introduce an infrared cut off in this space and calculate the corresponding string energy. We find a deconfining phase transition at a critical temperature T_C. Above T_C the string tension vanishes representing the deconfined phase. Below T_C we find a linear confining behavior for large quark anti-quark separation. This simple phenomenological model leads to…
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.
According to string theory, string ball is a highly excited long string which decays to standard model particles at the Hagedorn temperature with thermal spectrum. If there are extra dimensions, the string scale can be $\sim$ TeV, and we should produce string balls at CERN LHC. In this paper we study top quark production from string balls at LHC and compare with the parton fusion results at NNLO using pQCD. We find significant top quark production from string balls at LHC which is comparable to standard model pQCD results. We also find that $\frac{dσ}{dp_T}$ of top quarks from string balls doe…
We propose a simple but realistic pattern of quark mass matrices at the string scale, which can be derived from orbifold models of superstring theory with no use of gauge symmetries. This pattern is left-right symmetric and preserves the structural parallelism between up and down quark sectors. Its phenomenological consequences on flavor mixing and $CP$ violation are confronted with current experiments at the weak scale by use of the renormalization-group equations in the framework of the minimal supersymmetric standard model. We find that good agreement is achievable without fine-tuning.
We explore phenomenological signatures of light quark jet quenching within the AdS/CFT correspondence. Numerical studies of the instantaneous energy loss of light quarks, modeled as falling strings, suggest a linear path dependence. We propose a phenomenological model for the energy loss and use it to compute the nuclear modification factor $R_{AA}$ for light quarks in an expanding plasma with Glauber initial conditions. The results are compared to the light hadron $R_{AA}$ data at the LHC and, although they show qualitative agreement, the quantitative disagreement we found motivated the explo…
We consider the AdS bulk dual to an external massive quark in SYM following an arbitrary trajectory on Minkowski background. While a purely outgoing boundary condition on the gluonic field allows one to express the corresponding string worldsheet in a closed form, the setup has curious consequences. In particular, we argue that any quark whose trajectory on flat spacetime approaches that of a light ray in the remote past (as happens e.g. in the case of uniform acceleration) must necessarily be accompanied by an anti-quark. This is puzzling from the field theory standpoint, since one would expe…
Invited contribution to the collection of articles: `The Birth of String Theory', edited by Andrea Cappelli, Elena Castellani, Filippo Colomo and Paolo Di Vecchia.
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 potent…
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.
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.
Locating Quark-Antiquark String Breaking in QCD through Chiral Symmetry Restoration and Hawking-Unruh Effect
本文利用Schwinger模型结合安鲁效应研究QCD中夸克-反夸克弦断裂，确定临界距离为1.294±0.040 fm，并给出相应临界加速度和安鲁温度，揭示手征对称性恢复与弦断裂的关联。
We make an estimate of the quadratic correction in the pressure of cold quark matter using gauge/string duality.
The confining string in presence of dynamical quarks can behave in different ways, depending on the quark masses and on the number N_f N_c of charge species. For light masses and large N_f N_c the creation of quark pairs produces microscopic holes in the world- sheet swept by the string; as a consequence string breaking is invisible in the Wilson loop, while is manifest in operators composed of disjoint sources, as observed in many numerical experiments. Similar arguments apply also to the adjoint string breaking. For larger quark masses it is possible that the string world-sheet undergoes a t…
We study certain exclusive decays of high spin mesons into mesons in models of large N_c Yang-Mills with few flavors at strong coupling using string theory. The rate of the process is calculated by studying the splitting of a macroscopic string on the relevant dual gravity backgrounds. In the leading channel for the decay of heavy quarkonium into two open-heavy quark states, one of the two produced mesons has much larger spin than the other. In this channel the decay rate is only power-like suppressed with the mass of the produced quark-anti quark pair. We also reconsider decays of high spin m…
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 $Δ$-law at small distances and the Y-law at large distances.
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