Gaugino Determinant in Supersymmetric Yang-Mills Theory

We resolve an ambiguity in the sign of the gaugino determinant in supersymmetric models. The result, that the gaugino determinant can be taken positive for all background gauge configurations, is necessary for application of QCD inequalities and lattice Monte Carlo methods to supersymmetric Yang-Mills models.Comment: 5 pages, LaTeX. Revised version to appear in Modern Physics Letters

Percolation in high dimensions is not understood

The number of spanning clusters in four to nine dimensions does not fully follow the expected size dependence for random percolation.Comment: 9-dimensional data and more points for large lattices added; statistics improved, text expanded, table of exponents inserte

Anti-de Sitter Black Hole Thermodynamics in Higher Derivative Gravity and New Confining-Deconfining Phases in dual CFT

The thermodynamics of d5 AdS BHs with positive, negative or zero curvature spatial section in higher derivative (HD) gravity is described. HD contribution to free energy may change its sign which leads to more complicated regime for Hawking-Page phase transitions. Some variant of d5 HD gravity is dual to ${\cal N}=2$ $Sp(N)$ SCFT up to the next-to-leading order in large $N$. Then, according to Witten interpretation the stable AdS BH phase corresponds to deconfinement while global AdS phase corresponds to confinement. Unlike to Einstein gravity in HD theory the critical $N$ appears. It may influence the phase transition structure. In particulary, what was confining phase above the critical value becomes the deconfining phase below it and vice-versa.Comment: LaTeX 15 pages, several errors are correcte

A holographic computation of the central charges of d=4, N=2 SCFTs

We use the AdS/CFT correspondence to compute the central charges of the d=4, N=2 superconformal field theories arising from N D3-branes at singularities in F-theory. These include the conformal theories with E_n global symmetries. We compute the central charges a and c related to the conformal anomaly, and also the central charges k associated to the global symmetry in these theories. All of these are related to the coefficients of Chern-Simons terms in the dual string theory on AdS_5. Our computation is exact for all values of N, enabling several tests of the dualities recently proposed by Argyres and Seiberg for the E_6 and E_7 theories with N=1.Comment: 16 pages; v4: one reference adde

Anomalous diffusion at percolation threshold in high dimensions on 10^18 sites

Using an inverse of the standard linear congruential random number generator, large randomly occupied lattices can be visited by a random walker without having to determine the occupation status of every lattice site in advance. In seven dimensions, at the percolation threshold with L^7 sites and L < 420, we confirm the expected time-dependence of the end-to-end distance (including the corrections to the asymptotic behavior).Comment: 8 pages including figures, presentation improved, for Int.J.Mod.Phys.

Gross-Witten-Wadia transition in a matrix model of deconfinement

We study the deconfining phase transition at nonzero temperature in a SU(N) gauge theory, using a matrix model which was analyzed previously at small N. We show that the model is soluble at infinite N, and exhibits a Gross-Witten-Wadia transition. In some ways, the deconfining phase transition is of first order: at a temperature $T_d$, the Polyakov loop jumps discontinuously from 0 to1/2, and there is a nonzero latent heat $\sim N^2$. In other ways, the transition is of second order: e.g., the specific heat diverges as $C \sim 1/(T-T_d)^{3/5}$ when $T \rightarrow T_d^+$. Other critical exponents satisfy the usual scaling relations of a second order phase transition. In the presence of a nonzero background field $h$ for the Polyakov loop, there is a phase transition at the temperature $T_h$ where the value of the loop =1/2, with $T_h < T_d$. Since $\partial C/\partial T \sim 1/(T-T_h)^{1/2}$ as $T \rightarrow T_h^+$, this transition is of third order.Comment: 7pages, 1 figure; discussion on matrix models is extended; references are adde

Effective Theory of Wilson Lines and Deconfinement

To study the deconfining phase transition at nonzero temperature, I outline the perturbative construction of an effective theory for straight, thermal Wilson lines. Certain large, time dependent gauge transformations play a central role. They imply the existence of interfaces, which can be used to determine the form of the effective theory as a gauged, nonlinear sigma model of adjoint matrices. Especially near the transition, the Wilson line may undergo a Higgs effect. As an adjoint field, this can generate eigenvalue repulsion in the effective theory.Comment: 6 pages, LaTeX. Final, published version. Refs. 7, 39, and 40 added. In Ref. 37, there is an expanded discussion of a "fuzzy" bag mode

Unusual Symmetries in the Kugel-Khomskii Hamiltonian

The Kugel-Khomskii Hamiltonian for cubic titanates describes spin and orbital superexchange interactions between $d^1$ ions having three-fold degenerate $t_{2g}$ orbitals. Since orbitals do not couple along "inactive" axes, perpendicular to the orbital planes, the total number of electrons in $|\alpha >$ orbitals in any such plane and the corresponding total spin are both conserved. A Mermin-Wagner construction shows that there is no long-range spin ordering at nonzero temperatures. Inclusion of spin-orbit coupling allows such ordering, but even then the excitation spectrum is gapless due to a continuous symmetry. Thus, the observed order and gap require more symmetry breaking terms.Comment: 4 pages (two column format with 2 figures), to appear in Phys. Rev. Lett. (submitted on Dec. 2002