On the string description of confinement (original) (raw)

The confining string from the soft dilaton theorem

Nuclear Physics B, 2000

A candidate for the confining string of gauge theories is constructed via a representation of the ultraviolet divergences of quantum field theory by a closed string dilaton insertion, computed through the soft dilaton theorem. The resulting (critical) confining string is conformally invariant, singles out naturally d = 4 dimensions, and can not be used to represent theories with Landau poles.

The renormalization group approach to the confining string

Nuclear Physics B, 2000

The renormalization group approach towards the string representation of non abelian gauge theories translates, in terms of the string sigma model beta function equations, the renormalization group evolution of the gauge coupling constant and Zamolodchikov's c function. Tachyon stability, glueball mass gap, renormalization group evolution of the c function and the area law for the Wilson loop are studied for a critical bosonic string vacuum corresponding to a non abelian gauge theory in four dimensional space-time. We prove that the same intrinsic geometry for the string vacuum is universal in some sense, reproducing the Yang-Mills beta function to arbitrary loop order in perturbation theory.

On the confining potential in 4D SU(Nc) gauge theory with dilaton

2000

Using the formal analogy between the Dick superstring inspired model of ref.[6] and the problem of building of Eguchi Hanson metric in 4d N=2 harmonic superspace (hs), we derive a general formula for the quarkquark interaction potential V(r) including the Dick confining potential. The interquark potential V(r) depends on the dilaton-gluon coupling and may be related to the parameterization of confinement by the quark and gluon vacuum condensates. It is also shown how the axion field may be incorporated in agreement with 10d type IIB superstring requirements. Others features are also discussed. mchabab@ucam.ac.ma H-saidi@fsr.ac.ma

Confining strings, Wilson loops and extra dimensions

Physics Letters B, 2000

We study solutions of the one-loop β-functions of the critical bosonic string theory in the framework of the Renormalization Group (RG) approach to string theory, considering explicitly the effects of the 21 extra dimensions. In the RG approach the 26-dimensional manifold is given in terms of M 4 × R 1 × H 21 . In calculating the Wilson loops, as it is well known for this kind of confining geometry, two phenomena appear: confinement and over-confinement. There is a critical minimal surface below of which it leads to confinement only. The role of the extra dimensions is understood in terms of a dimensionless scale l provided by them. Therefore, the effective string tension in the area law, the length of the Wilson loops, as well as, the size of the critical minimal surface depend on this scale. When this confining geometry is used to study a field-theory β-function with an infrared attractive point (as the Novikov-Shifman-Vainshtein-Zakharov β-function) the range of the couplings where the field theory is confining depends on that scale. We have explicitly calculated the l-dependence of that range.

p–q superstrings in anti-de-Sitter spacetime

Journal of Physics A: Mathematical and Theoretical, 2009

We study a field theoretical model for p-q-superstrings in a fixed Anti-de-Sitter background. We find that the presence of the negative cosmological constant tends to decrease the core radius of the strings. Moreover, the binding energy decreases with the increase of the absolute value of the cosmological constant. Studying the effect of the p-q-strings on Anti-de-Sitter space, we observe that the presence of the negative cosmological constant tends to decrease the deficit angle as compared to asymptotically flat space-time.

Static strings in Randall-Sundrum scenarios and the quark-antiquark potential

Physical Review D, 2006

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.

Confining strings in SU(N) gauge theories

Physical Review D, 2001

We calculate the string tensions of kkk-strings in SU($N$) gauge theories in both 3 and 4 dimensions. In D=3+1, we find that the ratio of the k=2k=2k=2 string tension to the k=1k = 1k=1 fundamental string tension is consistent, at the 2sigma2 \sigma2sigma level, with both the M(-theory)QCD-inspired conjecture and with `Casimir scaling'. In D=2+1 we see a definite deviation from the MQCD formula, as well as a much smaller but still significant deviation from Casimir scaling. We find that in both D=2+1 and D=3+1 the high temperature spatial kkk-string tensions also satisfy approximate Casimir scaling. We point out that approximate Casimir scaling arises naturally if the cross-section of the flux tube is nearly independent of the flux carried, and that this will occur in an effective dual superconducting description, if we are in the deep-London limit. We estimate, numerically, the intrinsic width of kkk-strings in D=2+1 and indeed find little variation with kkk. In addition to the stable kkk-strings we investigate some ofthe unstable strings, finding in D=2+1 that they satisfy (approximate) Casimir scaling. We also investigate the basic assumption that confining flux tubes are described by an effective string theory at large distances. We estimate the coefficient of the universal L\"uscher correction from periodic strings that are longer than 1 fermi, and find cL=0.98(4)c_L=0.98(4)cL=0.98(4) in D=3+1 and cL=0.558(19)c_L=0.558(19)cL=0.558(19) in D=2+1. These values are within 2sigma2 \sigma2sigma of the simple bosonic string values and are inconsistent with other simple effective string theories.

Lectures on String Theory in Curved Spacetimes

1996

Recent progress on string theory in curved spacetimes is reviewed. The string dynamics in cosmological and black hole spacetimes is investigated. The different methods available to solve the string equations of motion and constraints in curved spacetimes are described. That is, the string perturbation approach, the null string approach, the τ -expansion, and the construction of global solutions (for instance by inverse scattering methods). The classical behaviour of strings in FRW and inflationary spacetimes is now understood in a large extent from the various types of explicit string solutions. Three different types of behaviour appear: unstable, dual to unstable and stable. For the unstable strings, the energy and size grow for large scale factors R → ∞, proportional to R. For the dual to unstable strings, the energy and size blow up for R → 0 as 1/R. For stable strings, the energy and proper size are bounded. (In Minkowski spacetime, all string solutions are of the stable type). Recent progress on self-consistent solutions to the Einstein equations for string dominated universes is reviewed. The energy-momentum tensor for a gas of strings is then considered as source of the spacetime geometry and from the above string behaviours the string equation of state is derived. The selfconsistent string solution exhibits the realistic matter dominated behaviour R ≃ T 2/3 for large times and the radiation dominated behaviour R ≃ T 1/2 for early times (T being the cosmic time). We report on the exact integrability of the string equations plus the constraints in de Sitter spacetime that allows to systematically find exact string solutions by soliton methods and the multistring solutions. Multistring solutions are a new feature in curved spacetimes. That is, a single world-sheet simultaneously describes many different and independent strings. This phenomenon has no analogue in flat spacetime and follows to the coupling of the strings with the geometry. Finally, the string dynamics next and inside a Schwarzschild black hole is analyzed and their physical properties discussed. • I. Introduction • II. Strings in Curved and Minkowski Spacetimes. A A brief review on strings in Minkowski spacetime. B The string energy-momentum tensor and the string invariant size. C Simple String Solutions in Minkowski Spacetime • III. How to solve the string equations of motion in curved spacetimes? A The τ -expansion. B Global Solutions. • IV. String propagation in cosmological spacetimes. A Strings in cosmological universes: the τ -expansion at work. B The perfect gas of strings. • V. Self-consistent string cosmology. A String Dominated Universes in General Relativity (no dilaton field). B Thermodynamics of strings in cosmological spacetimes. • VI. Effective String Equations with the String Sources Included. A Effective String Equations in Cosmological Universes B String driven inflation? • VII. Multi-Strings and Soliton Methods in de Sitter Universe. • VIII. Strings next to and inside black holes. A String Equations of motion in a Schwarzschild Black Hole. B Strings Near the Singularity r = 0 C String energy-momentum and invariant size near the singularity. D Axisymmetric ring solutions.

Strings and multi-strings in black hole and cosmological spacetimes

Arxiv preprint hep-th/9504007, 1995

Recent results on classical and quantum strings in a variety of black hole and cosmological spacetimes, in various dimensions, are presented. The curved backgrounds under consideration include the 2 + 1 black hole anti de Sitter spacetime and its dual, the black string, the ordinary D ≥ 4 black holes with or without a cosmological constant, the de Sitter and anti de Sitter spacetimes and static Robertson-Walker spacetimes. Exact solutions to the string equations of motion and constraints, representing circular strings, stationary open strings and dynamical straight strings, are obtained in these backgrounds and their physical properties (length, energy, pressure) are described. The existence of multi-string solutions, describing finitely or infinitely many strings, is shown to be a general feature of spacetimes with a positive or negative cosmological constant. Generic approximative solutions are obtained using the string perturbation series approach, and the question of the stability of the solutions is addressed. Furthermore, using a canonical quantization procedure, we find the string mass spectrum in de Sitter and anti de Sitter spacetimes. New features as compared to the string spectrum in flat Minkowski spacetime appear, for instance the fine-structure effect at all levels beyond the graviton in both de Sitter and anti de Sitter spacetimes, and the non-existence of a Hagedorn temperature in anti de Sitter spacetime. We discuss the physical implications of these results. Finally, we consider the effect of spatial curvature on the string dynamics in Robertson-Walker spacetimes.