118314406
Wrapping corrections beyond the sl(2) sector in N=4 SYM
The sl(2) sector of N=4 SYM theory has been much studied and the anomalous dimensions of those operators are well known. Nevertheless, many interesting operators are not included in this sector. We consider a class of twist operators beyond the sl(2) subsector introduced by Freyhult, Rej and Zieme. They are spin n, length-3 operators. At one-loop they can be identified with three gluon operators. At strong coupling, they are associated with spinning strings with two spins in AdS_5 space and charge in S^5. We exploit the Y-system to compute the leading weak-coupling four loop wrapping correction to their anomalous dimension. The result is written in closed form as a function of the spin n. We combine the wrapping correction with the known four loop asymptotic Bethe Ansatz contribution and analyze special limits in the spin n. In particular, at large n, we prove that a generalized Gribov-Lipatov reciprocity holds. At negative unphysical spin, we present a simple BFKL-like equation predicting the rightmost leading poles.
15615236
Mesons in marginally deformed AdS/CFT
We study the embedding of spacetime filling D7-branes in β-deformed backgrounds which, according to the AdS/CFT dictionary, corresponds to flavoring β-deformed = 4 super Yang-Mills. We consider supersymmetric and more general non-supersymmetric three parameter deformations. The equations of motion for quadratic fluctuations of a probe D7-brane wrapped on a deformed three-sphere exhibit a non-trivial coupling between scalar and vector modes induced by the deformation. Nevertheless, we manage to solve them analytically and find that the mesonic mass spectrum is discrete, with a mass gap and a Zeeman-like splitting occurs. Finally we propose the action for the dual field theory as obtained by -product deformation of super Yang-Mills with fundamental matter.
118612335
Wrapping corrections, reciprocity and BFKL beyond the sl(2) subsector in N=4 SYM
We consider N=4 SYM and a class of spin N, length-3, twist operators beyond the well studied sl(2) subsector. They can be identified at one-loop with three gluon operators. At strong coupling, they are associated with spinning strings with two spins in AdS5. We exploit the Y-system to compute the leading weak-coupling four loop wrapping correction to their anomalous dimension. The result is written in closed form as a function of the spin N. We combine the wrapping correction with the known four-loop asymptotic Bethe Ansatz contribution and analyze special limits in the spin N. In particular, at large N, we prove that a generalized Gribov-Lipatov reciprocity holds. At negative unphysical spin, we present a simple BFKL-like equation predicting the rightmost leading poles.
122501875
On marginally deformed meson spectroscopy
We review the results of 0710.4292 [hep-th] where we study the embedding of spacetime filling D7-branes in β-deformed backgrounds. This corresponds to flavoring β-deformed = 4 super Yang–Mills. For the supersymmetric and the more general non-supersymmetric three parameter deformations, we study quadratic fluctuations of a probe D7-brane wrapped on a deformed three-sphere, which correspond to mesonic configurations of the dual field theory. We manage to solve their equations exactly in the presence of a non-trivial coupling between scalar and vector modes induced by the deformation. We find a mesonic mass spectrum which is discrete, with a mass gap and a Zeeman-like splitting occurs.
118635378
From correlators to Wilson loops in Chern-Simons matter theories
We study n-point correlation functions for chiral primary operators in three dimensional supersymmetric Chern-Simons matter theories. Our analysis is carried on in $ \mathcal{N} = 2 $ superspace and covers $ \mathcal{N} = 2,3 $ supersymmetric CFT’s, the $ \mathcal{N} = 6 $ ABJM and the $ \mathcal{N} = 8 $ BLG models. In the limit where the positions of adjacent operators become light-like, we find that the one-loop n-point correlator divided by its tree level expression coincides with a light-like n-polygon Wilson loop. Remarkably, the result can be simply expressed as a linear combination of five dimensional two-mass easy boxes. We manage to evaluate the integrals analytically and find a vanishing result, in agreement with previous findings for Wilson loops.
118567905
Large spin expansion of the wrapping correction to Freyhult-Rej-Zieme twist operators
Twist operators in the closed $ \mathfrak{s}\mathfrak{l}(2) $ sector of planar $ \mathcal{N} = 4 $ SYM are characterized by their spin. The explicit dependence of anomalous dimensions on this important parameter is a source of interesting information. Wrapping corrections are a non trivial part of the calculation and are under control in the framework of thermodynamical Bethe Ansatz valid for the full theory and thoroughly checked in that sector. The extension to more general twist operators beyond $ \mathfrak{s}\mathfrak{l}(2) $ has been recently accomplished for the so-called 3-gluon operators that are a special case of the generalized twist operators introduced by Freyhult, Rej and Zieme. Such operators are dual to spinning strings configurations with two spins S1, S2 in AdS5 and charge in S5. We compute the expansion of the weak-coupling leading order wrapping correction in the gauge theory limit dual to large S1 and fixed S2. We present a simple algorithm for the calculation and provide explicit results illustrating the general structure of the expansion.
56465034
The chiral and deconfinement crossover transitions: PNJL model beyond mean field ∗
Abstract The Polyakov loop extended Nambu and Jona-Lasinio model (PNJL model) in a mean field framework shows astonishingly good agreement with lattice QCD calculations which needs to be better understood. The present work reports on further developments concerning both Polyakov loop and mesonic fluctuations beyond mean field approximation. Corrections beyond mean field are of special interest for the thermal expectation values of the Polyakov loop 〈 Φ 〉 and its conjugate 〈 Φ ∗ 〉 , which differ once the quark chemical potential is non-zero. Mesonic fluctuations are also considered with emphasis on the role of pionic modes.
11417469
Baryonic masses based on the NJL model
Abstract:We employ the Nambu-Jona-Lasinio model to determine the vacuum pressure on the quarks in a baryon and hence their density inside. Then we estimate the baryonic masses by implementing the local density approximation for the mean-field quark energies obtained in a uniform and isotropic system. We obtain a fair agreement with the experimental masses.
15677961
Phases of QCD: Lattice thermodynamics and a field theoretical model
We investigate three-color QCD thermodynamics at finite quark chemical potential. Lattice QCD results are compared with a generalized Nambu Jona-Lasinio model in which quarks couple simultaneously to the chiral condensate and to a background temporal gauge field representing Polyakov loop dynamics. This so-called PNJL model thus includes features of both deconfinement and chiral symmetry restoration. The parameters of the Polyakov loop effective potential are fixed in the pure-gauge sector. The chiral condensate and the Polyakov loop as functions of temperature and quark chemical potential are calculated by minimizing the thermodynamic potential of the system. The resulting equation of state, (scaled) pressure difference and quark number density at finite quark chemical potential are then confronted with corresponding Lattice QCD data.
15978114
Quark number susceptibilities : Lattice QCD versus PNJL model
Quark number susceptibilities at finite quark chemical potential are inves- tigated in the framework of the Polyakov-loop-extended Nambu Jona-Lasinio (PNJL) model. A detailed comparison is performed between the available lattice data, extrapolated using a Taylor expansion around vanishing chem- ical potential, and PNJL results consistently obtained from a Taylor series truncated at the same order. The validity of the Taylor expansion is then examined through a comparison between the full and truncated PNJL model calculations. Investigations of QCD thermodynamics using lattice simulations predict a tran- sition from the hadronic to the quark-gluon phase around a critical temperature of 0.2 GeV, at vanishing quark chemical potentialq. This transition is signalled by a steep rise in energy density, pressure and entropy density as functions of the temperature, and known to be a crossover (1) when quarks are included. Based on model calculations (2) as well as lattice QCD simulations (3), the exis- tence of a critical endpoint in the phase diagram is suggested. The precise location of this point is still under debate. It can possibily be identified by observables that are sensitive to singular parts of the free energy (4), such as quark number suscep- tibilities. Such susceptibilities have been studied both in lattice calculations (5,6), and using phenomenological models (7-10). Both diagonal and off-diagonal suscepti- bilities can serve as useful diagnostics to elucidate the nature of strongly interacting matter (11).
15445984
Evaporation of the gluon condensate: a model for pure gauge SU(3)c phase transition
Abstract We interpret lattice data for the equation of state of pure gauge SU (3) c by an evaporation model. At low temperatures gluons are frozen inside the gluon condensate, whose dynamics is described in terms of a dilaton Lagrangian. Above the critical temperature quasi-free gluons evaporate from the condensate: a first order transition is obtained by minimizing the thermodynamical potential of the system. Within the model it is possible to reproduce lattice QCD results at finite temperature for thermodynamical quantities such as pressure and energy. The gluonic longitudinal mass can also be evaluated; it vanishes below the critical temperature, where it shows a discontinuity. At very large temperatures we recover the perturbative scenario and gluons are the only asymptotic degrees of freedom.