26 Jul 2006 | Andreas Karch, Emanuel Katz, Dam T. Son, Mikhail A. Stephanov
This paper discusses the behavior of meson masses in a theory with linear confinement, such as QCD, where the squared masses $ m_{n,S}^2 $ of high spin S or high radial excitation number n mesons are expected to grow linearly with S and n. The authors show that this behavior can be reproduced in a 5-dimensional holographic theory dual to QCD (AdS/QCD). They argue that the asymptotic linear growth of $ m_{n,S}^2 $ imposes a strong constraint on the infrared behavior of the dual theory. In the simplest model that satisfies this constraint, they find $ m_{n,S}^2 \sim (n + S) $.
The paper reviews the use of AdS/QCD to study QCD, noting that while the exact form of the gravity dual is not known, two approaches are used: one starting from string theory and another bottom-up, matching QCD properties to the dual theory. The bottom-up approach has been successful in modeling experimental data, with the hard wall model being a common choice. However, this model predicts a quadratic growth of squared masses with excitation number, inconsistent with data showing linear growth.
The authors argue that the asymptotic behavior of the meson spectrum is not an intrinsic property of AdS/QCD but depends on the details of the infrared region. They present an explicit example of an IR wall that gives the desired linear growth of masses at large n and S. They also discuss the implications for higher spin mesons, showing that the linear growth of $ m_{n,S}^2 $ can be achieved with a specific background geometry. The results are consistent with semiclassical arguments in QCD and with the behavior of the 't Hooft model.
The paper concludes that the spectrum of highly excited mesons in AdS/QCD depends on the infrared behavior of the dual theory, and that the linear growth of $ m_{n,S}^2 $ is a generic property of any linearly confining gauge theory. The authors speculate that this behavior could arise from tachyon condensation in string theory. The results are consistent with the expectation that highly excited mesons behave like semiclassical strings, with their masses growing linearly with their excitation number or spin.This paper discusses the behavior of meson masses in a theory with linear confinement, such as QCD, where the squared masses $ m_{n,S}^2 $ of high spin S or high radial excitation number n mesons are expected to grow linearly with S and n. The authors show that this behavior can be reproduced in a 5-dimensional holographic theory dual to QCD (AdS/QCD). They argue that the asymptotic linear growth of $ m_{n,S}^2 $ imposes a strong constraint on the infrared behavior of the dual theory. In the simplest model that satisfies this constraint, they find $ m_{n,S}^2 \sim (n + S) $.
The paper reviews the use of AdS/QCD to study QCD, noting that while the exact form of the gravity dual is not known, two approaches are used: one starting from string theory and another bottom-up, matching QCD properties to the dual theory. The bottom-up approach has been successful in modeling experimental data, with the hard wall model being a common choice. However, this model predicts a quadratic growth of squared masses with excitation number, inconsistent with data showing linear growth.
The authors argue that the asymptotic behavior of the meson spectrum is not an intrinsic property of AdS/QCD but depends on the details of the infrared region. They present an explicit example of an IR wall that gives the desired linear growth of masses at large n and S. They also discuss the implications for higher spin mesons, showing that the linear growth of $ m_{n,S}^2 $ can be achieved with a specific background geometry. The results are consistent with semiclassical arguments in QCD and with the behavior of the 't Hooft model.
The paper concludes that the spectrum of highly excited mesons in AdS/QCD depends on the infrared behavior of the dual theory, and that the linear growth of $ m_{n,S}^2 $ is a generic property of any linearly confining gauge theory. The authors speculate that this behavior could arise from tachyon condensation in string theory. The results are consistent with the expectation that highly excited mesons behave like semiclassical strings, with their masses growing linearly with their excitation number or spin.