Continuum Limits of ``Induced QCD": Lessons of the Gaussian Model at d=1 and Beyond

We analyze the scalar field sector of the Kazakov--Migdal model of induced QCD. We present a detailed description of the simplest one dimensional {($d$$=$$1$)} model which supports the hypothesis of wide applicability of the mean--field approximation for the scalar fields and the existence of critical behaviour in the model when the scalar action is Gaussian. Despite the ocurrence of various non--trivial types of critical behaviour in the $d=1$ model as $N\rightarrow\infty$, only the conventional large-$N$ limit is relevant for its {\it continuum} limit. We also give a mean--field analysis of the $N=2$ model in {\it any} $d$ and show that a saddle point always exists in the region $m^2>m_{\rm crit}^2(=d)$. In $d=1$ it exhibits critical behaviour as $m^2\rightarrow m_{\rm crit}^2$. However when $d$$>$$1$ there is no critical behaviour unless non--Gaussian terms are added to the scalar field action. We argue that similar behaviour should occur for any finite $N$ thus providing a simple explanation of a recent result of D. Gross. We show that critical behaviour at $d$$>$$1$ and $m^2>m^2_{\rm crit}$ can be obtained by adding a $logarithmic$ term to the scalar potential. This is equivalent to a local modification of the integration measure in the original Kazakov--Migdal model. Experience from previous studies of the Generalized Kontsevich Model implies that, unlike the inclusion of higher powers in the potential, this minor modification should not substantially alter the behaviour of the Gaussian model.Comment: 31 page

Evaluation of Observables in the Gaussian N=∞N=\infty Kazakov-Migdal Model

We examine the properties of observables in the Kazakov-Migdal model. We present explicit formulae for the leading asymptotics of adjoint Wilson loops as well as some other observables for the model with a Gaussian potential. We discuss the phase transiton in the large $N$ limit of the $d=1$ model. One of appendices is devoted to discussion of the $N =\infty$ Itzykson-Zuber integrals for arbitrary eigenvalue densities.Comment: plain LATEX, 22pp, preprint UBC-27/93, ITEP-M5/9

Open string fluctuations in AdS_5xS^5 and operators with large R-charge

A semiclassical string description is given for correlators of Wilson loops with local operators in N=4 SYM theory in the regime when operators carry parametrically large R-charge. The OPE coefficients of the circular Wilson loop in chiral primary operators are computed to all orders in the alpha' expansion in AdS_5xS^5 string theory. The results agree with field-theory predictions.Comment: 16 pages, 2 figures; v2: five misprints correcte

An exact formula for the radiation of a moving quark in N=4 super Yang Mills

We derive an exact formula for the cusp anomalous dimension at small angles. This is done by relating the latter to the computation of certain 1/8 BPS Wilson loops which was performed by supersymmetric localization. This function of the coupling also determines the power emitted by a moving quark in N=4 super Yang Mills, as well as the coefficient of the two point function of the displacement operator on the Wilson loop. By a similar method we compute the near BPS expansion of the generalized cusp anomalous dimension.Comment: 22 pages, 5 figures. v2: references added, typos correcte

Comparing strings in AdS(5)xS(5) to planar diagrams: an example

The correlator of a Wilson loop with a local operator in N=4 SYM theory can be represented by a string amplitude in AdS(5)xS(5). This amplitude describes an overlap of the boundary state, which is associated with the loop, with the string mode, which is dual to the local operator. For chiral primary operators with a large R charge, the amplitude can be calculated by semiclassical techniques. We compare the semiclassical string amplitude to the SYM perturbation theory and find an exact agrement to the first two non-vanishing orders.Comment: 16 pages, 4 figures, LaTeX; v2: typos corrected; v3: clarification of boundary conditions at infinity adde

Finite Size Giant Magnon

The quantization of the giant magnon away from the infinite size limit is discussed. We argue that this quantization inevitably leads to string theory on a Z_M-orbifold of S^5. This is shown explicitly and examined in detail in the near plane-wave limit

Area Law and Continuum Limit in "Induced QCD"

We investigate a class of operators with non-vanishing averages in a D-dimensional matrix model recently proposed by Kazakov and Migdal. Among the operators considered are ``filled Wilson loops" which are the most reasonable counterparts of Wilson loops in the conventional Wilson formulation of lattice QCD. The averages of interest are represented as partition functions of certain 2-dimensional statistical systems with nearest neighbor interactions. The ``string tension" $\alpha'$, which is the exponent in the area law for the ``filled Wilson loop" is equal to the free energy density of the corresponding statistical system. The continuum limit of the Kazakov--Migdal model corresponds to the critical point of this statistical system. We argue that in the large $N$ limit this critical point occurs at zero temperature. In this case we express $\alpha'$ in terms of the distribution density of eigenvalues of the matrix-valued master field. We show that the properties of the continuum limit and the description of how this limit is approached is very unusual and differs drastically from what occurs in both the Wilson theory ($S\propto({\rm Tr}\prod U +{\rm c.c.})$) and in the ``adjoint'' theory ($S\propto\vert{\rm Tr}\prod U\vert^2$). Instead, the continuum limit of the model appears to be intriguingly similar to a $c>1$ string theory.Comment: 38 page

Phase Structure of QED3 at Finite Temperature

Dynamical symmetry breaking in three-dimensional QED with N fermion flavours is considered at finite temperature, in the large $N$ approximation. Using an approximate treatment of the Schwinger-Dyson equation for the fermion self-energy, we find that chiral symmetry is restored above a certain critical temperature which depends itself on $N$. We find that the ratio of the zero-momentum zero-temperature fermion mass to the critical temperature has a large value compared with four-fermion theories, as had been suggested in a previous work with a momentum-independent self-energy. Evidence of a temperature- dependent critical $N$ is shown to appear in this approximation. The phase diagram for spontaneous mass generation in the theory is presented in $T-N$ space.Comment: 9 page

The superstring Hagedorn temperature in a pp-wave background

The thermodynamics of type IIB superstring theory in the maximally supersymmetric plane wave background is studied. We compute the thermodynamic partition function for non-interacting strings exactly and the result differs slightly from previous computations. We clarify some of the issues related to the Hagedorn temperature in the limits of small and large constant RR 5-form. We study the thermodynamic behavior of strings in the case of $AdS_3 \times S^3 \times T^4$ geometries in the presence of NS-NS and RR 3-form backgrounds. We also comment on the relationship of string thermodynamics and the thermodynamic behavior of the sector of Yang-Mills theory which is the holographic dual of the string theory.Comment: 22 pages, JHEP style, minor misprints corrected, some comments adde