74 research outputs found

    Generalization of the BLM procedure and its scales in any order of pQCD

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    The Brodsky--Lepage--Mackenzie procedure is sequentially and unambiguously extended to any fixed order of perturbative QCD beyond the so called ``large--\beta_0 approximation''. As a result of this procedure, the obtained perturbation series looks like a continued-fraction representation. A subsequent generalization of this procedure is developed, in order to optimize the convergence of the final series, along the lines of the Fastest Convergence Prescription. This generalized BLM procedure is applied to the Adler D function and also to R_{e^+e^-} in QCD at N3^3LO. A further extension of the sequential BLM is presented which makes use of additional parameters to optimize the convergence of the power-series at any fixed order of expansion.Comment: 24 pages, JHEP3, 4 figures are enclosed as eps-file, final version to be published in JHE

    The Dressing Factor and Crossing Equations

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    We utilize the DHM integral representation for the BES dressing factor of the world-sheet S-matrix of the AdS_5xS^5 light-cone string theory, and the crossing equations to fix the principal branch of the dressing factor on the rapidity torus. The results obtained are further used, in conjunction with the fusion procedure, to determine the bound state dressing factor of the mirror theory. We convincingly demonstrate that the mirror bound state S-matrix found in this way does not depend on the internal structure of a bound state solution employed in the fusion procedure. This welcome feature is in perfect parallel to string theory, where the corresponding bound state S-matrix has no bearing on bound state constituent particles as well. The mirror bound state S-matrix we found provides the final missing piece in setting up the TBA equations for the AdS_5xS^5 mirror theory.Comment: LaTex, 48 pages, 10 figures; v2: a new section added where the dressing factor of the mirror theory is found; v3: formula (6.12) is corrected, a new figure is added, accepted for publication in J.Phys.

    On "Non-Geometric" Contribution To The Entropy Of Black Hole Due To Quantum Corrections

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    The quantum corrections to the entropy of charged black holes are calculated. The Reissner-Nordstrem and dilaton black holes are considered. The appearance of logarithmically divergent terms not proportional to the horizon area is demonstrated. It is shown that the complete entropy which is sum of classical Bekenstein-Hawking entropy and the quantum correction is proportional to the area of quantum-corrected horizon.Comment: Latex, 9 page

    Foundations of the AdS_5 x S^5 Superstring. Part I

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    We review the recent advances towards finding the spectrum of the AdS_5 x S^5 superstring. We thoroughly explain the theoretical techniques which should be useful for the ultimate solution of the spectral problem. In certain cases our exposition is original and cannot be found in the existing literature. The present Part I deals with foundations of classical string theory in AdS_5 x S^5, light-cone perturbative quantization and derivation of the exact light-cone world-sheet scattering matrix.Comment: 161 page

    Gauge-string duality for superconformal deformations of N=4 Super Yang-Mills theory

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    We analyze in detail the relation between an exactly marginal deformation of N=4 SYM - the Leigh-Strassler or ``beta-deformation'' - and its string theory dual (recently constructed in hep-th/0502086) by comparing energies of semiclassical strings to anomalous dimensions of gauge-theory operators in the two-scalar sector. We stress the existence of integrable structures on the two sides of the duality. In particular, we argue that the integrability of strings in AdS_5 x S^5 implies the integrability of the deformed world sheet theory with real deformation parameter. We compare the fast string limit of the worldsheet action in the sector with two angular momenta with the continuum limit of the coherent state action of an anisotropic XXZ spin chain describing the one-loop anomalous dimensions of the corresponding operators and find a remarkable agreement for all values of the deformation parameter. We discuss some of the properties of the Bethe Ansatz for this spin chain, solve the Bethe equations for small number of excitations and comment on higher loop properties of the dilatation operator. With the goal of going beyond the leading order in the 't Hooft expansion we derive the analog of the Bethe equations on the string-theory side, and show that they coincide with the thermodynamic limit of the Bethe equations for the spin chain. We also compute the 1/J corrections to the anomalous dimensions of operators with large R-charge (corresponding to strings with angular momentum J) and match them to the 1-loop corrections to the fast string energies. Our results suggest that the impressive agreement between the gauge theory and semiclassical strings in AdS_5 x S^5 is part of a larger picture underlying the gauge/gravity duality.Comment: 50 pages, Latex; v2:typos corrected, references added, clarifications in sec 8 and Appendix A, a discussion of a rational solution added in section 4.2; v3: minor corrections to coefficients in eq. 2.5, 5.2 and appendix A; v4: minor misprints correcte

    Uniform Light-Cone Gauge for Strings in AdS_5 x S^5: Solving su(1|1) Sector

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    We introduce a uniform light-cone gauge for strings propagating in AdS space-time. We use the gauge to analyze strings from the su(1|1) sector, and show that the reduced model is described by a quadratic action for two complex fermions. Thus, the uniform light-cone gauge allows us to solve the model exactly. We analyze the near BMN spectrum of states from the su(1|1) sector and show that it correctly reproduces the 1/J corrections. We also compute the spectrum in the strong coupling limit, and derive the famous \lambda^{1/4} asymptotics. We then show that the same string spectrum can be also derived by solving Bethe ansatz type equations, and discuss their relation to the quantum string Bethe ansatz for the su(1|1) sector.Comment: 26 pages, Latex, v2: comparison to the strong coupling expansion of the quantum string Bethe ansatz is added, discussion of the winding sector is extended, references adde

    Konishi operator at intermediate coupling

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    TBA equations for two-particle states from the sl(2) sector proposed by Arutyunov, Suzuki and the author are solved numerically for the Konishi operator descendent up to 't Hooft's coupling lambda ~ 2046. The data obtained is used to analyze the properties of Y-functions and address the issue of the existence of the critical values of the coupling. In addition we find a new integral representation for the BES dressing phase which substantially reduces the computational time.Comment: lots of figures, v2: improved numerics, c1=2, c2=0, c4 does not vanis

    On String S-matrix, Bound States and TBA

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    The study of finite J effects for the light-cone AdS superstring by means of the Thermodynamic Bethe Ansatz requires an understanding of a companion 2d theory which we call the mirror model. It is obtained from the original string model by the double Wick rotation. The S-matrices describing the scattering of physical excitations in the string and mirror models are related to each other by an analytic continuation. We show that the unitarity requirement for the mirror S-matrix fixes the S-matrices of both theories essentially uniquely. The resulting string S-matrix S(z_1,z_2) satisfies the generalized unitarity condition and, up to a scalar factor, is a meromorphic function on the elliptic curve associated to each variable z. The double Wick rotation is then accomplished by shifting the variables z by quarter of the imaginary period of the torus. We discuss the apparent bound states of the string and mirror models, and show that depending on a choice of the physical region there are one, two or 2^{M-1} solutions of the M-particle bound state equations sharing the same conserved charges. For very large but finite values of J, most of these solutions, however, exhibit various signs of pathological behavior. In particular, they might receive a finite J correction to their energy which is complex, or the energy correction might exceed corrections arising due to finite J modifications of the Bethe equations thus making the asymptotic Bethe ansatz inapplicable.Comment: 77 pages, 6 figures, v2: the statement about the periodicity condition for mirror fermions corrected; typos corrected; references added, v3: misprints correcte
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